Patent Publication Number: US-2022215824-A1

Title: Methods and devices for attenuating sound in a conduit or chamber

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This Application is a continuation of U.S. patent application Ser. No. 16/543,605, filed 18 Aug. 2019, which is a continuation of U.S. patent application Ser. No. 15/168,020 filed May 28, 2016, which claims the priority benefit of Provisional Patent Application No. 62/168,703 entitled “METHODS AND DEVICES FOR ATTENUATING SOUND IN A CONDUIT OR CHAMBER” filed on May 29, 2015, the entire contents of both are incorporated herein by reference in their entirety. 
    
    
     FIELD 
     The present embodiments relate to occluding elements used for attenuating sound or isolating sound from a closed conduit or chamber such as an ear canal. 
     BACKGROUND OF THE INVENTION 
     Non-Newtonian fluids and more particularly, shear thickening fluids are being considered and investigated for potential commercial use as materials for liquid body armour or protective clothing due to their unique properties. The primary focus of the investigations have revolved around adaptive stiffness and dampening properties that can prevent ballistic weapons or sharp knives or stakes from penetrating a piece of body armour or protective clothing. 
     People may be exposed to noise pollution from their ambient environment (for example, from traffic, from construction sites, from aircraft, etc.). People may also be intentionally exposed to high sound levels (for example, from cell phones, MP3 players, home theater equipment, rock concerts, etc.). Studies have shown that ear damage, which may lead to permanent hearing impairment, is not only increasing in the general population, but may be increasing at a significantly faster rate in younger populations. The potential for noise induced hearing loss (NIHL) may be a function of both a level and a duration of exposure to a sound stimulus. Studies have also indicated that hearing damage is a cumulative phenomenon. Although hearing damage due to industrial or background noise exposure is more thoroughly understood, there may also be a risk of hearing damage from the exposure to intentional excessive noise, such as with the use of headphones. 
     Devices which attenuate sound directly to the ear canal are known. Conventional devices typically fit in the ear, around the ear and/or beyond the ear. Examples of these devices include headphones, headsets, earbuds and hearing aids. Earpieces that occlude the ear canal may provide increased attenuation of the ambient environment, offering improved sound isolation. However, conventional in-ear, in-concha or in canal earpieces may be fitted for a cross-section of a population and may not provide adequate sound isolation. Conventional in-ear, in-concha or in canal earpieces, thus, may not be properly fitted to the individual user and may not be adequately sealed, leading to reduced sound attenuation of the ambient environment. Furthermore, even if property fitted, as the ambient environment becomes louder, the effectiveness of the existing materials used for sound attenuating or isolation in-ear earpiece (or other devices fitting outside the ear) may not provide adequate protection. Most often, they are static in their attenuation properties, whereby the maximum attenuation is provided regardless of the ambient sound level. 
     SUMMARY 
     The present embodiments can be embodied in a sound attenuating device, including an occluding element configured to form a closed conduit or chamber upon insertion into an open end of the conduit or chamber and the inclusion of non-Newtonian fluid forming at least a portion of the occluding element where the non-Newtonian fluid provides an increasing (or variable) attenuation response in response to an increasing sound pressure leveling impinging an surface exposed to the ambient environment of the occluding member. In some embodiments, the non-Newtonian fluid is a shear thickening fluid or a dilatant fluid and where the non-Newtonian fluid includes carrier liquid and rigid colloidal particles. In some embodiments, the non-Newtonian fluid can include carrier fluid selected from the group of water, ethylene glycol (EG) and the non-Newtonian fluid further includes particles, microspheres, and or microfibers selected from the group comprising silica, titanium, oxide, calcium carbonate, cornstarch, synthetically occurring minerals, naturally occurring minerals, polymers, glass, stainless steel or a mixture of any of the aforementioned particles. In some embodiments, the non-Newtonian fluid is a shear thickening fluid containing composites using rubber as a precursor and adding a catalyzing agent. In yet other variant embodiments, the first member is formed (or includes) using a shear thickening fluid combined with an open cell polyurethane to form a foam-shear thickening fluid composite. In yet other embodiments, the non-Newtonian fluid is a non-particle based shear thickening fluid. Examples of non-particle based shear thickening fluid can include poly vinyl alcohol containing boric acid or poly dimethylsiloxane containing boric acid. In some embodiments, the non-Newtonian fluid comprises anisotropic particles, spherical particles, or at least one of fibers, rod-like elements, nanoparticles, or nano-tubes. The non-Newtonian fluid can also be electrorheological fluids composed of dispersions of electrically polarizable particles in an insulating fluid that increases in shear viscosity when exposed to an electric field. Alternatively, the non-Newtonian fluid can also be magnetorheological fluids composed of dispersions of magnetic particles in an inert or non-magnetic carrier liquid that increases in shear viscosity when exposed to a magnetic field. In some embodiments, the first member can include a balloon filled with the non-Newtonian fluid. In some embodiments, the sound attenuating device is an earpiece configured to occlude an ear canal with the occluding element. In some embodiments, the sound attenuating device can further include an ear canal receiver and an ear canal microphone configured to reside in a sealed area when the occluding element is placed within an orifice or external opening of the ear canal. Note that the ear canal is just one example of a conduit or cavity that can be closed or occluded using the method and devices disclosed herein. Other biological and non-biological conduits can equally benefit from the methods and devices disclosed or claimed herein. 
     The present embodiments can also include a method of attenuating sound in a conduit or chamber. The method can include providing a open-ended conduit or chamber and forming a closed conduit or chamber using at least a first member that includes a non-Newtonian fluid where the first member is placed at an open end of the conduit or chamber and where the non-Newtonian fluid provides an increasing attenuation response in response to an increasing sound pressure level impinging an outer surface of the first member. The non-Newtonian fluid can include any of the fluids or particles or elements described above and in any combinations or permutation thereof. Furthermore, embodiments herein can increase the attenuation based on the ambient SPL, thus providing users the ability to maintain situational awareness without having to remove a protective device (such as an earpiece or headphone) in non-hostile acoustic environments. In other words, embodiments herein maintain situational awareness in a passive manner without the use of active components or electronics. The chemistry of the non-Newtonian fluid enables a dynamic or variable attenuation characteristic that can be tailored or configured by a designer with an increasing number of variables as explained further below. The non-Newtonian fluid can replace or enhance conventional headset materials (such as rubber or foam) or otherwise be incorporated into earpieces, headsets, or headphones to enhance the attenuation efficacy of such devices based on the ambient SPL. In other words, using non-Newtonian fluids, the greater the ambient SPL, the greater the attenuation properties of the earpiece, headset, earphone or earplug. This characteristic is in sharp contrast to the rubber, foam, and/or paraffin used in typical earpieces used for NIHL protection or other purposes. Non-Newtonian fluids provide for variable attenuation, rather than a static or fixed level of attenuation exhibited by existing products. The non-Newtonian fluids provide a maximum amount of acoustic protection regardless of the acoustic conditions such that the louder the acoustic conditions the greater the attenuation the earpiece (or other device using the non-Newtonian fluid) offers. The non-dynamic aspect of conventional products such as foam only provides a static amount of attenuation. 
     Thus, embodiments herein using non-Newtonian fluids can provide situation awareness without the additional use of active electronics. With conventional products such as an existing foam earplug, a user would need to remove the earplug in quiet conditions to hear ones voice in a non-hostile acoustical environment whereas the non-Newtonian embodiments herein become more acoustically transparent at low sound pressure levels (e.g., 75 dB) and increases its acoustical impendence (attenuation) as the sound pressure level above 75 dB is increased. Thus, the user in conditions where the volume is comfortable does not need to pull the product out of their ear. The non-Newtonian embodiments herein can be designed to have no or reduced attenuation such that all acoustic acuity is preserved below a predetermined sound pressure level (such as 75 dB). Furthermore, the behavior of a product incorporating non-Newtonian fluids can be designed to be instantaneous such that attenuation occurs immediately once a certain sound pressure level (shearing force) reaches the exposed material. The non-Newtonian fluids can also be designed such that the exposed material can then immediately become flaccid once the sound pressure level drops below a certain sound pressure level. In yet other embodiments, the non-Newtonian fluids can be designed or configured or combined with other materials to exhibit a delayed transition to a flaccid state after hardening or exhibit a delayed transition to a hardened state after being in a flaccid state. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention may be understood from the following detailed description when read in connection with the accompanying drawing. It is emphasized, according to common practice, that various features of the drawings may not be drawn to scale. On the contrary, the dimensions of the various features may be arbitrarily expanded or reduced for clarity. Moreover, in the drawing, common numerical references are used to represent like features. Included in the drawing are the following figures: 
         FIG. 1  is a cross section diagram of an ear illustrating a general physiology of the ear; 
         FIG. 2A  is a cross section diagram of an exemplary earpiece device inserted in an ear canal, according to an embodiment of the present invention and  FIG. 2B  is a similar earpiece in a different form factor; 
