Abstract:
A wave generator has a wave emitter including an elongated dispersive waveguide and a source operatively connected to a first end of the waveguide. The source covers at least partially a surface area thereof. A signal generator is in operative connection with the transducer to create electrical signals. A computer is in operative connection with the signal generator to cause it to generate the electrical signals. A mechanical input wave is created by the source at the first end of the waveguide. The mechanical input wave is constructed independently of data related to a mechanical wave received from a source in the medium and taking into account the different predetermined propagation velocities of at least two component waves of the mechanical input wave so that they combine with each other at a second end of the waveguide to form the desired mechanical output wave in the medium.

Description:
CROSS REFERENCE 
     The present application is a U.S National Phase Aplication pursuant to 35 U.S.C. §371 of International Application No. PCT/IB2011/002701, filed Aug. 29, 2011, which claims priority to U.S. Provisional Patent Application No. 61/377,519, entitled ‘Mechanical Wave Generator and Method Thereof’, filed Aug. 27, 2010. The entire disclosure contents of these applications are herewith incorporated by reference into the present application. 
    
    
     TECHNICAL FIELD 
     This invention relates to devices for generating mechanical waves and methods thereof. 
     BACKGROUND 
     A “mechanical wave” is a disturbance that propagates through a medium due to the restoring forces it produces upon deformation of the medium. Solids, liquids, gases, and gels are examples of media through which a mechanical wave may travel. 
     If desired, the energy of a mechanical wave can be exploited to deform and potentially fracture an object placed in the medium. For example, high intensity compression pulses (i.e., a brief wave of great amplitude) can be sent in the body of a patient to break a kidney stone apart. 
     One protocol for kidney stone destruction consists of emitting a compression pulse having a sufficient amount of energy for traveling through the body, reaching the stone, and potentially rupturing the kidney stone upon contact. Machines used in medical kidney stone destruction are known in the art as lithotripters. The external lithotripters send externally-applied, focused, high-intensity compression pulses toward the kidney stone. As the high intensity compression pulses travel through the body of the patient, non-linear effects eventually deform these pulses into shockwaves. When a shockwave encounters a non-homogeneity such as the kidney stone, a relatively large amount of energy is transferred from the shockwave to the kidney stone in a (relatively) very short period of time. Ideally, this energy transfer is sufficient to break enough of the bonds between the stone particles to destroy the stone. With external lithotripters, the location of the kidney stone within the body of the patient must be known in order to direct the high-intensity compression pulses toward the kidney stone. 
     Despite their widespread use, conventional lithotripters are cumbersome apparatuses. First, they have the drawbacks of potentially damaging tissue adjacent to the kidney stone and producing large kidney stone fragments. Second, they have a limited focal length. Occasionally, conventional machines even fail to fragment the hardest kidney stones. Finally, conventional lithotripters often require the inclusion of apparatuses such as fluoroscopy (x-ray) or ultrasound machines for locating the kidney stone. 
     Montaldo et al. ‘ Generation of very high pressure pulses with  1- bit time reversal in a solid waveguide ’, J. Acoust. Soc. Am. 110(6), December 2001 have developed a way to focus high amplitude pressure pluses at predetermined locations in a fluid. The system of Montaldo et al. works according to the time-reversal mirror concept, which exploits the temporal reversibility (or reciprocity) of the wave equation of motion. Reciprocity says that if the wave equation has a solution, the time reversal (using a negative time) of that solution is also a solution of the wave equation. 
     The system S proposed by Montaldo et al., shown in  FIG. 1 , is composed of seven small independent bi-directional piezoelectric transducers T glued to one end of an aluminum bar (waveguide), which acts as a reverberative cavity RC. The transducers T can both emit and receive mechanical waves. The walls of the reverberative cavity RC are in contact with the air while the end of the reverberative cavity RC distal to the transducers T lies in water. In their experiment, Montaldo et al. use a source placed in the water to emit a pressure pulse toward the reverberative cavity RC. The pressure pulse is, after propagation through the reverberative cavity RC, recorded by each of the transducers T. As it travels through the reverberative cavity RC, the pressure pulse P undergoes some deformation due to reverberations R inside the reverberative cavity RC, as described below. The transducers T convert the recorded pressure pulse into an electric signal. The signal of each transducer T is then time reversed and processed to excite the same transducer T. The mechanical waves produced by each transducer T propagate through the reverberative cavity RC, by reverberations R, toward the other end of the reverberative cavity RC, and emerge at that end thereof to produce a focused pressure pulse W 2  (shown in  FIG. 2 ) at the location of the source. 
     As shown in  FIG. 2 , when a mechanical wave W 1  created by one or more of the transducers T is propagated inside the cavity RC, reverberations R at the wall of the cavity RC redirected it to the core of the cavity RC. The reverberations R are a consequence of the difference of acoustic impedance between the reverberative cavity RC and the surrounding air. Since the wall reverberations R are with almost no energy loss, the mechanical wave W 1  can travel inside the reverberative cavity RC without undergoing major attenuation. Each reverberation R creates the illusion of having originated from a virtual transducer VT. The assembly of these virtual transducers VT is perceived by an observer at a focal point FP as a source of great dimension, although only a limited number of real transducers RT is used. 
     As a consequence, the technology proposed by Montaldo et al. uses a limited number of low-power transducers to temporally and spatially concentrate trains of low amplitude waves in order to obtain a high amplitude and short-lasting focused wave. The spatial focalisation is made possible by the reverberating nature of the cavity while the temporal compression is made possible by the time reversal operation. Montaldo et al. sends the pulses at predetermined locations which correspond to locations where a source was originally positioned. 
     Montaldo et al.&#39;s device reaches some limits, especially when applied to lithotripsy. A simple calculation can show that their proposed device is not capable of reaching focal distances compatible with applications where the target is typically remote from the wave emitting device. Further, to reach typical focal distances required for kidney stones destruction in human subjects, one would need to construct a device having an unrealistic number of transducers or else have the reverberative cavity of a cumbersome length or diameter. A device of such a size is far from Montaldo et al.&#39;s main object which was to present a simple and compact alternative to current commercial lithotripters, and this probably explains why there is no evidence of the construction of such a device in literature. 
     Thus, in summary, in terms of the use of wave generators of high intensity acoustic pulses with possible applications in lithotripsy, it is believed that conventional technology has reached its limits in what it will allow, and the disadvantages noted above remain. While the wave generator proposed by Montaldo et al. may assist in ameliorating the situation, room for improvement would nonetheless still exist. 
     SUMMARY 
     It is an object of the present invention to ameliorate at least some of the inconveniences mentioned above. It is also an object of the present invention to provide an improved wave generator that generates mechanical waves by, amongst other things, exploiting the dispersive properties of a waveguide. It is also an object of the invention to provide an improved wave generator that generates high intensity pulses from low power components. It is also an object of the invention to provide an improved wave generator that generates one or more mechanical waves as desired and chosen by a user, independently of an emitting source in the environing medium of the wave generator. 
