It is common to measure the response of devices and structures to sound due to an imposed sound source. Unfortunately, acoustic reflections from walls and/or instruments often contaminate the results. In this paper , methods of acoustic characterization are described to minimize the influence of acoustic reflections. It is shown that this process results in clean and smooth data. A simple time -domain window is implemented for diminishing the contribution from reflection waves. Moreover, a single frequency curve fitting approach is employed for better parameter identification and noise reduction, compared to traditional fast Fourier Transform analysis. Results obtained from a theoretical acoustic model with a reflection source are compared with measured results. Different cases of data acquisition with time and frequency analysis are experimentally demonstrated and validated. All experimental measurement s are performed in an anechoic chamber. Results show that the approach presented here significantly reduces noise and also the influences of reflection waves in experimental data acquisition outcomes. 2 1 Introduction A traveling sound wave is often described by fluctuations of sound pressure and media particle velocity over space and time. Acoustic sensors are designed to detect these fluctuations. A s a crucial process of sensor design , acoustic characterization often refers to the measurements of the values of sounds and noises in terms of their intensities and various qua ntitative features including their spectra or the growth and decay of the sound over time [1-3]. During most characterizations, the principal values measured in acoustics are usually sound p ressure, and sound induced velocity, which are important characteristics of sound in order to have a complete and exact prediction of sound behaviors [4-6]. For sound pressure measurements a standard microphone is often used by transducing the received aco ustic signals (pressures) into proportional electrical voltages for readout. For acoustic induced vibration velocity, a laser vibrometer is often utilized in which the received signals (velocity) are transduced to proportional electrical voltages [7,8]. Th e difficulties experienced in acoustic measurements are due to the complicated spatial distribution of the acoustic values in rooms as well as the variability of sounds and noises over time. Electro -magnetic noise and a coustic noise is another main contributor as it can contaminate the incident sound wave and final data . Sound wave reflection occurs when sound waves (incident wave) leave one medium and enter another, with a portion of the wave passing through the medium, while the remai nder of the wave reflect ing back. The reflected wave will either sum up or cancel out with the incident wave, and thus greatly skew the expected results [9,10] . The anechoic chamber can greatly reduce the effect of the acoustic noise and sound wave reflect ions, which we shall discuss more later in the paper . Electromagnetic noise, especially inside the chamber, cannot be easily eliminate . Acoustic 3 measurements are closely associated with electrical measurements and are performed chiefly with electronic meas uring instruments. All of which could be sources of electromagnetic noise that may impact nearby devices and pollute the data with associated frequency noise . The approach presented in the following is intended to minimize the influence of both unwanted noise and acoustic reflections. To reduce acoustic reflections, it is common to employ conventional sound -absorbent foams and fibers that are used to cover reflecting surfaces [11-15]. Liao et al. [16] introduced novel adaptive metamaterials for b roadband sound absorption at low frequencies , which are typically very difficult to attenuate passively . It has been shown that the absorption coefficient of the adaptive metamaterial can be greater than 0.9 in the frequency region, 112 –236 Hz. Shen et al. [17] studied hierarchical pore structure based on cellulose nanofiber/melamine composite foam to enhanced sound absorption performance. The sound absorption coefficient of the composite foam has an improvement of 80 %. Noise reduction in acoustic measure ment characterization has remained a primary research interest for decades . The very first techniques used for denoising the acoustic signals are use of analog or digital