         FIG. 3  is a cross section diagram of a portion of the earpiece device shown in  FIG. 2 , according to an embodiment of the present invention; 
         FIGS. 4A and 4B  are respective perspective view and cross section diagrams of an exemplary earpiece device in an expanded state, according to another embodiment of the present invention; 
         FIGS. 4C and 4D  are respective perspective view and cross section diagrams of the earpiece device shown in  FIGS. 4A and 4B  in a contracted state; 
         FIG. 5A  is a cross section diagram of an exemplary expandable element in a tube illustrating a change in static pressure, according to an embodiment of the present invention; 
         FIG. 5B  is graph of volume as a function of pressure difference for the expandable element shown in  FIG. 5A ; 
         FIG. 6A  is a cross section diagram of an exemplary acoustical system, according to an embodiment of the present invention and  FIG. 6B  is an electro-acoustical circuit diagram representing the acoustical system shown in  FIG. 6A , according to an embodiment of the present invention; 
         FIG. 7  is a graph of transmission as a function of frequency for the electro-acoustic circuit diagram shown in  FIG. 6B , for various capacitance values of an expandable element; 
         FIG. 8A  is a cross section diagram of an exemplary acoustical system, according to another embodiment of the present invention and  FIG. 8B  is an electro-acoustical circuit diagram representing the acoustical system shown in  FIG. 8A , according to an embodiment of the present invention; 
         FIG. 9  is a graph of transmission as a function of frequency for the electro-acoustic circuit diagram shown in  FIG. 8B , for various capacitance values of expandable elements; 
         FIG. 10A  is a cross section diagram of an exemplary acoustical system, according to another embodiment of the present invention and  FIG. 10B  is an electro-acoustical circuit diagram representing the acoustical system shown in  FIG. 10A , according to an embodiment of the present invention 
         FIG. 11  is a graph of transmission as a function of frequency for the electro-acoustic circuit diagram shown in  FIG. 10B , for various leak sizes between expandable elements; 
         FIG. 12A  is a cross section diagram of an exemplary acoustical system, according to another embodiment of the present invention,  FIG. 12B  is a circuit diagram of a transfer network associated with the acoustical system shown in  FIG. 12A , and  FIG. 12C  is an electro-acoustical circuit diagram representing the acoustical system shown in  FIG. 12A , according to an embodiment of the present invention; and 
         FIG. 13  is a graph of transmission as a function of frequency for the electro-acoustic circuit diagram shown in  FIG. 12C , for various capacitance values of an expandable element. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Aspects of the present embodiments include methods and devices for occluding an ear canal which provide a predetermined sound attenuation characteristic over various parameters. For example, the predetermined sound attenuation characteristic can be over a sound pressure level impinging on a surface of an occluding member such as a balloon containing (or incorporating) non-Newtonian fluid or a member that is just made of the non-Newtonian fluid. Using the non-Newtonian fluid, the attenuation characteristic will likely provide for greater attenuation as the sound pressure level (SPL) in an ambient field that impinges on the exterior surface of the non-Newtonian fluid. If the non-Newtonian fluid is a shear thickening fluid (STF), the higher SPL or higher volume would cause the STF to become more viscous and harder, thereby providing greater sound attenuation properties in the material itself as a sound gets louder. In other words, as the sound volume exposure to the material increases, the greater sound attenuating properties the material (made of STFs) will provide as a result of the shear thickening effect that STFs provide. Normally, this is considered a benefit for reducing penetration by ballistic weapons such as bullets or for knives, but STFs and non-Newtonian fluids further provide the acoustic benefit of sound attenuation. Of particular benefit is the increased attenuation provided as the volume or SPL exposure becomes greater. The STFs may also provide predetermined attenuation characteristics over other parameters such as over a frequency band, such that sound is attenuated more in one frequency range than in another frequency range of the frequency band. Exemplary earpiece devices of the present embodiments include an occlusion section or member that can be part of an earpiece. The Occlusion member can be a balloon or expandable member filled with non-Newtonian fluid or STFs or the occlusion member can just be a non-Newtonian fluid itself. In one embodiment, it can be composed of material similar to “Silly Putty”™ by Crayola, LLC. Silly Putty is based on silicone polymers that have unusual physical properties. It bounces, but breaks when given a sharp blow and can also flow like a liquid. It contains a viscoelastic liquid silicone, a type of non-Newtonian fluid, which makes it act as a viscous liquid over a long time period but as an elastic solid over a short time period. If a balloon or expandable element is used, it can be configured to receive a medium such as the non-Newtonian fluid and to expand to contact and conform to the ear canal. The sound attenuation characteristic of the earpiece device may be selected based on physical parameters of the occlusion member. 
     Referring to  FIG. 1 , a cross section diagram of ear  100  is shown, which illustrates the general physiology of ear  100 . An external portion of ear  100  includes pinna  102  and concha  104 . An internal portion of ear  100  includes ear canal  108  and tympanic membrane  112 . 
     Pinna  102  is a cartilaginous region of ear  100  that focuses acoustic information from an ambient environment to ear canal  108 . Concha  104  is a bowl shaped region in proximity to ear canal opening, indicated by dashed line  106 . 
     Wall  110  (also referred to herein as ear canal wall  110 ) of ear canal  108  forms an acoustic chamber, which terminates with tympanic membrane  112 . Sound enters ear canal  108  (at dashed line  106 ) and is subsequently received by tympanic membrane  112 . Tympanic membrane  112  is a flexible membrane in the middle ear that couples to components of the inner ear. In general, acoustic information resident in ear canal  108  vibrates tympanic membrane  112 . The vibration is converted to a signal (corresponding to the acoustic information) that is provided to an auditory nerve. 
     Ear canal  108  typically includes cartilaginous region  116  (between dashed lines  106  and  114 ) and bony region  118  (between dashed line  114  and tympanic membrane  112 ). Cartilaginous region  116  includes a layer of cartilage underlying the skin layer. Bony region  118  represents an area where bone underlies ear canal wall  110 . Vibrations may be conducted through the bone (in bony region  118 ), pass through ear canal wall  110 , and may be radiated as sound into ear canal  108 . 
     In bony region  118 , a skin layer of ear canal wall  110  may be sensitive to pressure. In general, the skin layer in bony region  118  is approximately one tenth a thickness of a skin layer in ear cartilaginous region  116 . Thus, in bony region  118 , there is little tissue separating skin from bone. Accordingly, placement of an object (such as an earplug) in bony region  118  can stimulate nerves (due to skin being pressed against bone), which can be uncomfortable and even induce significant pain. 
     In contrast to bony region  118 , cartilaginous region  116  is a highly flexible region having no substantial rigid structure. Thus, cartilaginous region  116  may be more easily deformed when a force is applied ear canal wall  110  (in cartilaginous region  116 ). In general, cartilaginous region  116  is much less sensitive to pressure than bony region  118 . 
     In general, application of pressure to ear canal wall  110  (such as by an earplug which occludes ear canal  108 ), may deform ear canal wall  110 . The deformation may, for example, stretch ear canal wall  110  and may place the skin layer under tension. Accordingly, it may be desirable to configure earpiece devices to be inserted within cartilaginous region  116 . Earpiece devices may be inserted (and expanded) in cartilaginous region  116  without inducing discomfort and pain. 
     In general, ear canal  108  may vary substantially in shape and size over the human population. In general, ear canal  108  is not straight or regularly shaped. Although not illustrated in  FIG. 1 , ear canal  108  typically includes an upward tilt of approximately 45 degrees, such that tympanic membrane  112  is above the opening (i.e., dashed line  106 ) of ear canal  108 . Ear canal  108  typically includes a first bend near the opening to ear canal  108  and a second bend that is proximate to tympanic membrane  112 . 
     Because the volume, shape, and length of ear canal  108  may substantially vary, there has been difficulty in providing a system that may effectively seal ear  100 , attenuate noise, mitigate the occlusion effect, operate under different environmental conditions, and may fit a majority of the population. For example, hearing aid manufacturers typically generate a full custom earpiece for individuals that include a mold of the patient&#39;s ear canal. The ear canal mold is then used to form a hearing aid housing. The procedure to create an ear canal mold is costly, cumbersome, and is not easily adaptable for high volume production. A earpiece and more particularly an occluding member of the earpiece made of a non-Newtonian fluid can be molded and customized for a particular user&#39;s ear canal and most likely by the user themselves by the mere process of insertion of the occluding member into the ear canal. 
     Referring next to  FIG. 2A , a cross section diagram of an exemplary earpiece device  200  is shown. Earpiece device  200  is shown relative to ear  100 . Earpiece device  200  may include occlusion member or section  202  and housing unit  204  coupled to occlusion section  202 . Occlusion section  202  may be configured to be inserted in ear canal  108 , at a location between the entrance to the ear canal  108  and tympanic membrane  112 . As discussed above, it may be desirable to position occlusion section  202  within cartilaginous region  116  ( FIG. 1 ) of ear canal  108 . Housing unit  204  may be positioned outside of ear canal  108 . In  FIG. 2A , housing unit  204  is illustrated as being disposed in ear  100 . It is understood that housing unit  204  may also be configured to be placed behind ear  100  or may be placed partially behind ear  100  and partially in ear  100 . 