     In a first aspect, the wave generator of the present invention includes an elongated dispersive waveguide and a source covering at least partially one end of the waveguide. The source is programmable to generate one or more mechanical waves in the dispersive waveguide. Because the waveguide is dispersive, a mechanical wave gets typically distorted as it travels through the waveguide. When reaching the end of the waveguide distal to the source, at least components waves composing the mechanical waves recombine due to the dispersive effects to form a desired wave that is emitted in the medium in contact with the end of the waveguide distal to the source. Because the source is programmable and at least some of the dispersive properties of the waveguide can be predetermined, the mechanical wave generated in the dispersive waveguide can be determined so as to form, when recombined, an emitted wave as chosen by the user. The device of the present invention works by beneficially exploiting dispersion. Dispersion is an intrinsic property of the geometry and composition of the waveguide. 
     Any waveform can be decomposed into a finite sum of component waves. The components waves each include a function in time and a function in space. Each component wave has an associated frequency, magnitude and phase in time and an associated deformation field in space. A specific shape of the deformation field corresponds to a mode of the waveguide. Thus for the purposes of this application, we will consider that a component wave has an associated frequency, an associated magnitude, an associated phase and an associated mode of the waveguide. As a consequence, two component waves can have a same frequency and excite different modes. Two component waves can also have different frequencies and excite a same mode. Two component waves can also have different frequencies and excite different modes. For the purpose of this application, we will consider that the modes are longitudinal modes propagating in a longitudinal axis of an elongated waveguide. For a mechanical wave traveling in the waveguide, a component wave has an associated propagation velocity. When the propagation velocity in the waveguide depends on the frequency and the mode of the component wave, the waveguide is qualified as ‘dispersive’. Thus, a dispersive waveguide compels a relative phase difference of the component waves of a mechanical wave, which transforms a pulse (ordered phase component waves) into an oscillation train having a lower amplitude and a longer temporal span (rearranged component waves). 
     An example of dispersion in a dispersive waveguide is shown in  FIGS. 3A-3F . It is contemplated that the dispersion would be similar in a dispersive medium other than a waveguide. A pulse P (characterized by its amplitude A distribution in function of time t, as shown in  FIG. 3A ) has a plurality of component waves (shown in 
       FIG. 3B ), each of them being characterized by their unique frequency f, their associated phase φ (or relative phase) (shown  FIG. 3C ), their magnitude M (shown in  FIG. 3B ) and their mode. The pulse P becomes a dispersed wave DW (characterized by its amplitude A distribution in function of time t, as shown in  FIG. 3D ) after propagation in the dispersive waveguide. The dispersed wave DW has the same component waves (shown in  FIG. 3E ) characterized by the same frequencies f, the same magnitude M (shown in  FIG. 3E ) but different associated phases φ (shown in  FIG. 3F ). As shown in  FIGS. 3C and 3F , the dispersive properties of the waveguide have introduced a phase shift between the component waves traveling through the dispersive waveguide. It is assumed that the waveguide is dispersive with no attenuation, as illustrated in  FIGS. 3B and 3E  where a maximum magnitude M 1  is the same for in  FIGS. 3B and 3E . It is contemplated that some attenuation could be present. 
     The inventors have realized that, when the dispersive properties of a waveguide are known, it is possible to program a source so as to generate a mechanical wave where the component waves of the mechanical wave have associated phases such that, once phase shift is introduced by the dispersive waveguide, the mechanical wave recombines at the other end of the waveguide into the desired mechanical wave. The wave generator of the present invention works according to this principle, by exploiting the dispersive properties of a waveguide to generate desired mechanical waves. Since the emitted mechanical waves are chosen by the user, in some cases, the wave generator can also be used as a ‘passive amplifier’ to generate high amplitude acoustic pulses. 
     Contrary to the present device, the wave generator of Montaldo et al. exploits reverberations, and not dispersion, to amplify mechanical waves. However, it should be noted that Montaldo et al. in ‘ Generation of very high pressure pulses with  1- bit time reversal in a solid waveguide ’, J. Acoust. Soc. Am. 110(6), December 2001, refer wrongly to reverberation as a ‘dispersion’. Indeed, similarities between this device and the one previously described by their colleagues Roux et al. in ‘ Time - reversal in an ultrasonic waveguide ’, Applied Physics Letters 70(14), February 1997, show that the amplification is attributable to reverberations rather than to dispersion. It may be that some actual dispersion does occur, but as Montaldo et al. noted, this dispersion is compensated for (as opposed to being exploited by) by the time reversal operation. Thus, Montaldo et al. rely on reverberation and not dispersion to operate their device. 
     To generate the desired mechanical waves, the dispersive properties of the waveguide are predetermined. Knowing the dispersive properties consists in knowing the relationships between component waves and propagation velocities in the waveguide. A unique calibration step is sufficient to determine the dispersive properties. The calibration step can be done experimentally or analytically. In one example, the finite element method is used to determine the dispersion relationships. In another example, a hydrophone can be used to experimentally determine the dispersive properties. 
     Initial calibration of the wave generator is done independently of an emitting source present in the medium. Montaldo et al., however, rely on an emitting source to calibrate initially their device. Further, the wave generator of the present invention uses the same calibration whatever the focal point is, whereas Montaldo et al. require a moving emitting source to calibrate different focal points. In addition, the present device can generate selected desired mechanical output waves that are designed according to the application the user intends to use the mechanical waves for, contrary to Montaldo et al. which device only generates mechanical output waves according the emitting source. 
     Furthermore, because the present invention uses a source (e.g. a single transducer) covering totally or partially an end of the waveguide, the mechanical waves generated can be one dimensional. The device of Montaldo et al. has instead a plurality of bi-directional transducers covering only partially the end of the reverberative cavity RC (as can be seen in  FIG. 1 ) and this arrangement generates multi-dimensional waves. Opposite to what Montaldo et al. implies, a one-dimensional source (e.g. single transducer) can as much exploit dispersion as a tridimensional source (e.g. plurality of transducers), and that even when the wavelength of the mechanical wave is small compared to the waveguide diameter. For example, Puckett et al. in ‘ A time -  reversal mirror in a solid circular waveguide using a single, time - reversal element ’, ARLO 4(2), April 2003, cleans the echoes present in a buffer rod placed between a target medium and a transducer by using the temporal reverse mirror method in order to cancel the undesired effects of dispersion. Thus, since it is possible to eliminate the phase difference of a signal caused by dispersion with only one transducer covering a whole end of the buffer rod, it is as much possible to efficiently exploit that dispersion in order to increase tenfold a one-dimensional source power. 
     Because the present wave generator can use a one-dimensional source, the wave generator can generate planar waves, which can propagate at relatively long distances away from the emitting end of the waveguide. In comparison, the device of Montaldo et al. generates pulses focused at locations relatively close to the emitting end of the waveguide. 
     The present wave generator can generate planar waves which excite a single mode. In some cases, the wave generator can excite solely the fundamental (first) mode of the waveguide. Although the present wave generator may be capable of exciting multiple modes, the present wave generator does not require to excite more than one mode. 