filters [18]. These filters have a simple structure and are easy to implement but cannot provide significant distinction between signal and noise. Excellent denoising algorithms have been developed. For instance, Boashash and Mesbah [19] used time -frequency peak filtering (TFPF) to enhance signal on both simulated and real data. Moreover, Xiang and Yan [20] proposed a new time -frequency analysis method, called self -adaptive Wigner -Ville distribution based on local mean decomposition, to effectively analyze non -stationary amplitude - modulated and frequency -modulated signals. They showed that the proposed model could analyze the multi -component signal with multiple frequency components, and evidently remove 4 the cross -terms of Wigner -Ville distribution, and keep all its advantages. In addition, a noise reduction technique for acoustic -based syst ems was proposed based on Empirical Mode Decomposition (EMD) and improved fruit fly optimization algorithm (IFFOA) [21]. The validity of the noise reduction technique was verified by simulation and an actual acoustic -based diagnosis system. Based on simula tions and comparison results, they demonstrated that the automatic denoising method could effectively eliminate noise and outperform the others. Fast Fourier Transform (FFT) is the most widely used technique in signal analysis [22]. Noise and reflection reduction are significant problems in diverse areas and applications in acoustic measurements . The development of methods for minimizing these effects is ongoing. In this paper , we will show that even with the use of a highly -absorbent anechoi c chamber, there can still be detectable reflection from the wall s and/or the equipment, that can contaminate the results of measurements . In the following, we describe a process that successfully eliminate s the effect of reflections and unwanted noise wh en performing acoustic measurements. 5 2 Methods All experiments are conducted in the anechoic chamber at Binghamton University, show n in figure 1. The chamber interior dimensions are 4.2 m wide, 5.4 m long, and 3.2 m tall. The absorbent wedges shown are made of fiberglass . The chamber has been certified by the manufacturer to provide an anechoic environment at all frequencies above 80 Hz. The anechoic chamber was tested using methods specified in: ISO Standard 3745 -2003, Annex A, “General procedures for qualification of anechoic and hemi -anechoic rooms”. Figure 2a show s a plan view of the anechoic chamber . Figure 2b shows the experimental setup and system diagram . Here, sound pressure is measured by a B&K Type 4138 1/8” reference microphone and amplified by a B&K dual microphone power supply Type 5935L. A Polytec OFV -534 laser vibrometer is used for measuring the velocity of various test samples . The laser beam c an be maneuvered by a set of motorized stages. The signal of the microphone and the Fig. 1 Anechoic chamber at Binghamton University 6 laser vibrometer are collected by a National Instrument s PXI 1033 data acquisition system. The stimulus signal is generated by MATLAB and sent through the data acquisition system. After the crossover filter dbx Model 234xs , the signal is divided to low frequency, mid -range frequency, and high frequency , amplified by Crown D -75and Techron 5530 , and sent to the woofer, midrange , and tweeter, respectively. The loudspeaker is pl aced 3 m away from the microphone location. (a) (b) 7 A complete description of a sound field requires both the sound pressure p (r, t) and the medi um particle velocity vector u (r, t), where 𝑟 the spatial vector , 𝑡 is time. The pressure may be taken as proportional to density variations, while the velocity vector describes the velocity of disturbance of the physical particles in the medi um. The definition of a plane wave requires a wave that only propagates in one dire ction in a cartesian coordinate system and has a velocity fluctuation direction that is parallel to the propagation direction. In such wave , the acoustic pressure and velocity are uniform anywhere across the fluctuation plane. It’s possible to show the wave generated can be considered as a plane wave. If we consider the loud speaker is generating a harmonic spherical wave that propagates in the radial direction r , the wave equation has the solutio n form of [23]: 𝑃(𝑟,𝑡)=𝐴 𝑟𝑒𝑖(𝜔𝑡−𝑘𝑟) (2.0.1 ) Where 𝐴 is a constant, 𝑟 is the radius of the sphere wave, 𝑘=𝜔 𝑐 is the wave number. Using the Euler equation, the velocity can be calculated: 𝑈(𝑟,𝑡)=𝐴 𝑟𝑒𝑖(𝜔𝑡−𝑘𝑟)1 𝜌0𝑐(1+1 𝑖𝑘𝑟) (2.0.2 ) For a plane wave: 𝑃(𝑥,𝑡) 𝑈(𝑟,𝑡)=1 𝜌0𝑐 (2.0.3 ) For the spherical wave, the relation between 𝑃(𝑟,𝑡) and 𝑈(𝑟,𝑡) can be written as: Fig. 2 (a) Top-down Chamber diagram . The speaker is located 3m away from the reference microphone for approximate plane sound wave. The side wall of the chamber is 2m away from the center line of the experimental setup. (b) Detailed e xperiment al setup and system diagram . 