     Occlusion section  202  may include insertion element  206  and expandable element  208 . The expandable element  208  can be a balloon containing a non-Newtonian fluid, but alternatively it can be a material that is just a non-Newtonian fluid without the use of a balloon. Insertion element  206  may be coupled to expandable element  208  and may be used to position expandable element  208  in ear canal  108 . Expandable element  208  is configured to be expanded or manipulated in shape, via medium  228 . Again, the medium  228  can be a non-Newtonian fluid. In general, expandable element  208  may be configured to form an acoustic seal with a portion of ear canal wall  110 . Expandable element  208  may be configured to partially or fully occlude ear canal  108 , to provide various degrees of acoustic isolation (i.e., attenuation of one or more frequencies of ambient sound) at tympanic membrane  112 . Furthermore, with the use of a non-Newtonian fluid, the attenuation characteristic can have increased attenuation as the surface of the element  208  is exposed to greater sound pressure levels (SPL) or volume of sound. In the case of shear thickening fluids, the greater the SPL exposure that the element  208  is exposed to, the greater shear thickening and viscosity the material of element  208  will exhibit. Correspondingly, the greater viscosity will provide greater attenuation characteristics to element  208 . As the ambient sound increases, the greater attenuation element  208  will exhibit. As the ambient sound subsides or decreases, the less attenuation element  208  will exhibit. The non-Newtonian essentially operates as a dynamic attenuation device that is passive. In some embodiments, an active component can be added or substituted to provide a user greater control of the attenuation characteristics. For example, if the non-Newtonian fluid comprises electrorheological fluids composed of dispersions of electrically polarizable particles in an insulating fluid, an exposure of the non-Newtonian fluid to an electric field controls the shear viscosity (and hence attenuation characteristics) of the non-Newtonian fluid. Typically a non-Newtonian fluid such as electrorheological fluids increases in shear viscosity when exposed to an electric field. Alternatively, the non-Newtonian fluid can also be magnetorheological fluids composed of dispersions of magnetic particles in an inert or non-magnetic carrier liquid that increases in shear viscosity when exposed to a magnetic field. Thus, controlling the magnetic field about the magnetorheological fluids controls a level of the attenuation characteristic of the element containing the non-Newtonian fluid. 
     In operation, expandable element  208  may be inserted in ear canal  108  in a contracted state or in a shape that would generally have a smaller diameter than the orifice of the ear canal. After insertion, expandable element  208  may be subsequently expanded (e.g., by being filled with medium  228 ) or manipulated by squeezing, or pinching, such that expandable element  208  conforms to ear canal  108  and forms at least a partial acoustic seal with ear canal  108 . To remove earpiece device  200 , expandable element  208  may be manipulated again or contracted (e.g., by removing at least part of medium  228  or manipulating part of the medium towards an external surface) back to the contracted state. Accordingly, earpiece device  200  may then be easily removed from ear canal  108 . 
     Expandable element  208  may be formed from any compliant material that has a low permeability to medium  228 . Examples of materials of expandable element  208  include any suitable elastomeric material, such as, without being limited to, silicone, rubber (including synthetic rubber) and polyurethane elastomers (such as Pellethane® and Santoprene™). Materials of expandable element  208  may be used in combination with a barrier layer (for example, a barrier film such as SARANEX™) to reduce the permeability of expandable element  208 . In general, expandable element may be formed from any suitable material having a range of Shore A hardness between about 5 A and about 30 A, with an elongation of about 500% or greater. 
     Medium  228  may include any suitable liquid, gas or gel capable of expanding and contracting expandable element  208  and that would maintain a comfortable level of pressure for a user of earpiece device  200 . Examples of medium  228  include, for example, silicone, non or low permeable-based polymers, gels, fully-fluorinated liquids, ethylene glycol, isopropyl alcohol, air or other gasses (for example sulfur hexafluoride (SF6) or hydrogen). In particular embodiments emphasized herein, the medium can include non-Newtonian fluids such as shear thickening fluids and or fluids as described above. 
     Insertion element  206  may be formed from, for example, thermoplastic elastomer (TPE) materials, materials having an elastomeric property (such as silicone), or other malleable materials capable of conforming to the ear canal. Expandable element  208  may be attached to insertion element  206  via any suitable attachment method, such as, but not limited to, bonding, adherence with an adhesive, thermal bonding, molding and ultrasonic bonding. 
     Although expandable element  208  is illustrated as being of an annular-disc shape, it is understood that expandable element  208  may be formed of other shapes, such as conical-shaped, or toroidal-shaped. Although  FIG. 2A  illustrates a single expandable element  208 , occlusion section  202  may include multiple co-located expandable elements  208  (such as an inner expandable element in an outer expandable element, where each expandable element  208  may be filled with different mediums  228 ). Although  FIG. 2A  illustrates a single expandable element  208 , it is understood that occlusion section  202  may include more than one expandable element  208  (for example, as shown in  FIG. 8A ), where each expandable element  208  may be filled with a same medium  228  or with different mediums  228 . As noted previously, the expandable element  208  can include a balloon, but in some embodiments, the non-Newtonian fluid itself can form the element  208  without the use of a balloon or other exterior element. For example, in  FIG. 2B , the earpiece  200  can have an occluding member  208 A (similar to expandable element  208  of  FIG. 2A ) that is either made of a non-Newtonian fluid (such as a material like “Silly Putty” described above or non-Newtonian fluids that are capable of being self contained) or comprised of a balloon which has or encloses a medium comprising the non-Newtonian fluid. The earpiece can include a flange  299  that can cover the orifice of the ear but is not intended to completely seal the ear as the balloon is designed for such purpose further into the external auditory canal (EAC). In one embodiment, the flange can also be made of a non-Newtonian fluid. Further note that the embodiments herein are not limited to earpieces, but can include all types of headphones and headsets. In the case of headphones, particularly circum aural headphones that are configured to cover a user&#39;s ears can have various portions made of or incorporate non-Newtonian fluids. For example, the foam padding that typically contacts a user&#39;s ears can be alternatively made with non-Newtonian fluids or with composites with polyurethane or other alternative materials. The exterior housing of such headphones can also include or be made of non-Newtonian fluids or composites (with microfibers, for example) to provide additional sound attenuation 
     As described further below with respect to  FIGS. 5-13 , physical parameters of occlusion section  202  may be selected to provide a predetermined sound attenuation characteristic over a frequency band or over ambient SPL levels. For example, a compliance of expandable element  208 , the type of medium  228  (such as non-Newtonian fluid), as well as the number of expandable elements  208 , may be used to design occlusion section  202  with a specific sound attenuation characteristic (such as a high pass filter or a low pass filter) or a dynamic attenuating filter based on the level of amplitude of an ambient SPL. According to an embodiment of the present invention, a selection of a material for the medium or a selection of particles in a non-Newtonian fluid or other parameters such as an amount of expansion pressure (of medium  228 ) with which expandable element  208  is expanded may also be selected to control the amount of overall sound attenuation, as well as the amount of occlusion, over the frequency band. 
     For example, sleep apnea is an example of a noisy environment that can have an impact on the health of the listener. Because snoring typically has a large portion of its power in the lower frequencies in the acoustic range, a listener subjected to snoring could benefit from a high pass filter earpiece that allows higher frequencies of the acoustic signal to be transmitted through the earpiece, while attenuating the lower frequencies. In the case of non-Newtonian fluids, concentration of particles, particle size, and particle shape can all play a roll in configuring and optimizing an occluding element that can attenuate frequencies associated with snoring (or other sources of undesired noise). Other factors that can be used to configure attenuation characteristics can include the specific gravity of the fluid used for the non-Newtonian fluid and the density of the particles, fibers, microparticles or microfibers used for the non-Newtonian fluid. Note that the term “particles” as used herein is intended to be interpreted in a broad sense to include all types of objects that can be used in a non-Newtonian fluid such as spheres, microspheres, fibers, microfibers, or microparticles. In some embodiments, the specific gravity of the fluid is made to match the density of the particles. Furthermore, the location or placement of the non-Newtonian fluid within a device can be varied and the composition of the non-Newtonian fluid can be varied to provide specific attenuation profiles. In other words, the fluid can be customized or designed to have variable compression and decompression or recovery times. As the non-Newtonian fluid hardens or forms clumps under shear forces, the amount of time that the non-Newtonian fluid recuperates or returns to a non-clumped or softened state can also be a factor in its attenuation characteristics. Furthermore, the various variables above can also be selectively manipulated to design a material or composite material that exhibits the shear thickening and attenuation characteristics that begins to manifest at a particular threshold sound pressure level. Non-Newtonian fluids introduces a entire host of additional variables for designing acoustic products (and non-acoustic products that still utilize acoustics in some form) that can benefit from customized attenuation characteristics or parameters not previously available before. 