     Thus, in a first aspect, as embodied and broadly described herein, the present invention provides a wave generator for emitting a desired mechanical output wave into a medium. The generator comprises a wave emitter including an elongated dispersive waveguide having a first end and a second end. When in operation the second end is at least partially in contact with the medium. A source is operatively connected to the first end of the dispersive waveguide covering at least partially a surface area of the first end. The source is operative to generate a mechanical input wave in the dispersive waveguide based on electrical signals input to the source. A signal generator is in operative connection with the source. The signal generator is operative to create the electrical signals converted by the source into the mechanical input wave in the dispersive waveguide. A computer is in operative connection with the signal generator, the computer having a processor and a machine-readable storage medium. The machine-readable storage medium contains instructions that when executed by the processor cause the signal generator to create electrical signals converted by the source into the mechanical input wave. The mechanical input wave has at least two component waves. Each of at least two of the component waves has a unique predetermined propagation velocity through the dispersive waveguide. The mechanical input wave is constructed (i) independently of data related to a mechanical wave received from a source in the medium and (ii) taking into account the different predetermined propagation velocities of the at least two component waves so that the at least two component waves combine at least partially with each other at the second end of the dispersive waveguide to form the desired mechanical output wave emitted into the medium. 
     In some embodiments, the desired mechanical output wave has an amplitude greater than an amplitude of the mechanical input wave, and in some other embodiments the desired mechanical output wave is temporally compressed relative to the mechanical input wave. A constructive recombination can occur when slower component waves of the mechanical input wave are sent in the dispersive waveguide before faster component waves, at time intervals that compensate for the relative phase shift introduced by the dispersive waveguide. The slower and the faster component waves interact with each other at a specific location in the dispersive waveguide. When the interaction is constructive (i.e. when the components waves have both a positive magnitude), the resultant mechanical wave has an increased amplitude. It is contemplated that, in other embodiments, a destructive recombination (or another type of combination of the two component waves) could be preferred to create specific output mechanical waves. Resulting to the interaction, one can create a desired mechanical output wave that is temporally compressed after traveling through the dispersive waveguide. 
     By programming the source so as to have slower component waves sent before faster component waves, the constructive interaction can be used for the generation of high intensity pulses. Whereas dispersion is typically avoided in wave-guiding devices, the inventors have found a way to use and exploit a dispersive waveguide as a wave amplifier (or wave compressor). As a consequence, in the device proposed by the inventors, it is no longer required to have high energy components to generate high intensity mechanical waves. For example, a low voltage transducer with large frequency domain is sufficient to create high intensity pulses. In some cases, it is even possible to create a high intensity pulse having an amplitude over ten times larger than that of a train of low intensity waves input into the dispersive waveguide. 
     In some embodiments, the at least two component waves have an associated frequency and an associated mode of the waveguide. The at least two component waves have different associated frequencies. The at least two component waves have a same associated mode. 
     In some embodiments, the same associated mode is a single mode of the waveguide. 
     In some embodiments, the single mode is a fundamental longitudinal mode of the waveguide. 
     In other embodiments, the at least two component waves have different associated modes. The at least two component waves have a same associated frequency. 
     In some embodiments, the source is a transducer. 
     In some embodiments, the source has a frequency bandwidth. The at least two component waves have each an associated frequency. The associated frequencies of the at least two component waves are within the frequency bandwidth of the source. a frequency bandwidth of the source, an attenuation coefficient of the dispersive waveguide is such that the wave emitter has a positive gain. To ensure that the source generates mechanical waves that have frequency components in the dispersive region of the waveguide, it is preferable to have the frequency bandwidth of the source at least partially within the dispersive region of the waveguide. 
     In some embodiments, the source covers at least entirely the surface area of the first end of the dispersive waveguide. When the source covers entirely the surface area of the first end of the dispersive waveguide, little reverberation interfere with the mechanical wave traveling through the dispersive waveguide, and the output mechanical wave corresponds to the desired mechanical wave as computed from the dispersion relations. While Montaldo et al. rely on reverberations to amplify the mechanical waves, reverberations are not exploited for the operation of the wave generator of the present invention. 
     In some embodiments, the dispersive waveguide has a constant cross-section. In applications where the dispersive waveguide has a constant cross-section, reverberations are limited. 
     In some embodiments, the wave generator further comprises at least one of an acoustic impedance coupler and an acoustic lens operatively connected to the second end of the dispersive waveguide. To optimize energy transmission of the output mechanical wave between the dispersive waveguide and the medium, the acoustic impedance coupler can be positioned between the wave emitter and the medium. The acoustic impedance coupler is used to match the acoustic impedance of the dispersive waveguide with the acoustic impedance of the medium, thereby minimizing reflection between the two. In some embodiments, the acoustic impedance coupler includes at least one layer. The at least one layer has an acoustic impedance intermediate to an acoustic impedance of the dispersive waveguide and to an acoustic impedance of the medium. The at least one layer is chosen as a function of its acoustic impedance so as to maximize energy transmission of the desired mechanical output wave between the second end of the dispersive waveguide and the medium. An acoustic lens can be used to geometrically focus the desired mechanical output wave. In some applications where a target is at a known location and it is desired to generate spatially concentrated mechanical waves, the desired mechanical output wave can be further geometrically focused. 
     In some embodiments, within a frequency bandwidth of the source, an attenuation coefficient of the dispersive waveguide is such that the wave emitter has a positive gain. For some applications, the dispersive waveguide is chosen to have a low attenuation coefficient at frequencies of interest in order to maximize gain. The frequencies of interest are the frequencies comprised within the source&#39;s frequency bandwidth which are also frequencies for which the waveguide is dispersive. The attenuation coefficient describes the extent to which the intensity of a wave is reduced as it passes through a specific material (i.e., the waveguide) due to internal friction and heat losses. 
     In some embodiments, the dispersive waveguide is one of the group consisting of a metal and a ceramic. Metals and ceramic have preferably a low attenuation coefficient of the frequencies of interest. A material for the dispersive waveguide is preferably chosen to have a high Poisson coefficient, low attenuation coefficient, and low propagation velocity. An acoustic impedance is preferably as close as possible to that of the source and the medium in order to maximize transmission of energy. 
     In some embodiments, an aspect ratio of the dispersive waveguide is at least 10. For a cylindrical waveguide, the aspect ratio could preferably be approximately be between 10 and 1000. A somewhat large aspect ratio enhances amplification in embodiments where high intensity mechanical waves are desired. The longer the rod, the more amplification can be obtained. The waveguide has a length that preferably allows a significant amplification gain and allows the user to identify the signal from noise at the calibration step. A somewhat low aspect ratio has for consequence that the waveguide may be weakly dispersive. 
     In some embodiments, the desired mechanical output wave is generally planar. In applications where the source covers most or more of the first end of the dispersive waveguide, the desired mechanical output wave is generally planar (one dimensional). 
     In some embodiments, the desired mechanical output wave is unfocused. In applications where planar mechanical waves are generated, the desired mechanical output wave is unfocused. 