8 𝑃(𝑥,𝑡) 𝑈(𝑟,𝑡)=1 𝜌0𝑐(𝑖𝑘𝑟 1+𝑖𝑘𝑟) (2.0.4 ) To consider the wave as a plane wave at measured location, we need 𝑘𝑟≫1. That is: 𝑟≫𝜆 2𝜋 (2.0.5 ) Where 𝜆 is wave length of the sound wave. If the distance is larger than a wave length 𝑟≥𝜆, we should be able to consider 𝑃(𝑥,𝑡)=1 𝜌0𝑐𝑈(𝑟,𝑡). Thus, for the acoustic measurement setup shown in figure 2, the sound wave can be considered as plane wave above 100Hz. 2.1 Effect of reflections in an anechoic chamber Figure 3 shows measured sound pressure levels (SPL) obtained in the chamber using the setup described in figures 1 and 2. A constant amplitude swept sinusoidal signal from 100Hz to 10kHz is played through the loudspeaker as the stimulation. The predict ed and measured results show a significant, fluctuation in SPL that appears to be periodic in frequency. Note that the frequency axis has a logarithmic scale. 9 Anechoic chambers are typically designed to minimize ambient noise, and more importantly, absorb internal reflection s ound waves during an acoustic characterization involving sound generation. However, the result show n in Fig. 3 shows that even in a state-of-the-art anechoic chamber, there are still reflection waves which are not fully attenuated. The data influenced by reflections will show a frequency dependent response with peaks and dips , caused by the reflection wave. Specifically, around 1500Hz, the sound pressure level (SPL) variation is over 10dB, which means the difference of sound pressure in pascal s will be over 330 percent. The main cause of this issue is that although anechoic chambers have extremely absorbent walls compare d to a normal wall, it cannot absorb all incident sound waves. That little amount of Fig. 3 Reflections cause fluctuations in measured sound pressure levels . The sound output o f the source is constant in frequency but the measured sound pressure level varies significantly as a function of frequency. The dashed line shows sound pressure level ( SPL) predicted for a frequency independent sound source with a single mirror reflectio n source model according to the dimensions of the chamber. The solid line shows the measured SPL with the effect of the reflection wave. 10 reflection is usually neglected. But , unfortunately, a small contribution from a reflected wave can have a significant influence on the total sound field . It is worthwhile to briefly consider a highly simplified system in which we can readily account for reflections from absorbing surfaces to see how the variations in pressure across frequency depend on the absorption of the surface. When a sound field consists of the combination of an incident and reflected wave, the pressure can be expressed as: 𝑃(𝑥,𝑡)=𝑒𝑖𝜔𝑡(𝑃1𝑒−𝑖𝑘𝑥+𝑃2𝑒𝑖𝑘𝑥) (2.1.1 ) where p1 and p2 are the complex amplitudes of the incident and reflected waves, respectively and the wave number is k=ω/c. ω is frequency in rad/s and c is the sound speed. The sound pressure at a distance l to the left of the reflecting surface, may be computed from Eq. ( 2.1.1 ), at x=−l, 𝑃(−𝑙,𝑡)=𝑒𝑖𝜔𝑡𝑃1𝑒𝑖𝑘𝑙(1+𝑟𝑒−2𝑖𝑘𝑙) (2.1.2 ) where r=p2/p1 is called reflection coefficient . The mean square pressure can be determined as follows: <𝑃2>=ℜ[𝑃(−𝑙,𝑡)𝑃∗(−𝑙,𝑡)] 2=|𝑃1|2 2(1+𝑟𝑒−2𝑖𝑘𝑙)(1+𝑟∗𝑒2𝑖𝑘𝑙) =|𝑃1|2 2(1+2ℜ[𝑟𝑒−2𝑖𝑘𝑙]+|𝑟|2) (2.1.3 ) where ℜ[·] denotes the real part and the superscript * denotes the complex conjugate. We will assume that the reflecting surface is relatively absorbent so that r<<1. Neglecting | r|2 in Eq. ( 2.1.3 ) gives 11 <𝑃2>≈|𝑃1|2 2(1+2𝑟𝑐𝑜𝑠(2𝑘𝑙)) (2.1.4 ) Sound pressure level (SPL) can be express as follows: 𝑆𝑃𝐿=10 𝑙𝑜𝑔10(<𝑃2> 𝑃𝑟𝑒𝑓2) (2.1.5 ) where Pref=20×10−6 pascal is the standard reference pressure. Substituting Eq. ( 2.1.4 ) into Eq. (2.1.5 ), Sound pressure level will give [23] 𝑆𝑃𝐿=10 𝑙𝑜𝑔10(|𝑃1|2(1+2𝑟𝑐𝑜𝑠(2𝑘𝑙)) 2𝑃𝑟𝑒𝑓2) =10 𝑙𝑜𝑔10(|𝑃1|2 2𝑃𝑟𝑒𝑓2)+10 𝑙𝑜𝑔10(1+2𝑟𝑐𝑜𝑠(2𝑘𝑙)) (2.1.6 ) The sound absorption coefficient may be written as: 𝛼=1−|𝑃2 𝑃1|2 =1−𝑟2 (2.1.7 ) It can be seen that by decreasing the absorption coefficient, the sound pressure variation increases dramatically. To be specific, if the absorption coefficient is 𝛼 =0.9, the sound pressure level fluctuation is calculated to be SPL=+ -2.75dB. That means that when viewed as a function of frequency, the fluctuating maximum sound pressure in pascal s will be approximately twice the value of the minimum. 