     Housing unit  204  may include inflation management system  210  for controlling the transfer of medium  228  to and from occlusion section  202 , for expanding and contracting expandable element  208 . Housing unit  204  may also include user interface  212  coupled to inflation management system  210 . Inflation management system  210  may be activated responsive to user interface  212 , in order to expand and contract expandable element  208 . Housing unit  204  may also include further electrical components. Inflation management system may include any suitable system capable of transferring medium  228  to and from expandable element  208 . For example, inflation management system may include a pump actuator and a valve housing (not shown). In some embodiments, no inflation management system would be used. For example, a system using non-Newtonian fluid can operate by allowing the user to apply pressure to the element  208  itself to manipulate the shape of the element  208  for insertion and removal from the ear canal. 
     According to one embodiment, earpiece device  200  may include inflation management system  210  and user interface  212 , without any electro-acoustic elements. In this example embodiment, earpiece device  200  may be configured simply as a sound isolation device, with a predetermined sound attenuation characteristic selected according to the physical parameters of occlusion section  202 . In another embodiment, the, earpiece device  200  may be without an inflation management system  210  as described above. 
     According to another embodiment, housing unit  204  may include electrical components as well as one or more electro-acoustical components. For example, housing unit  204  may include speaker  214 , controller  220 , memory  222 , battery  224  and communication unit  226 . 
     Speaker  214 , memory  222 , communication unit  226 , user interface  212  and inflation management system  210  may be controlled by controller  220 . Controller  220  may include, for example, a logic circuit, a digital signal processor or a microprocessor. 
     Communication unit  226  may be configured to receive and/or transmit signals to earpiece device  200 . Communication unit  226  may be configured for wired and/or wireless communication with an external device (e.g., an MPEG player or a mobile phone). 
     Battery  224  may power the electrical and electro-acoustic components in housing unit  204 . Battery  224  may include a rechargeable or replaceable battery. 
     The acoustic seal provided by occlusion section  202  may significantly reduce a sound pressure level at tympanic membrane  112  from an ambient sound field at the entrance to ear canal  108  (to provide sound isolation). For example, occlusion section  202  having a high pass filter characteristic may substantially attenuate lower frequencies. Because of the sound isolation of occlusion section  202 , speaker  214  may generate a full range bass response time when reproducing sound in earpiece device  200 . 
     According to another embodiment, housing unit  204  may include an ear canal (EC) microphone  216  located adjacent to speaker  214 , which may also be acoustically coupled to ear canal  108 . EC microphone  216  may be configured to measure a sound pressure level in ear canal  108 . The sound pressure level in ear canal  108  may be used, for example, to test the hearing acuity of a user, to confirm an integrity of the acoustic seal, and/or to confirm the operation of EC microphone  216  and speaker  214 . Further note that the ear canal microphone can be located in other locations than shown, for example, the ear canal microphone  216  can be located on the other side of the insertion element  206  residing well within the ear canal in some embodiments. The wiring for the ear canal microphone  216  in such instance can be fed through the insertion element  206  which can be a tube or channel that goes through the element  208 . 
     According to another embodiment, housing unit  204  may include ambient microphone  218 , as well as EC microphone  216  and speaker  214 . Ambient microphone  218  may be configured to monitor a sound pressure of the ambient environment at the entrance to ear  100 . In at least one exemplary embodiment, earpiece device  200  may actively monitor a sound pressure level both inside and outside ear canal  108  and may enhance spatial and timbral sound quality, while maintaining supervision to ensure safe sound reproduction levels. Earpiece device  200 , in various embodiments may conduct listening tests, filter sounds in the environment, monitor sounds in the environment, present notification based on the monitored sounds, maintain constant audio content to ambient sound levels, and/or filter sound in accordance with a personalized hearing level. 
     Earpiece device  200  may be configured to generate an ear canal transfer function (ECTF) to model ear canal  108  (via speaker  214  and EC microphone  216 ), as well as an outer ear canal transfer function (OETF) (via ambient microphone  218 ). Earpiece device  200  may be configured to determine a sealing profile with ear  100  to compensate for any acoustic leakage. Earpiece device  200  may be configured to monitor a sound exposure to ear canal  108  (for example, from speaker  214  as well as from ambient noise measured via ambient microphone  218 ). 
     Referring to  FIG. 3 , a cross section diagram of earpiece device  200  is shown, which illustrates further components of insertion element  206 . In  FIG. 3 , only some of the components of housing unit  204  are shown, for convenience. According to an exemplary embodiment, insertion element  206  may include pneumatic channel  302 . Pneumatic channel  302  may be coupled to expandable element  208  and to inflation management system  210 . Pneumatic channel  302  may be used to transfer medium  228  (illustrated by double headed arrow A) to and from expandable element  208  via port  308 . 
     In at least one exemplary embodiment, insertion element  206  may include at least one acoustic channel (e.g., acoustic channel  304  and/or acoustic channel  306 ) for receiving or delivering audio content. For example, housing unit  204  may include speaker  214 . Insertion element  206  may, thus, include acoustic channel  304  for delivering sound from speaker  214  to ear canal  108 . As another example, housing unit  204  may include speaker  214  and EC microphone  216 . In this example, insertion element  206  may include acoustic channels  304 ,  306 , respectively coupled to speaker  214  and EC microphone  216 . Acoustic channel  306  may deliver sound from ear canal  108  to EC microphone  216 . 
     As described above, expandable element  208  may form an acoustic seal with ear canal wall  110  at a location between the entrance (the orifice) to ear canal  108  and tympanic membrane  112 . The acoustic seal by expandable element  208  may substantially attenuate sound in ear canal  108  from the ambient environment (thus providing sound isolation to ear canal  108 ). Insertion element  206  may also include one or more acoustic channels (e.g., acoustic channel  304  and/or acoustic channel  306 ) for acoustically coupling sound between ear canal  108  and one or more respective transducers (e.g., speaker  214  and/or EC microphone  216 ). Accordingly, sound transmitted to and/or from ear canal  108  via acoustic channel  304  (and/or 306) may be substantially isolated from the ambient environment. 
     Referring next to  FIGS. 4A-4D , exemplary earpiece device  200 ′ is shown. In particular,  FIG. 4A  is a perspective view diagram of earpiece device  200 ′ with expandable element  208  in an expanded state;  FIG. 4B  is a cross section diagram of earpiece device  200 ′ with expandable element  208  in the expanded state:  FIG. 4C  is a perspective view diagram of earpiece device  200 ′ with expandable element  208  in a contracted state; and  FIG. 4D  is a cross-section diagram of earpiece device  200 ′ with expandable element  208  in the contracted state. 
     Earpiece device  200 ′ is similar to earpiece device  200  except that earpiece device  200 ′ includes flange  402  coupled to insertion element  206  of occlusion section  202 . Flange  402  may provide sound attenuation (in addition to the sound attenuation by expandable element  208 ). Flange  402  may also help to seat occlusion section  202  in ear canal  108  ( FIG. 2 ). Flange  402  may be formed of materials similar to expandable element  208 . 
     The selection of physical parameters of occlusion section  202  ( FIG. 2 ) to provide predetermined sound attenuation characteristics is described below. 
     It is often possible and convenient to represent an acoustical system with a lumped element model, as an acoustical circuit analogous to an electrical circuit. For example, an acoustical system may be represented as an acoustic impedance (or acoustic mobility). In acoustic impedance analogs, for example, the sound pressure and volume velocity correspond to voltage and current, respectively. For example, occlusion section  202  ( FIG. 2 ) in ear canal  108  may be modeled by an acoustical impedance circuit. 
     Referring to  FIGS. 5A and 5B , an equivalent acoustical element representation of balloon  502  (an example of an expandable element) filled with medium  510  in tube  504  is described. In particular,  FIG. 5A  is a cross section diagram of balloon  502  in tube  504 ; and  FIG. 5B  is an example of a volume of one face of balloon  502  (for example, face  508 ) with pressure difference. 
     Balloon  502  and medium  510  may each be represented as acoustical elements. Because balloon  502  is within tube  504 , the band of balloon material in contact with tube walls  506  does not move. This effectively separates balloon  502  into two parts, upstream face  508  and downstream face  512 . It is understood that the acoustical element representation of downstream face  512  is the same as that of upstream face  508 . Thus, only upstream face  508  is considered below. 
     Face  508  of balloon  502  (filled with medium  510 ) includes a static DC pressure P 2  on the outside and a static interior pressure P g . If the outside pressure is changed to P 2 ′, there will be a change in the static equilibrium of the balloon. Face  508  moves to a new position and may have a different shape (represented as face  508 ′), sweeping out a volume ΔV. Thus, the interior pressure will change to a new value P g ′. The shape of the balloon face  508  is controlled by the difference in pressure across the material, i.e., P D =P 2 −P g  and P D ′=P 2 ′−P g ′. 
     Although, in general, the relationship between the change in pressures and the volume of balloon  502  may be complicated, for the acoustical behavior, it is assumed that these changes are very small, so that a simple acoustical representation of balloon  502  may be determined. 
       FIG. 5B  illustrates an example of the volume change of face  508  of balloon  502  with a change in pressure difference across the material. Over a small change in pressure difference ΔP D , the curve is very nearly linear and the volume change ΔV may be represented as: 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     V 
                   