     In some embodiments, the desired mechanical output wave is focused. In one example, the desired mechanical output wave is geometrically focused. In another example, diffraction effects at the second end of the dispersive waveguide are used to focus energy at a predetermined spatial location within the medium. 
     In other embodiments, the dispersive waveguide is curved along its length at least in part between the first end and the second end. 
     In yet other embodiment, the dispersive waveguide has a radius of curvature at least an order of magnitude of wavelengths of the at least two component waves. 
     In some embodiments, the dispersive waveguide is flexible. By ‘flexible’ it should be understood a material capable of being (relatively easily—during the intended application of the device) bent or curved, but not necessarily foldable. A waveguide that is flexible can be used for space saving or when reaching places with restricted access. In some cases, the procedure requires that the mechanical waves be emitted in the vicinity of a target and/or for increasing the transmission of energy. Thus, a flexible waveguide might allow for the positioning of the wave emitter right in front of the target, even when the target may be difficult to access. 
     In some embodiments, the wave generator further comprises an amplifier operatively connected to the signal generator. The amplifier is operative to modify an amplitude of at least a portion of the electric signals input to the source. In one example, the amplifier is used to saturate the electric signals input to the source. 
     In some embodiments, the source is a bi-directional transducer and is further operative to generate electrical signals from a reverse direction mechanical wave. The reverse direction mechanical wave propagates through the waveguide from the second end toward the first end of the waveguide. The wave generator further comprises a switch in operative connection with the bi-directional transducer and the coupler. The switch separates input electric signals from output electric signals to the bi-directional transducer. A digitizer is in operative connection with the switch and with the computer. The digitizer is operative to digitize the output electrical signals. In some applications, for example where the location of a target is to be known, it is possible to use a bi-directional transducer for sensing (in addition to emitting mechanical waves) perturbations of the medium (or environment). When a mechanical wave is sent into a medium having a non-homogeneity (such as a kidney stone in the body), the non-homogeneity reflects this wave. A wave emitter having reception capability is able to detect that reflected wave and, and with the help of the computer, a position of the non-homogeneity can be calculated. 
     In another aspect, a wave generator for emitting a desired mechanical output wave into a medium is provided. The wave generator comprises a wave emitter including an elongated dispersive waveguide having a first end and a second end. When in operation the second end is at least partially in contact with the medium. A source is operatively connected to the first end of the dispersive waveguide and covers at least partially a surface area of the first end. The source is operative to generate a mechanical input wave in the dispersive waveguide based on electrical signals input to the source. A signal generator is in operative connection with the source. The signal generator is operative to create the electrical signals convertible by the source into the mechanical input wave in the dispersive waveguide. A computer is in operative connection with the signal generator. The computer has a processor and a machine-readable storage medium. The machine-readable storage medium contains instructions that when executed by the processor cause the signal generator to create electrical signals convertible by the source into the mechanical input wave. The mechanical input wave has at least two component waves. Each of the at least two component wave has a unique associated predetermined propagation velocity through the dispersive waveguide. The at least two component waves have a first relative phase shift. The first relative phase shift is determined so as to be become, at the second end of the dispersive waveguide, a second relative phase shift different from the first relative phase shift owing to the predetermined propagation velocities through the dispersive waveguide of the at least two component waves. 
     In some embodiments, the mechanical input wave has a first amplitude. The desired mechanical output wave has a second amplitude. The second relative phase shift is determined so that the second amplitude is greater than the first amplitude. 
     In some embodiments, the at least two component waves have an associated frequency and an associated mode of the waveguide. The at least two component waves have different associated frequencies, and the at least two component waves have a same associated mode. In yet other embodiments, the at least two component waves have different associated modes, and the at least two component waves have a same associated frequency. 
     In yet another aspect, a method of emitting a desired mechanical output wave into a medium is provided. The method comprises providing an elongated dispersive waveguide having a first end and a second end. The second end is at least partially in contact with the medium. The method comprises determining the desired mechanical output wave; determining a mechanical input wave. The mechanical output wave has at least two component waves. Each of the at least two component waves having a unique associated predetermined propagation velocity through the dispersive waveguide. At least two of the component waves have different predetermined propagation velocities through the dispersive waveguide. The mechanical input wave when inputted at the first end of the dispersive waveguide and once having propagated through the dispersive waveguide combine at least partially at the second end of the dispersive waveguide to form the desired mechanical output wave. The mechanical input wave is constructed (i) independently of data related to a mechanical wave received from a source in the medium and (ii) taking into account the different predetermined propagation velocities of the at least two component waves. The method comprises generating the mechanical input wave at the first end of the dispersive waveguide; allowing the mechanical input wave to propagate through the dispersive waveguide toward the second end; combining the mechanical input wave to form the desired mechanical output wave at the second end of the dispersive waveguide owing to differences in the predetermined propagation velocities of the at least two component waves; and emitting the desired mechanical output wave into the medium at the second end of the dispersive waveguide. 
     In an additional aspect, the method comprises combining the mechanical input wave having a first duration in time to form the desired mechanical output wave having a second duration in time includes shortening the first duration in time into the second duration in time. 
     In a further aspect, the method comprises combining the mechanical input wave to form the desired mechanical output wave includes combining the mechanical input wave having a first amplitude to form the desired mechanical output wave having a second amplitude. The second amplitude is greater than the first amplitude. 
     In an additional aspect, the at least two component waves have an associated frequency and an associated mode of the waveguide. The at least two component waves have different associated frequencies. The at least two component waves have a same associated mode. 
     In a further aspect, the same associated mode is a single mode of the waveguide. 
     In some embodiments, the single mode is a fundamental longitudinal mode of the waveguide. 
     In an additional aspect, the at least two component waves have each an associated frequency and an associated mode of the waveguide. The at least two component waves have different associated modes. The at least two component waves have a same associated frequency. 
     In an additional aspect, the source is a transducer. 
     In a further aspect, the source has a frequency bandwidth. The at least two component waves have each an associated frequency. The associated frequencies of the at least two component waves are within the frequency bandwidth of the source. 
     In an additional aspect, the source covers at least an entirety of the surface area of the first end of the dispersive waveguide. 
     In a further aspect, the dispersive waveguide has a constant cross-section. 
     In an additional aspect, the method further comprises emitting the desired mechanical output wave in at least one of an acoustic impedance coupler and an acoustic lens before emitting the desired mechanical output wave in the medium. 
     In a further aspect, the acoustic impedance coupler includes at least one layer before emitting the desired mechanical output wave in the medium. The at least one layer has an acoustic impedance intermediate to an acoustic impedance of the dispersive waveguide and to an acoustic impedance of the medium. The at least one layer is arranged as a function of its acoustic impedance so as to maximize energy transmission of the desired mechanical output wave between the second end of the dispersive waveguide and the medium. 
     In an additional aspect, within a frequency bandwidth of the source, an attenuation coefficient of the dispersive waveguide is such that the wave emitter has a positive gain. 