12 In the calculated results shown in figure 4, different absorption coefficients are applied, and the corres ponding sound pressure levels are calculated over frequency for a highly simplified one- dimensional (1D) sound field. It shows the effects of different sound absorption coefficient α, on SPL for various frequencies. Moreover, the presence of the equipment and experimental setups will further increase the reflection which will create periodic, variations in the results when viewed in t he frequency domain . To solve this problem, one can reduce the reflection wave by increasing the absorption ratio for the reflected surfaces, in this case, the chamber walls, which is not practical since there is little room to improve the wedges to be mor e absorbent. That is why a more general method is Fig. 4 Variations of SPL versus frequencies for different absorption coefficients 13 adopted to get rid of the reflection wave effect. A time domain window method is introduced as an effective way to ‘filter’ out the unwanted reflection wave. Before demonstrating the details of the method, consider a simplified example for analyzing the time domain signal with a reflection wave, as indicated in figure 5 a. A flat surface is added to the setup 36.5cm away behind the reference microphone. By creating a solid wall of reflection on the path of so und wave propagation, we can analyze the timing of the reflection wave and its interaction with the incident wave. A single frequency signal at 500Hz is generated by the speaker 3m away from the microphone. The time domain response of the acoustic pressure fluctuation collected by the microphone is shown in figure 5b. The signal acquired by the microphone is divided to 4 parts. Before the time ‘tstart ’ is when sound wave hasn’t travelled to the microphone diaphragm, where tstart is the time when the sound w ave reaches the microphone. Transient response is acquired in the time period soon after tstart . As the sound wave travels to the wall behind the microphone, reaches the wall, and reflects back, the microphone signal in this period is completely reflection free. After the reflection wave arrives at the microphone again, the reflection wave interacts with the incident wave. The predicted time at which the reflected wave first arrives at the microphone can be expressed as: t_reflection= tstart +2*d/c (2.1.8 ) where c is the speed of sound at room temperature , 344 m/s, and d is the distance between the microphone and the reflecting surface, which can be verified by calculating d from Eq. ( 2.1.8 ) using measured time domain data. To avoid the effect of the reflection wave, the analysis should be cast within the reflection free section. Using the experiment setup shows in Fig. 5, t he times shown in Fig. 6 are identified on the plot of the measured data. A manual identificati on process 14 is added to start the analysis of the data after the transient response died out, and stop the analysis before the reflection wave arrives. This way, the data analyzed will not be contaminated by the speaker transient response or the interaction with the reflection wave. Fig. 5 Experiment setup for analyzing reflection wave . A simple reflection case is created to analyze the time domain signal. Single frequency plane sound wave is sent through speaker from 3m away from the reference microph one. A solid vertical wall is 36.5cm behind the microphone. 15 Fig. 6 Time domain pressure acquired by the microphone. The sound arrives at the microphone at time tstart. The transient response of the sound source then influences the signal for a time, TransientDuration. After the transient has died out, the signal is an alyzed until the reflected wave arrives. 