                   ≈ 
                   
                     
                       
                         ( 
                         
                           
                             ∂ 
                             V 
                           
                           
                             ∂ 
                             
                               P 
                               D 
                             
                           
                         
                         ) 
                       
                       
                         P 
                         D 
                       
                     
                     ⁢ 
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       P 
                       D 
                     
                   
                   ≡ 
                   
                     
                       C 
                       2 
                     
                     ⁢ 
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         P 
                         D 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     For acoustic pressures, the pressures acting on face  508  may be considered to oscillate sinusoidally in time about their static values, and may be represented by complex notation as 
         P   2   ′=P   2 +Re{ p   2   e   iωt }  (2)
 
         P   g   ′=P   g +Re{ p   g   e   iωt }  (3)
 
     where p g  and p 2  are the (complex) sound pressures on either side of the balloon section, so that 
       Δ P   D =Re{( P   2   −p   g ) e   iωt }.  (4)
 
     Similarly, the volume changes harmonically as 
       Δ V=V′−V =Re{ V*e   iωt }  (5)
 
     where V is the static volume enclosed by face  508  of the balloon. Thus, the volume velocity U (i.e., the rate change of volume with time) may be represented as 
     
       
         
           
             
               
                 
                   
                     U 
                     ≡ 
                     
                       Re 
                       ⁢ 
                       
                         { 
                         
                           
                             u 
                             2 
                           
                           ⁢ 
                           
                             e 
                             
                               i 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               ω 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               f 
                             
                           
                         
                         } 
                       
                     
                   
                   = 
                   
                     
                       
                         dV 
                         ′ 
                       
                       
                         d 
                         ⁢ 
                         t 
                       
                     
                     = 
                     
                       Re 
                       ⁢ 
                       
                         
                           { 
                           
                             i 
                             ⁢ 
                             ω 
                             ⁢ 
                             
                               V 
                               * 
                             
                             ⁢ 
                             
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                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
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                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 f 
                               
                             
                           
                           } 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Accordingly, the sound pressure difference is related to the complex volume velocity u 2 , as 
     
       
         
           
             
               
                 
                   
                     
                       p 
                       2 
                     
                     - 
                     
                       p 
                       g 
                     
                   
                   = 
                   
                     
                       u 
                       2 
                     
                     
                       i 
                       ⁢ 
                       ω 
                       ⁢ 
                       
                         C 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     where C 2  is the acoustical capacitance of one side (for example face  508 ) of balloon  502 . The value of capacitance C 2  may be determined by the slope of the tangent line in  FIG. 5B . 
     Medium  510  may include, for example, a gas or a liquid. The acoustical element representation of medium  510  may be different depending on whether medium  510  is a gas or a liquid. The consideration of medium  510  as a liquid is discussed with respect to  FIG. 12 . The acoustical representation of medium  510  that includes a gas is considered below. Accordingly, medium  510  is referred to below as gas  510 . 
     An enclosed volume of gas may store energy in its compressions. Thus, gas  510  (for example, air) within balloon  502  may also be represented as an acoustic capacitance. The volume velocity u 2 , as defined, acts to compress gas  510  contained within balloon  502 . The volume velocity corresponding to face  512  of balloon  502  may be defined in the opposite sense, such that the volume velocity u 1  acts to uncompress the air. The net volume velocity (u 2 -u 1 ) is related to the sound pressure p g  inside the balloon by: 
         u   2   −u   1   =iωC   g   p   g   (8)
 
     where capacitance C g  is given by: 
     