     In a further aspect, the dispersive waveguide is one selected from the group consisting of a metal and a ceramic. 
     In an additional aspect, an aspect ratio of the dispersive waveguide is at least 10. 
     In an additional aspect, emitting the desired mechanical output wave into the medium includes emitting the desired mechanical output wave as a generally planar wave. 
     In a further aspect, emitting the desired mechanical output wave into the medium includes emitting the desired mechanical output wave unfocused in the medium. 
     In an additional aspect, emitting the desired mechanical output wave into the medium includes emitting the desired mechanical output wave focused in the medium. 
     In a further aspect, the dispersive waveguide is curved along its length at least in part between the first end and the second end. 
     In yet a further aspect, the dispersive waveguide has a radius of curvature at least an order of magnitude of wavelengths of the at least two component waves. 
     In an additional aspect, the dispersive waveguide is flexible. 
     In a further aspect, the method further comprises determining a cut-off amplitude; saturating the input electrical signal to the cut-off amplitude to become a saturated signal; and amplifying at least a portion of the saturated signal, before inputting the input electrical signal to the source. 
     In an additional aspect, generating the mechanical input wave at the first end of the dispersive waveguide includes: generating an input electrical signal corresponding to the mechanical input wave; and inputting the input electrical signal to a source disposed at the first end of the dispersive waveguide. The source transforms the input signal into the mechanical input wave. 
     A method of emitting a desired mechanical output wave into a medium is also provided. The method comprises providing an elongated dispersive waveguide having a first end and a second end. The second end is at least partially in contact with the medium. The method comprises determining the desired mechanical output wave; and determining a mechanical input wave. The mechanical input wave has at least two component waves. Each of at least two of the component waves has a unique predetermined propagation velocity through the dispersive waveguide. The at least two component waves having a first relative phase shift. The first relative phase shift is determined so as to be become, at the second end of the dispersive waveguide, a second relative phase shift different from the first relative phase shift owing to the predetermined propagation velocities through the dispersive waveguide of the at least two component waves. The method comprises generating the mechanical input wave at the first end of the dispersive waveguide; allowing the mechanical input wave to propagate through the dispersive waveguide toward the second end; combining the mechanical input wave to form the desired mechanical output wave at the second end of the dispersive waveguide owing to differences in the predetermined propagation velocities of the at least two component waves; and emitting the desired mechanical output wave into the medium at the second end of the dispersive waveguide. 
     For the purpose of this application, the term “wave”, as used herein, includes all mechanical waves, i.e., waves that propagate through a medium due to restoring forces they produce upon deformation of the medium. The term “component waves” refers to functions of space and time on which a mechanical wave can be decomposed. The term “medium”, as used herein, refers to any substance (e.g. gas, liquid, solid, gel, non-biological or biological material) that allows for the propagation of a mechanical wave through it. The term “waveguide”, as used herein, refers to a structure that conveys mechanical waves between its endpoints. The term “shockwave”, as used herein, refers to a region of abrupt change of pressure that moves a wave front at a relatively rapid velocity through a medium. The term “acoustic”, as used herein, refers to mechanical waves in gases, liquids, and solids at frequencies in the range of the sound, ultrasound and infrasound. The term “dispersion”, as used herein, refers to a physical property of a waveguide by which component waves have different propagation velocities through that waveguide. The term “source” refers to any element capable of generating a generally planar longitudinal mechanical wave. 
     Embodiments of the present invention each have at least one of the above-mentioned objects and/or aspects, but do not necessarily have all of them. It should be understood that some aspects of the present invention that have resulted from attempting to attain the above-mentioned objects may not satisfy these objects and/or may satisfy other objects not specifically recited herein. 
     Additional and/or alternative features, aspects, and advantages of embodiments of the present invention will become apparent from the following description, the accompanying drawings, and the appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a better understanding of the present invention, as well as other aspects and further features thereof, reference is made to the following description which is to be used in conjunction with the accompanying drawings, where: 
         FIG. 1  is a perspective view of a wave generator used in the prior art; 
         FIG. 2  is an illustration of reverberations inside the wave generator of  FIG. 1 ; 
         FIG. 3A  is a graph of a pulse P (amplitude A vs. time t); 
         FIG. 3B  is a graph of frequency components of the pulse P of  FIG. 3A  (magnitude M vs. frequency f); 
         FIG. 3C  is a graph of phases of the frequency components of the pulse P of  FIG. 3A  (phase φ vs. frequency f); 
         FIG. 3D  is a graph of a dispersed wave DW (amplitude A vs. time t); 
         FIG. 3E  is a graph of frequency components of the dispersed wave DW of  FIG. 3D  (magnitude M vs. frequency f); 
         FIG. 3F  is a graph of phases of the frequency components of the dispersed wave DW of  FIG. 3D  (phase φ vs. frequency f); 
         FIG. 4  is a wave emitter according to a first embodiment of the invention; 
         FIG. 5  is an embodiment of a waveguide for the wave emitter of  FIG. 4 ; 
         FIG. 6  is yet another embodiment of a waveguide for the emitter of  FIG. 4 . 
         FIG. 7  is another embodiment of a waveguide for the wave emitter of  FIG. 4 ; 
         FIG. 8  is a wave emitter according to a second embodiment of the invention; 
         FIG. 9  is the wave emitter of  FIG. 4  with an acoustic impedance coupler; 
         FIG. 10  is the wave emitter of  FIG. 4  with an acoustic lens; 
         FIG. 11  is a schematic representation of a wave generator for the wave emitter of  FIG. 4 ; 
         FIG. 12  is a schematic representation of a wave generator for the wave emitter of  FIG. 7 ; 
         FIG. 13  is a flow chart illustrating a method for emitting a desired mechanical output wave; 
         FIG. 14  is a graph of amplitude A vs. time t of an example of a mechanical input wave; 
         FIG. 15  is a graph of an example of a desired mechanical output wave (amplitude A vs. time t); and 
         FIG. 16  is a graph of another example of a desired mechanical output wave (amplitude A vs. time t); and 
         FIG. 17  is a graph of the desired mechanical output wave of  FIG. 15  (amplitude A vs. time t) recorded at some distance from the waveguide. 
     
    
    
     DETAILED DESCRIPTION 
     Referring to  FIG. 4 , a first embodiment of a wave emitter  10  will be described. The wave emitter  10  has a waveguide  14  and a single transducer  12  disposed at a first end  15  of the waveguide  14 . A second end  16  of the waveguide  14  is free. When in operation, the second  16  is put into contact with a medium  104  in which the wave emitter  10  emits mechanical waves. The medium  104  and a method for generating mechanical waves will be described below. 
     The transducer  12  is fixedly disposed to the first end  15  by two screws (not shown) which exert pressure to retain the transducer  12  on the waveguide  14 . It is contemplated that other ways to affix the transducer  12  to the waveguide  14  could be used. For example, the transducer  12  could be glued to the first end  15  of the waveguide. It is also contemplated that a gel (similar to the ones used in ultrasound imaging) could be disposed between the transducer  12  and the waveguide  14  to enhance energy transmission between the transducer  12  and the waveguide  14 . The single transducer  12  is one example of source that could be used to generate mechanical waves into the waveguide  14 . 