2.2 Noise rejection and reflection windowing Measuring the acoustic frequency response is a significant process for characterizing structures and acoustical devices. Typical ways include using broadband white noise or swept sinusoidal signal s as sound stimuli, analyze the measured signal using fast Fourier Transform to process the data and acquire broadband frequency response. Through the use of the FFT, the acquired signal data is weighted in the frequency domain. In our case, u sing random broadband signals means the sound power generated by the loudspeaker is spread to all the frequencies involved. Instead, we can send just one frequency at a time ; all available sound power can be concentrated at this single tone. Th is way, the system doesn’t need to be driven at all frequencies at the same time. All available energy can be focused 16 to increase the sound power at the targeted frequency, which will result in a higher signal to noise ratio, thus cleaner data. Another benefit of sending one frequency tone at a time is that it facilitates the creation of a time -domain analysis window as depicted in Fig 6. By sending out just one frequency, the duration of the pure tone can be actively controlled. Since we know the reflection wave will arrive at some point, the microphone recording needs to be shut off before that. By adjusting the time range when the microphone is listening to the signal, we created a time window in which we are receiving the signal, and shut off and stop receiving the reflection contaminated signal. For lower frequencies, a specific number of cycles are used to compensate the long wavelength. Because the acquired signal contains only one frequency component, a curve fitting process is used to analyze the data with better accuracy, especially for lower frequencies. The effective reflections in an anechoic chamber can be very difficult to eliminate . However, using pure tone signals with a dedicated ti me window, the reflection can be eliminated. To attenuate the effective noise, a narrow band least square curve fitting process has been used [23]. Fig. 7 Signal acquisition process . A series of sinusoidal signals are generated. The actual measured signal at each frequency is always combined with noise during the measurement. 17 Assuming there is a sinusoidal signal generated by the signal generator, the voltage is denoted as 𝑉𝑖𝑛, 𝑉𝑖𝑛=𝑉0sin(𝜔𝑡) (2.2.1 ) where 𝜔 is the known driving frequency. The signal has been through the data acquisition process, and noise has been introduce d during the process. Possible noise sources include electronic noise due to ground loop s, random thermal noise, environmental acoustic n oise, etc. 𝑉𝑜𝑢𝑡 is the signal acquired by the data acquisition system. 𝑉𝑜𝑢𝑡=𝑉0sin(𝜔𝑡+𝜑)+𝑁(𝑡) (2.2.2 ) Where 𝜑 is the phase shift due to the room dynamics or structure effect during the measurement process. 𝑁(𝑡) is the introduced effective noise. If we account for DC shift in the process, the desired response without noise 𝑉𝑜 can be assume d to be: 𝑉𝑜=𝑎cos(𝜔𝑡)+𝑏sin(𝜔𝑡)+𝑐 (2.2.3 ) Where a, b, and c are constants to be found. Since the measured time data is discrete, t is replaced as 𝑡𝑖, where 𝑖=1,2,⋯,𝑁, is the number of data points. Thus, Eq. ( 2.2.3 ) can be rewritten as follows: 𝑉𝑜𝑖(𝑡𝑖)=𝑎cos(𝜔𝑡𝑖)+𝑏sin(𝜔𝑡𝑖)+𝑐 (2.2.4 ) To curve fit the measured data, different sets of parameter a, b, c will be found to ensure 𝑉𝑜𝑖 can represent the data as well as possible. The error at each 𝑡𝑖 is 𝜖𝑖=𝑎cos(𝜔𝑡𝑖)+𝑏sin(𝜔𝑡𝑖)+𝑐−𝑉𝑜𝑖(𝑡𝑖) (2.2.5 ) 18 There are N equations and 3 unknowns. By solving the overdetermined system for a, b, and c, the optimum 𝑉𝑜𝑖 can be found to represent the data. Simply assume 𝜖𝑖 to be 0, Eq. ( 2.2.5 ) can be written as: [ cos(𝜔𝑡1)sin(𝜔𝑡1)1 cos(𝜔𝑡2) cos(𝜔𝑡3) ⋮sin(𝜔𝑡2) sin(𝜔𝑡3) ⋮1 1 ⋮ cos(𝜔𝑡𝑁)sin(𝜔𝑡𝑁)1] 𝑁×3(𝑎 𝑏 𝑐) 3×1= ( 𝑉𝑜1 𝑉𝑜2 𝑉𝑜3 ⋮ 𝑉𝑜𝑁) 𝑁×1 (2.2.6 ) Solve Eq. ( 2.2.6 ) for a, b, c. The curve fitted signal amplitude is 𝐴=√𝑎2+𝑏2 (2.2.7 ) Phase with respect to the signal origin is 𝜑=tan−1𝑏 𝑎 (2.2.8 ) The added narrow band curve fitting process uses least square s to minimize the fitting error. The fitted signal should be the closest representation of the measured data. Since the acoustic signal is carefully sent, the frequency to expect for curve fitting is known. It is highly unlikely for the curve fitting proces s to be confused with noise at other frequencies. Therefore, the effective noise has been greatly attenuated . 