       
         
           
             
               
                 
                   
                     C 
                     g 
                   
                   = 
                   
                     
                       V 
                       g 
                     
                     
                       γ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         P 
                         g 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     and where V g  is the enclosed volume, P g  is the static pressure inside balloon  502 , and γ is the specific heat ratio. 
     Referring to  FIGS. 6A and 6B , acoustical system  600  representing an expandable element in an ear canal is shown. In particular,  FIG. 6A  is a cross section diagram of acoustical system  600  including balloon  502  in tube  504  having anechoic termination  602 ; and  FIG. 6B  is an electro-acoustical circuit diagram of acoustical system  600 . Acoustical system  600  represents an expandable element (balloon  502 ) in an ear canal (tube  504 ) having a tympanic membrane (anechoic termination  602 ). Although not illustrated, balloon  502  may be formed on an insertion element (such as insertion element  206  shown in  FIG. 2 ). 
     If the lateral dimensions of tube  504  are less than a wavelength of sound, sound waves may propagate along both forward and backward longitudinal directions. Because tube  504  includes anechoic termination  602 , there are no reflected sound waves, only forward propagating waves. 
     Consider pressure P 1  and volume velocity u 1  at a position in tube  504 . For a plane wave traveling in a single direction, the pressure and the volume velocity are in phase and are related as: 
         P   1   =R   c   u   1   (10)
 
     where the characteristic acoustical resistance of tube  504  (at anechoic termination  602 ) is 
     
       
         
           
             
               
                 
                   
                     
                       R 
                       c 
                     
                     = 
                     
                       
                         ρ 
                         ⁢ 
                         c 
                       
                       A 
                     
                   
                   . 
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     Here, A is the internal cross-sectional area of tube  504 , p is the density of the gas (e.g., air), and c is the sound speed in the gas (e.g., air). 
     As discussed above, faces  508 ,  512  of balloon  502  may each be represented as acoustical compliance C b . Gas  510  within balloon  502  may be represented as acoustical compliance C g . Finally, tube  504  with anechoic termination  602  may be represented as resistance R c . 
     Based on the acoustical elements representing balloon  502 , gas  510  and tube  504 , acoustical system  600  may be represented as an equivalent electro-acoustical circuit (i.e., an acoustical impedance analog), as shown in  FIG. 6B . Thus capacitance C b  of face  508  receives pressure p 2 . Capacitance C b  is coupled to capacitance C g  of gas  510  and capacitance C b  of face  512 . Capacitance C b  of face  512  is coupled to resistance R c  of the termination of tube  504 . Thus, pressure p 2  is provided at an output terminal of the circuit. It is understood that the electro-acoustic circuit may be modified to account for the finite size of insertion element  206  ( FIG. 2 ) on which balloon  502  may be mounted. 
     Network methods may be applied to calculate the various quantities of the acoustical elements if values for the various circuit elements are available. Both R c  and C b  may be determined from the expressions provided above. 
     For a sample calculation, it is assumed that tube  504  has an inner diameter of 9.53 mm (0.375″) and that balloon  502  contains a volume of 0.713 cm 3  at an inflation pressure of 300 mbar. Capacitance C b  corresponding to each face of balloon  502  may be determined, for example, based on a calculation of the inflation dynamics of balloon materials, taking into account the Mooney-Rivlin type of stress-strain relationship. In the sample calculation, several different values of capacitance including C b =0.3C g , C b =C g , and C b =3 C g  are selected. The transmission coefficient of acoustical energy may be determined as: 
     
       
         
           
             
               
                 
                   T 
                   = 
                   
                     20 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     log 
                     ⁢ 
                     
                       
                          
                         
                           
                             p 
                             1 
                           
                           
                             p 
                             2 
                           
                         
                          
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     Referring to  FIG. 7 , the calculated transmission coefficients for these three values of capacitance C b  are shown. Curves  702 ,  704  and  706  represent capacitance values C b =3 C g , C b =C g  and C b =0.3C g , respectively. All curves show about a 6 decibel (dB) per octave drop off at the lower frequencies. Accordingly, balloon  502  acts as a first order high-pass filter. 
     Referring next to  FIGS. 8A and 8B , acoustical system  800  is shown, which represents two expandable elements in an ear canal. In particular,  FIG. 8A  is a cross section diagram of acoustical system  800  including balloons  802 -A,  802 -B in tube  504  having anechoic termination  602 ; and  FIG. 8B  is an electro-acoustical circuit diagram of acoustical system  800 . Balloons  802 -A,  802 -B are filled with gas  808 -A,  808 -B. 
     Acoustical system  800  is similar to acoustical system  600  ( FIGS. 6A and 6B ), except that acoustical system  800  includes two balloons  802 -A,  802 -B (i.e., two expandable elements), and balloons  802 -A,  802 -B are illustrated as being mounted on insertion element  804 . Two balloons  802 -A,  802 -B may be formed, for example, from a single balloon material attached to insertion element  804  at attachment points  805  and  806 . In an exemplary embodiment, attachment point  806  represents an O-ring approximately midway along a length of a single balloon. As another example, balloons  802 -A,  802 -B may be formed from different balloon materials attached at respective attachment points  805 ,  806 . Gas  808 -B may be the same as gas  808 -A or may be different from gas  808 -A. 
     Balloons  802 -A,  802 -B have respective volumes of V A  and V B , with respective sound pressures of p A  and p B . Gap  810  between balloons  802 -A,  802 -B (at attachment point  806 ) has volume V c  and sound pressure p c . The motion of the right-hand face of balloon  802 -A includes a volume velocity u A . Similarly, the motion of the left-hand face of balloon  802 -B includes a volume velocity u B . 
     Based on the acoustical elements described above for balloon  502  ( FIGS. 6A and 6B ), gas  510  and tube  504 , acoustical system  800  may also be represented as an equivalent electro-acoustical circuit (i.e., an acoustical impedance analog), as shown in  FIG. 8B . Thus, capacitances C bA1 , C gA , C bA2  are associated with the left face of balloon  802 -A, gas  808 -A and the right face of balloon  802 -A, respectively. Capacitance C c  is associated with gap  810 . Capacitances C bB1 , C gB , C bB2  are associated with the left face of balloon  802 -B, gas  808 -B and the right face of balloon  802 -B, respectively. Although not shown, it is understood that the electro-acoustic circuit shown in  FIG. 8B  may be modified to account for insertion element  804 . 
     Referring to  FIG. 9 , example transmission coefficients are shown for the electro-acoustical circuit shown in  FIG. 8B , using several different values of capacitance. In this example, both balloons  802 -A,  802 -B have a volume of 0.222 cm 3  and an inflation pressure of 300 mbar, so that C gA =C gB . Gap  810  between balloons  802 -A,  802 -B is at atmospheric pressure and has a volume of 0.095 cm 3 . Three different selections of balloon capacitances are used. For curve  902 , the capacitances are C bA1 =C bA2 =C bB1 =C bB2 =3C gA . For curve  904 , the capacitances are C bA1 =C bB1 =3C gA  and C bA2 =C bB2 =C gA . For curve  904 , the capacitances are C bA1 =C bA2 =C bB1 =C bB2 =C gA . 
     As shown in  FIG. 9 , the acoustical transmission for two balloons  802 -A,  802 -B is similar to the acoustical transmission of a single balloon (shown in  FIG. 7 ). Thus, similar to the single balloon ( FIG. 7 ), the combination of two balloons  802 -A,  802 -B also acts like a first-order high-pass filter, with approximately a 6 dB/octave slope at low frequencies. 
       FIG. 8A  illustrates acoustical system  800  including two balloons  802 -A,  802 -B disposed along a length of insertion element  804  (i.e., in series arrangement, as illustrated in  FIG. 8B ). According to another embodiment, balloons  802 -A,  802 -B may be co-located on insertion element  804 . Balloons  802 -A,  802 -B, thus, may be formed in a parallel arrangement. 
     Measurements on several double balloons, however, have revealed a more complicated variation with frequency. This variation may be due to small leaks between balloons  802 -A,  802 -B. 
     Referring next to  FIGS. 10A and 10B , acoustical system  1000  is shown, which represents two expandable elements in an ear canal. In particular,  FIG. 10A  is a cross section diagram of acoustical system  1000  including balloons  802 -A,  802 -B in tube  504  having anechoic termination  602 ; and  FIG. 10B  is an electro-acoustical circuit diagram of acoustical system  1000 . Acoustical system  1000  is similar to acoustical system  800  ( FIGS. 8A and 8B ), except that acoustical system  1000  includes leak  1002  at attachment point  806 . 
     Leak  1002  may be modeled as a short, circular passage between balloons  802 -A,  802 -B. The volume velocity entering leak  1002  is represented as u LA  and the volume velocity exiting leak  1002  is represented as u LB . A volume of fluid (gas or liquid) that has a length comparable or greater than a wavelength (or a radius that is comparable or smaller than a viscous boundary layer thickness) may not be capable of being treated as a simple volume. Accordingly, a general theory is described below for acoustical propagation along a circular passage (i.e., leak  1002 ). 
     Consider that leak  1002  is a hollow, circular passage of radius a L  and length l. At one end of leak  1002 , there is a pressure p A  and volume velocity u LA ; at the other end, there is a pressure p B  and volume velocity u LB . These quantities are related, generally, through a transfer matrix T L  as: 
     