     The waveguide  14  is an elongated rod of circular cross-section. It is contemplated that a waveguide  14  could have a cross-section different from circular. As shown in  FIG. 5 , the waveguide  14  could be embodied as a waveguide  14   a  having a C-shape, and as shown in  FIG. 6 , the waveguide  14  could also be embodied as a waveguide  14   b  being hollow and having a hole  8  along its length. It is also contemplated that the waveguide  14  could be a combination of the waveguides  14   a  and  14   b , and could have a C-shape and one or more hole  8  with same or different shape and sizes. It is also contemplated that the waveguide  14  could have yet different shapes of cross-section. 
     The waveguide  14  has a constant cross-section. It is contemplated that the waveguide  14  could not have a constant cross-section. For example, the waveguide  14  could have one end squared and another end circular and could transition smoothly between the two along its length. In another example, the waveguide is tapered. 
     The waveguide  14  has an aspect ratio of  40 . It is contemplated that the aspect ratio of the waveguide  14  could range between 10 and 1000. A length of the waveguide  14  is 1000 mm, and a cross-section area is 25 mm (area: 490 mm 2 ). The length of the waveguide  14  is preferably chosen, on one end to accommodate the fact that the longer the waveguide  14 , the more dispersed a mechanical wave will be (and therefore the higher the gain) and on the other end, to accommodate the fact that the longer the waveguide  14 , the more attenuated the mechanical wave will be after propagation through the waveguide  14 . It is contemplated that the waveguide  14  could have other dimensions. For example, the length of the waveguide  14  could be between 200 mm and 1500 mm, and the diameter could be between 1 mm and 50 mm. 
     The waveguide  14  is straight and inflexible. It is contemplated that the waveguide  14  could have some curvature. For example, a radius of curvature of the waveguide  14  could be one order of magnitude greater than a wavelength of a signal propagating through waveguide  14 . As shown in  FIG. 7 , the waveguide  14  could be embodied as a waveguide  14 C that is flexible. The flexible waveguide  14 C could have a size and mechanical compliance adapted to allow insertion of the waveguide  14 C in place where access is restricted. 
     The waveguide  14  is made of aluminum 6061-T6. It is contemplated that the waveguide  14  could be made of a different type of aluminum or a different material. It is also contemplated that the waveguide  14  could be made of an alloy of materials. For example the waveguide  14  could be made of aluminum, magnesium, stainless steel, titanium, etc. It is also contemplated that the waveguide  14  could be formed of two or more adjacently arranged waveguides. For example the waveguide  14  could be made of two concentrically arranged waveguides, each waveguide being made of a different material. The waveguide  14  is dispersive within a bandwidth of the transducer  12 . The waveguide  14  also has a low attenuation coefficient around the central frequency of the transducer  12  for maximizing amplification gain. 
     The transducer  12  is a single gas matrix piezoelectric of The Ultran Group model GWC-D28-10. The transducer  12  has a diameter of 25 mm and is sized to cover an entirety of the first end  15  of the waveguide  14 . It is contemplated that the transducer  12  could be bigger or smaller than the first end  15 . When the transducer  12  is of the size or bigger than the cross-section of the waveguide  14 , a planar wave can be generated. When the transducer  12  is smaller than the cross-section of the waveguide  14  multiple reflections at walls of the waveguide  14  may deform the planar wave as it travels the waveguide  14 . The planar waves are generally unfocused and excite one or more longitudinal modes of the waveguide  14 . It is contemplated that the mechanical waves could not be planar, could not be unfocused, and could excite modes other than longitudinal modes. 
     The transducer  12  is disposed at the first end  15  perpendicularly to a longitudinal direction of the waveguide  14 . It is contemplated that the transducer  12  could be positioned at the first end  15  not perpendicularly to the longitudinal direction of the waveguide  14 . It is contemplated that some reverberations could occur when the transducer  12  is not disposed perpendicularly to the longitudinal direction of the waveguide  14 . 
     The transducer  12  has a central frequency of 600 kHz. It is contemplated that the transducer  12  could have a central frequency different from 600 kHz. The transducer&#39;s  12  central frequency is preferably chosen in accordance with the dispersive properties of the waveguide  14 . In the present case, a central frequency of 600 kHz is desired because the waveguide  14  is made of aluminum and is dispersive within a range around 600 kHz for the dimensions of the waveguide  14  recited above. A bandwidth of the transducer  12  is from 300 kHz to 900 KHz. It is contemplated that the transducer  12  could have a different bandwidth. 
     Referring now to  FIG. 8 , a second embodiment of a wave emitter  20  will now be described. The wave emitter  20  is similar to the wave emitter  10  but features a bi-directional transducer  22  in place of the unidirectional transducer  12 . Elements of the wave emitter  20  common to the wave emitter  10  will have same reference numerals, and will not be described in detail herein again. 
     The bi-directional transducer  22  can convert electric signals into mechanical waves and reversely, mechanical waves into electrical signals. The bi-directional transducer  22  enables the wave emitter  20  to detect mechanical waves in a medium  104  (shown in  FIG. 11 ) in addition to emitting mechanical waves in the medium  104 . It is contemplated that a transducer assembly could replace the bi-directional transducer  22 . The transducer assembly could be formed by the association of two transducers, the assembly covering the first end  15  of the waveguide  14 . The two transducers could be disposed adjacent to each other or concentrically arranged. One of the two transducers could be used to emit mechanical waves, and the other to receive mechanical waves. 
     An acoustic impedance coupler  18  (shown in  FIG. 9 ) can be coupled to any of the wave emitters  10  and  20  for increasing energy transmission of the mechanical wave between the second end  16  of the waveguide  14 , and the medium  104 . The acoustic impedance coupler  18  includes a layer of glass and a layer of epoxy between the glass and the second end  16  of the waveguide  14 . The epoxy is used to glue the glass to the waveguide  14 . Each of the layers of epoxy and glass is disk shaped to match the circular cross-section of the waveguide  14 . The layer of epoxy has a thickness of 730 μm, and the layer of glass has a thickness of 300 μm. The acoustic impedance coupler  18  has an acoustic impedance intermediate to an acoustic impedance of the waveguide  14  and to an acoustic impedance of the medium  104 . It is contemplated that the acoustic impedance coupler  18  could be embodied as a structure having different shape or material, or be even a gel or a softer material. It is also contemplated that the acoustic impedance coupler  18  could include a plurality of layers of glass and epoxy. 
     An acoustic lens  23  (shown in  FIG. 10 ) can be disposed at the second end  16  of the waveguide  14  of any of the wave emitters  10  and  20 , to geometrically focus the mechanical waves emitted into the medium  104 . It is also contemplated that the wave emitters  10  and  20  could have the acoustic lens  23  and the acoustic impedance coupler  18  disposed is series at the second end  16  of the waveguide  14 . It is also contemplated that the acoustic lens  23  could not be used for focusing the mechanical waves emitted into the medium  104 . For example, the wave emitters  10  and  20  could exploit diffraction effects at the second end  16  of the waveguide  14  to focus energy at a predetermined spatial location within the medium  104 . Diffraction patterns are dependent on the shape and size of the second end as well as on a wavelength of the desired output wave. In other example, the second end  16  of the waveguide  14  could be shaped so as to geometrically focus the mechanical waves. 
     Referring to  FIG. 11 , a wave generator  100  will now be described. The wave generator  100  is a system powering the wave emitter  10  and used to program the wave emitter  10  to generate desired mechanical waves. 
     The wave emitter  10  is powered by a signal generator  114 , which is programmable by a computer  106 . The signal generator  114  is a National Instruments, PXI 5412 (14-Bit 100 MS/s). The computer  106  is a general purpose computer well known in the art. It is contemplated that the computer  106  could be another type of computing interface. It is contemplated that the signal generator  114  could be different. The computer  106  has a processor  107  in communication (data  108 ) with a machine-readable storage medium  110 . The machine-readable storage medium  110  is used to store the data  108 , which are digitized input signals corresponding to mechanical input waves  128 . The computer  106  constitutes an interface used by a user to program an input signal  112  that will lead to the generation of one or more mechanical input waves  128 . 
     The signal generator  114  transforms the input signal  112  into a low voltage signal  116 . The low voltage signal  116  is transformed into a higher voltage signal  120  by an amplifier  118 . The amplifier  118  is a RITEC, GA-2500A (400 Watts). It is contemplated that the amplifier  118  could be different. The higher voltage signal  120  goes through a coupler  122  which optimizes power transfer between the amplifier  118  and the wave emitter  10  by coupling electric impedances of the amplifier  118  and the wave emitter  10 . It is contemplated that the amplifier  118  could be omitted. After passage through the coupler  122 , the higher voltage signal  120  becomes input voltage signal  124  to the wave emitter  10 . It is contemplated that the coupler  122  could be omitted. 
     The transducer  12  converts the input voltage signal  124  into the mechanical input wave  128 , and the waveguide  14  propagates the mechanical input wave  128  towards the second end  16  of the waveguide  14  which is being put in contact with the medium  104  for generating mechanical waves  102  in the medium  104 . The medium  104  is degassed tap water at room temperature. It is contemplated that the medium  104  could be different. The waveguide  14  being dispersive, the mechanical input wave  128  is distorted into a mechanical output wave  102  by the time the mechanical input wave  128  has reached the second end  16 . Some component waves of the mechanical input wave  128  travel faster than others and can reach the second end  16  at the same time as the slower component waves. When the slower and faster components waves reach simultaneously the second end  16  an interaction occurs to form the mechanical output wave  102 . The mechanical output wave  102  is a recombination of the mechanical input wave  128 . At the second end  16  of the waveguide  14 , the mechanical output wave  102  is emitted into the medium  104 . 
     To use the wave generator  100 , the user starts with determining the desired mechanical output wave  102  that he/she wishes to emit in the medium  104 . The user uses the computer  106  to determine the input signal  112  input to the signal generator  114  that ultimately will lead to the mechanical output wave  102  after conversion by the transducer  12  and propagation through the dispersive waveguide  14 . A method for generating the mechanical output waves  102  will be described below. 
     The input signal  112  is calculated taking into consideration the dispersive properties of the waveguide  14  and in some cases taking into consideration the physical properties of the medium  104 . The dispersive properties of the waveguide  14  and the physical properties of the medium  104  are determined in a prior calibration step typically done only once. The waveguide  14  is calibrated using the impulse response method. It is contemplated that other methods well known in the art could be used to calibrate the waveguide  14 . For example, time reversal mirror, inverse filter, or analytical calculation of dispersion curves could be used. In the impulse response method, a known pulse is sent by the transducer  12  into the waveguide  14 , and after traveling through the waveguide  14  and being deformed due to the dispersive properties of the waveguide  14 , the pulse propagates in the medium  104  until reaching a hydrophone (not shown) priory placed in front of the waveguide  14 . An advantage of the impulse response calibration method is that it allows to take into consideration the characteristics of the medium  104  itself. It is possible that the choice of medium  104  influences a shape of the mechanical output waves  102 , after having been generated at the second end  16 , when the mechanical output waves  102  enter the medium  104 . Therefore, it is preferable that the calibration takes into consideration the medium  104 . It is contemplated that the medium  104  could be calibration in a separate calibration step. It is also contemplated that the physical properties of the medium  104  could not be calibrated. The hydrophone is a Müller-Platte Needleprobe 100-100-1 with a sensitive diameter inferior to 0.5 mm. It is contemplated that the hydrophone could be different. The hydrophone records the emitted wave which is used along with the impulse to characterize a frequency response function of the wave emitter  10 . The frequency response function is a key of the system (wave emitter  10 ) which once known allows to determine how any wave will be modified into, after propagation in the dispersive waveguide  14 . It is contemplated that if the transducer  12  were bi-directional, it could be possible to use, instead of the hydrophone, a reflection of the impulse itself at the second end  16  of the waveguide  14  in order to determine the frequency response function of the wave emitter  10 . 
     Referring now to  FIG. 12 , a wave generator  200  will now be described. The wave generator  200  is a system powering the wave emitter  20  used to generate the desired mechanical output waves  102  and further to record information coming from the medium  104  for the purpose of, for example, locating a non-homogeneity in the medium  104 . The wave generator  200  is similar to the wave generator  100 , but features a diplexer  222  and a digitizer  240 . Elements of the wave generator  200  common to the wave generator  100  will have same reference numerals, and will not be described herein again. 
     The diplexer  222  is located between the amplifier  118  and the coupler  122 . The diplexer  222  acts as a switch to separate electric signals  124  incoming and outgoing the bi-directional transducer  22 . For example, the diplexer  222  separates signals  234  incoming from the medium  104  through the waveguide  14  from signals  134  incoming from the signal generator  114 . The diplexer  222  is only one example of a switch. The digitizer  240  transforms a signal  216  outgoing from the diplexer  222  into a signal  212  readable by the computer  106 . The bi-directional transducer  22  converts the voltage signal  124  into the corresponding mechanical input wave  128 , and reversely converts a mechanical wave  228  coming from the waveguide  14  (reverse direction mechanical wave) into a corresponding electric signal  224 . 
     Emission of mechanical waves by the wave generator  200  is similar to the one described below for the wave generator  100 , except that the higher voltage signal  120  goes through the diplexer  222  and the coupler  122  before entering the wave emitter  20  without being noticeably deformed. 