       
         
           
             
               
                 
                   
                     
                       [ 
                       
                         
                           
                             
                               p 
                               A 
                             
                           
                         
                         
                           
                             
                               u 
                               LA 
                             
                           
                         
                       
                       ] 
                     
                     = 
                     
                       
                         
                           T 
                           L 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 
                                   p 
                                   B 
                                 
                               
                             
                             
                               
                                 
                                   u 
                                   
                                     L 
                                     ⁢ 
                                     B 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                       = 
                       
                         
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                                   cosh 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
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                                   ⁢ 
                                   
                                       
                                   
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                                   ⁢ 
                                   
                                       
                                   
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                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   where 
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   Γ 
                   = 
                   
                     i 
                     ⁢ 
                     
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                       c 
                     
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                   ( 
                   14 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     = 
                     
                       
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                         ⁢ 
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                         ⁢ 
                         
                             
                         
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                               β 
                             
                           
                         
                       
                     
                   
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                   ⁢ 
                   with 
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
             
               
                 
                   
                     T 
                     α 
                   
                   = 
                   
                     1 
                     + 
                     
                       
                         2 
                         ⁢ 
                         
                           ( 
                           
                             γ 
                             - 
                             1 
                           
                           ) 
                         
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                             1 
                           
                           ⁡ 
                           
                             ( 
                             
                               
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                             ) 
                           
                         
                       
                       
                         
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                         ⁢ 
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                         ⁢ 
                         
                           
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                               ⁢ 
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                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
             
               
                 
                   
                     T 
                     β 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         2 
                         ⁢ 
                         
                           
                             J 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             
                               
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                               ⁢ 
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                             ) 
                           
                         
                       
                       
                         
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                         ⁢ 
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                         ⁢ 
                         
                           
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                             0 
                           
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                             ( 
                             
                               
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                   ( 
                   17 
                   ) 
                 
               
             
             
               
                 
                   α 
                   = 
                   
                     
                       
                         
                           - 
                           i 
                         
                         ⁢ 
                         ρ 
                         ⁢ 
                         ω 
                         ⁢ 
                         
                           N 
                           
                             p 
                             ⁢ 
                             r 
                           
                         
                       
                       μ 
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
             
               
                 
                   β 
                   = 
                   
                     
                       
                         
                           - 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ρ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ω 
                       
                       μ 
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     where μ represents the coefficient of viscosity of the gas (e.g., air), γ represents the ratio of specific heats, N pr  represents the Prandtl number and J 0 (*),J 1 (*) represent Bessel functions of the first kind for respective integer orders 0 and 1. 
     Leak  1002  that is a circular tube, in general, does not have a simple lumped-element representation. However, leak  1002  may be represented as a network block in an electro acoustical circuit. Accordingly, based on the acoustical elements described above, acoustical system  1000  having leak  1002  may also be represented as an equivalent electro-acoustical circuit (i.e., an acoustical impedance analog), as shown in  FIG. 10B . In  FIG. 10B , network block  1004  with transfer matrix T L  represents leak  1002 . The circuit shown in  FIG. 10B  is similar to the circuit shown in  FIG. 8B , except for the inclusion of network block  1004 . Network block  1004  may act in parallel to some of the circuit elements representing balloons  802 -A,  802 -B. 
     Referring to  FIG. 11 , example transmission coefficients are shown for the electro-acoustical circuit shown in  FIG. 10B , using several different leak sizes (and eq. (13) for the transfer matrix T L ). The leak sizes include radii of 0 cm (i.e., no leak), 0.017 cm, 0.05 cm and 0.1 cm. In particular, curves  1102 ,  1104 ,  1106  and  1108  represent respective leak sizes of 0 cm, 0.017 cm, 0.05 cm, and 0.1 cm. As shown in  FIG. 11 , there is a transition from one type of behavior to another with leak size. For a large radius leak (curve  1108 ), acoustical system  1000  effectively represents a single large balloon, with a 6 dB/octave drop at low frequencies. For a zero leak (curve  1102 ), acoustical system  1000  represents a double balloon system, also with a 6 dB/octave low frequency behavior. At intermediate sized leaks (curves  1104  and  1106 ), acoustical system  1000  transitions from a single balloon mode at low frequencies to a double balloon mode at high frequencies, thus producing a more complex frequency variation over approximately the 200 Hz-2000 Hz range. In the example shown in  FIG. 11 , the attenuation is relatively flat for the 0.017 cm leak (curve  1104 ). Accordingly, it may be possible to design leaks between balloons  802 -A,  802 -B to selectively shape the transmission (and attenuation) to a desired response over a range of frequencies. 
     Referring next to  FIGS. 12A-12C , acoustical system  1200  is shown, which represents a liquid-filled expandable element in an ear canal. In particular,  FIG. 12A  is a cross section diagram of acoustical system  1200  including balloon  502  filled with liquid  1202  in tube  504  having anechoic termination  602 ;  FIG. 12B  is a circuit diagram of a transfer network associated with balloon  502  filled with liquid  1202 ; and  FIG. 12C  is an electro-acoustical circuit diagram of acoustical system  1200 . 
     Acoustical system  1200  is similar to acoustical system  600  ( FIGS. 6A and 6B ), except that acoustical system  1200  includes balloon  502  filled with liquid  1202 . Filling balloon  502  with liquid  1202  (for example, water instead of air), may change the acoustical behavior of balloon  502 . If balloon  502  is of sufficiently short length, it may be treated as a small volume (similar to holding a volume of gas as described above). For balloon  502  having a length comparable to a wavelength, balloon  502  may be treated as a transmission line. This may be the case for liquid  1202 , because the sound speed in liquids is considerably higher than in air, such that the wavelengths are correspondingly longer. In the case of non-Newtonian liquids, the sound speeds may vary from conventional liquids. 
     The pressure just inside face  508  of balloon  502  is represented as P A  and the pressure just inside face  512  is represented as p B . Let L be the length of the balloon and a, the internal diameter of the constraining tube. The sound pressures (p A , p B ) and volume velocities (u 1 , u 2 ) may be related through a transfer matrix T liq  by: 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             p 
                             A 
                           
                         
                       
                       
                         
                           
                             u 
                             2 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         T 
                         liq 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               
                                 p 
                                 B 
                               
                             
                           
                           
                             
                               
                                 u 
                                 1 
                               
                             
                           
                         
                         ] 
                       
                     
                     = 
                     
                       
                         [ 
                         
                           
                             
                               
                                 cosh 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 Γ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 L 
                               
                             
                             
                               
                                 Z 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 sinh 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 Γ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 L 
                               
                             
                           
                           
                             
                               
                                 
                                   Z 
                                   
                                     - 
                                     1 
                                   
                                 
                                 ⁢ 
                                 sinh 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 Γ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 L 
                               
                             
                             
                               
                                 cosh 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 Γ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 L 
                               
                             
                           
                         
                         ] 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               
                                 p 
                                 B 
                               
                             
                           
                           
                             
                               
                                 u 
                                 1 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     If a is sufficiently large, viscous and thermal boundary layer effects may be ignored, such that the arguments αα and αβ are also large and T α ≈T β ≈1. Then, 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             p 
                             A 
                           
                         
                       
                       
                         
                           
                             u 
                             2 
                           
                         
                       
                     
                     ] 
                   
                   ≈ 
                   
                     
                       [ 
                       
                         
                           
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               kL 
                             
                           
                           
                             
                               i 
                               ⁢ 
                               
                                 Z 
                                 
                                   l 
                                   ⁢ 
                                   i 
                                   ⁢ 
                                   q 
                                 
                               
                               ⁢ 
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               kL 
                             
                           
                         
                         
                           
                             
                               
                                 iZ 
                                 liq 
                                 
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               kL 
                             
                           
                           
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               kL 
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               p 
                               B 
                             
                           
                         
                         
                           
                             
                               u 
                               1 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     where k=ω/c liq  is the wavenumber and Z liq  is the characteristic impedance of the liquid, given as 
     
       
         
           
             
               
                 
                   
                     
                       Z 
                       liq 
                     
                     = 
                     
                       
                         
                           ρ 
                           liq 
                         
                         ⁢ 
                         
                           c 
                           liq 
                         
                       
                       
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           a 
                           2 
                         
                       
                     
                   
                   . 
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     As shown in  FIG. 12B , eq. (21) may be represented as a transfer network. For the transfer network: 
     
       
         
           
             
               
                 
                   
                     
                       Z 
                       1 
                     
                     = 
                     
                       
                         Z 
                         2 
                       
                       = 
                       
                         
                           Z 
                           3 
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               kL 
                             
                             - 
                             1 
                           
                           ) 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   where 
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     3 
                   
                   = 
                   
                     
                       Z 
                       liq 
                     
                     
                       i 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       kL 
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
     If it is further assumed that kL is small, the expressions simplify further, yielding 
     
       
         
           
             
               
                 
                   
                     
                       Z 
                       1 
                     
                     = 
                     
                       
                         Z 
                         2 
                       
                       = 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           L 
                           liq 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   where 
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     3 
                   
                   = 
                   
                     
                       1 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           C 
                           liq 
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
     In eqs. (25) and (26), L liq  represents an inductance and C liq  represents a capacitance, respectively, where: 
     
       
         
           
             
               
                 
                   
                     
                       L 
                       liq 
                     
                     = 
                     
                       
                         
                           ρ 
                           liq 
                         
                         ⁢ 
                         L 
                       
                       
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           a 
                           2 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   and 
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
             
               
                 
                   
                     C 
                     liq 
                   
                   = 
                   
                     
                       
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           a 
                           2 
                         
                         ⁢ 
                         L 
                       
                       
                         
                           ρ 
                           liq 
                         
                         ⁢ 
                         
                           c 
                           liq 
                           2 
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
           
         
       
     
     The inductance L liq  is directly related to the mass of the liquid contained in the volume. The capacitance C liq  is related to the compliance of the liquid. 
     Accordingly, based on the acoustical elements described above, and the transfer network shown in  FIG. 12B , acoustical system  1200  may be represented as an equivalent electro-acoustical circuit (i.e., an acoustical impedance analog), as shown in  FIG. 12C . The circuit shown in  FIG. 12C  is similar to the circuit shown in  FIG. 6B , except for the inclusion of inductances L liq , and the replacement of capacitance C g  with capacitance C liq . 
     Referring to  FIG. 13 , example transmission coefficients are shown for the electro-acoustical circuit shown in  FIG. 12C , using several values of capacitance for a water-filled balloon. For the example, the balloon volume is 0.713 cm 3  and the constraining tube has an inner diameter of 0.953 cm. The capacitance C b  of faces  508 ,  512  may be estimated according to the following argument. The shape of balloon  502  on inflation may depend mainly on the pressure difference across the membrane and not on what liquid  1202  (e.g., water) balloon  502  contains. If water-filled balloon  502  is inflated to a volume comparable to that of an air-filled balloon, there may be a comparable inflation pressure. In the example, the inflation pressure is selected as 300 mbar. The capacitances C b  include 3C g , C g , and 0.3C g . In particular, curve  1302  represents C b =C g , curve  1304  represents C b =0.3C g  and curve  1306  represents C b =3C g . As shown in  FIG. 13 , the transmission is quite low up to about 2 or 3 kHz. Curves  1302  and  1304  include a low frequency resonance due to the mass of the water and the stiffness of the balloon material. In general, by filling balloon  502  with liquid  1202 , system  1200  may act as a low pass filter. Presumably filling the balloon  502  with a non-Newtonian liquid (instead of water) will alter the characteristics of the curve in  FIG. 13  reflecting even greater attenuation overall. 
     Referring generally to  FIGS. 2 and 6A-13 , exemplary occlusion sections  202  of the present invention may be formed to produce a predetermined sound attenuation characteristic over a frequency band, for an expanded state of one or more expandable elements  208 . The predetermined sound attenuation characteristic may be produced by selecting physical parameters of occlusion section  202  (such as the material of expandable element  208 , medium  228 , as well as the effects of insertion element  206 ) in accordance with an electro-acoustical circuit model of occlusion section  202  in ear canal  108 . Thus, appropriate materials and mediums may be selected that substantially match acoustical element characterizations of expandable element  208  and medium  228 , to produce the predetermined sound attenuation characteristic. The predetermined sound attenuation characteristic, in general, may include a first frequency range over which sound is substantially attenuated and a second frequency range over which sound is substantially passed. Use of different non-Newtonian fluids in terms of size of particles, concentration of particles, shapes of particles, types of mixtures with other materials (such as fibers or with polyurethane to form foam), types of particles (e.g., spheres, rods, nanotubes, fibers, etc.) used and whether no particles are used will provide even more options in customizing sound attenuation characteristics unavailable to designers previously before. 
     It is understood that a predetermined sound attenuation characteristic may also be produced by combining multiple expandable elements  208  (with similar or different materials) filled with different mediums  228 . For example, a first expandable element  208  filled with gas (to produce a high pass filter) may be coupled with a second expandable element  208  filled with a liquid (to produce a low pass filter). The combination of the two expandable elements  208  with different mediums  228  may produce a band pass filter. The combinations of different non-Newtonian fluids or non-Newtonian fluids in one expandable element and other fluids or gas in a separate expandable element may also provide further options in providing customized predetermined sound attenuations characteristics. 
     Although the invention is illustrated and described herein with reference to specific embodiments, the invention is not intended to be limited to the details shown. Rather, various modifications may be made in the details within the scope and range of equivalents of the claims and without departing from the invention.