     Reception of mechanical waves by the wave generator  200  starts with the waveguide  14  receiving a mechanical wave  202  (e.g. perturbation) from the medium  104  at the second end  16 . The mechanical wave  202  could be emitted from a source in the medium  104  or reflected by a non-homogeneity in the medium  104 . The mechanical wave  202  propagates through the waveguide  14  toward the bi-directional transducer  22 . When the mechanical wave  202  reaches the bi-directional transducer  22 , the mechanical wave  202  has been transformed into the mechanical wave  228  which is a dispersed version of the mechanical wave  202 . The bi-directional transducer  22  converts the mechanical wave  228  into a corresponding electric signal  224 . The electric signal  224  goes through the coupler  122 , becomes signal  234 , goes through the diplexer  222  becomes the signal  216 , before reaching the digitizer  240 , and being transformed into the signal  212  readable by the computer  106 . 
     As mentioned above, the wave emitter  20  can be used as a location device for a non-homogeneity. The calibration of the wave emitter  20  can be done in a unique calibration step, analytically or experimentally. The calibration of the wave emitter  20  is similar to the calibration for the wave emitter  10  described above. A method for locating a non-homogeneity in the medium  104  starts with the wave emitter  200  emitting a pulse. Then, the pulse is reflected by the non-homogeneity and reaches back the wave emitter  20  (with some distortion due to propagation in the medium  104 ). Dispersion in the waveguide  14  is taken into consideration by the prior calibration of the wave emitter  20 . The reflected mechanical wave from the non-homogeneity is compared with the original pulse sent toward the non-homogeneity to determine a distance between the second end  16  of the waveguide  14  and the non-homogeneity. Comparison can be performed by the computer  106 . It is also possible to exploit the waves reflected by the non-homogeneity to characterize heterogeneities in the medium  104 . 
     Referring now to  FIG. 13 , a method  300  for generating a desired mechanical wave by exploiting waveguide dispersion of the wave emitter  10  in the wave generator  100  will now be described. The method  300  will be described assuming the wave emitter  10  has been priory calibrated and the dispersive properties of the waveguide  14  (and optionally the physical properties of the medium  104 ) are known, as described above. It is contemplated that the method  300  could be used for generating a desired mechanical wave by exploiting waveguide dispersion of the wave emitter  20  in the wave generator  200 . 
     The method  300  starts at step  302 , with the user determining the desired mechanical output wave  102 . As described above, the desired mechanical output wave  102  has at least two component waves having relative phases between them. Each component wave has (among other characteristics) an associated frequency and an associated mode within the predetermined range of frequencies and modes for which the waveguide  14  is dispersive. 
     At step  304 , the input signal  112  is calculated by the computer  106 . The input signal  112  corresponds to the mechanical input wave  128  produced by the transducer  12 , which once distorted by the dispersive waveguide  14  will recombine into the desired mechanical output wave  102 . As mentioned above, the input signal  112  is calculated taking into account the dispersive relations of the waveguide  14 , so as to compensate at the end  16  of the waveguide  14  for the relative phase shifts introduced by the waveguide  14  as the components waves of the mechanical input wave  128  travel through it. 
     From step  304  the method  300  can go either through step  305 , or directly to step  306 . At step  305 , the input signal  112  is amplified. One way to amplify the input signal  112  is to saturate it before amplifying it. To do so, a magnitude of the input signal  112  for the different frequencies composing it, is fixed to a limit value, and consequently amplified. Saturating and amplifying the input signal  112  allows to amplify without affecting relative phases. It is contemplated that one could amplify and then saturate the input signal  112 . It is contemplated that the saturation and amplification could be done differently. An example of amplification by saturation is given below. 
     At step  306 , the input signal  112  is transformed by the transducer  12  into the mechanical input wave  128 . The mechanical input wave  128  travels through the waveguide  14  and gets distorted due to the dispersive properties of the waveguide  14 . 
     A step  310 , the desired mechanical output wave  102  is generated from a recombination of the mechanical input wave  128  at the second end  16 . Once the desired mechanical output wave  102  is generated, it is emitted into the medium  104  at step  310 . If at step  312 , the wave emitter  10  is coupled to the acoustic impedance coupler  18 , the desired mechanical output wave  102  propagates through the acoustic impedance coupler  18  before reaching the medium  104 . If at step  314  the wave emitter  10  is coupled to the acoustic lens  23 , the desired mechanical output wave  102  propagates through the acoustics lens  23  before reaching the medium  104  at step  314 . The wave emitter  10  could also be coupled to the acoustic lens  23  and the acoustic impedance coupler  18 . 
     Turning now to  FIGS. 14 to 17 , an example of mechanical input wave  128  and a resulting desired mechanical output wave  102  will be described. In the experiment leading to the results shown in  FIGS. 14 to 17 , the wave emitter  10  is connected to the impedance acoustic coupler  18  but has no acoustic lens  23  attached to it. As mentioned earlier, the medium  104  is degassed tap water at room temperature. The wave emitter  10  is positioned so as to have the second end  16  in contact with the medium  104 . In this experiment, the user desires to emit a pulse of a normalized amplitude of 3 and a desired time signature of 1.67 μs. It is contemplated that the experiment could be performed for generating a pulse other than the one above. It is also contemplated that the experiment could be performed for generating mechanical waves other than a pulse. The user uses the computer  106  to determine a mechanical input wave  400  that needs to be generated by the transducer  12  in order to generate at the second end  16  of the waveguide  14 , the desired pulse.  FIG. 14  shows the mechanical input wave  400  as generated by the transducer  12 . As can be noticed, the wave  400  is characterized by a time signature of 0.2 ms and an amplitude of 1 ( FIG. 14  showing the amplitude normalized). As shown in  FIG. 15 , a pulse  410  characterized by a time signature of approximately 1.67 μs and an amplitude of 3 ( FIG. 15  showing the amplitude normalized) is recorded at the second end  16  of the waveguide  14 . It can be seen that, the wave generator  10  has passively compressed in time and has amplified the wave  400  to form the pulse  410 . The gain is 3 and the temporal compression is of a factor of  120 . As mentioned above, the user can also saturate the signal leading to the generation of the mechanical input wave  400 , so as to amplify even further the amplitude of the desired pulse  410 . As shown in  FIG. 16 , when recorded at the second end  16  of the waveguide  14  is a pulse  420  having the same time signature as the pulse  410 , but having an amplitude of  8  ( FIG. 16  showing the amplitude normalized). Saturation did not affect the time signature, and has increased the amplitude by about 2.7 times compared to the same experiment without saturation. With saturation the overall gain of this experiment is 8. Once the pulses  410  and  420  are emitted in the medium  104 , non-linear effects of the medium  104  distort the pulses  401 ,  402  as they travel through it. As shown in  FIG. 17  for the pulse  410 , at 70 mm along a longitudinal axis of the waveguide  14 , the pulse  410  has becomes a shockwave  430 . The shockwave  430  is characterized by a time signature of less than 1 μs and an amplitude of 100 bars. This amplitude of the shockwave  430  is 20 times more than a wave that would be created by the same transducer  12  (without waveguide  14 ), driven by the same electrical power and emitting in the same medium  104  (water). 
     Modifications and improvements to the above-described embodiments of the present invention may become apparent to those skilled in the art. The foregoing description is intended to be exemplary rather than limiting. The scope of the present invention is therefore intended to be limited solely by the scope of the appended claims.