3 Results and discussions 3.1 Acoustic pressure As presented above , when measuring sound pressure alone, reflection from the anechoic chamber wall wil l contaminate the result. With the time -domain window rejecting the reflection 19 wave, and narrow band curve fitting filtering the noise which has been shown in Fig 5 (a) and (b), respectively, a clean and smooth frequency response can be achieved as shown i n Fig. 8 (a). (a) (b) 20 As shown in Fig. 8 , the method is extremely effective at removing the effect of the reflection wave. The signal local variation as a function of frequency is reduced from 12dB to less than 3dB after the reflection is removed. The time domain data sho ws the time interval before and after the reflection wave arrives at the microphone and the data used in the curve fitting proces s. Since the reflection wave arrived after the data used in the curve fit, the results are not influenced by reflections. 3.2 Sound induced velocity Another example of taking advantage of this method is when measuring the acoustic induced velocity. The experimental setup used is the same as shown in figure 2, with the addition of a n extremely thin fiber suspended in the sound field th at is used to estimate the acoustic particle velocity [ 24,25 ]. The fiber used consists of spider silk that is placed adjacent to the reference microphone. We have shown that the spider silk can provide an accurate means of measuring the acoustic particle velocity. The sound -induced velocity of the silk is measured using a laser vibrometer. The laser is pointing at the silk strand from 29 cm away. The silk strand is simply supported by two thin pins with minimal internal tensile stress. Based on our previously published result [24,25], the velocity frequency response of the spider silk is nearly independent of frequency and close to that of the surrounding air particle velocity. With the reflection from Fig. 8 The time domain window leads to smoother measured data when plotted in the frequency domain. (a) Frequency domain data b efore and after elimination of reflection . The reflections within the anechoic chamber cause significant fluctuation in the data when plotted versus frequency. (b) Time domain data obtained at a particular frequency and the results of windowing and curve fitting to filter out measurement noise . 21 the already absorptive chamber wall removed usin g the previously introduced method, the measured velocity frequency response is found to be nearly independent of frequency . Since at the measured location, the sound wave can be considered as a uniform free field plane wave, the acoustic air particle velo city nearby the measured location 𝑢(𝑡) has a linear relationship with the measured acoustic pressure 𝑝(𝑡) and can be determined by: 𝑢(𝑡) = 𝑝(𝑡)/𝜌0𝑐 (3.2.1 ) where 𝜌0 is the density of air, 𝑐 is the speed of sound in air. The velocity of the silk sample can be measured by the laser doppler vibrometer. All measured time signals are processed with least square curve fitting thus most acoustical, electronic and electromagnetic noise can be avoide d when analyzing the signals in the frequency domain. This way, the acquired data should be free of contamination from the reflection and noise. As shown in figure 8 (a), (b) , the velocity of the silk is closely representing the expected acoustic particle velocity of the air. The method used here is similar to the method used when measuring the acoustic motion of the spider orb -web expe riment [ 25]. 22 (a) (b) Fig. 9 Measurement of the acoustic induce d velocity using the method . (a) Acoustic setup of the measurement and detailed photo of the measured sample. The speaker is 3m away from the measured location. The reference mic is set adjacent to the object measured. Laser vibrometer 23 Having a good measure of the acoustic particle velocity is useful in many situations. If a structure can move closely with the air, it can be calibrated for velocity sensing during acoustic characterizations . Spider silk can be difficult to handle and contains too much random variables during the fabrication process, whereas a microfabricated silicon cantilever beam that is thin enough to move with the air is better suited as a reliable velocity probe. The ca libration process is similar to measuring the velocity of the silk. However, the velocity frequency response of a cantilever beam is more frequency dependent than a compliant strand of silk. To represent the velocity of the air particles due to a sound wav e, velocity compensation should be considered in low frequencies. The calibration of the sensing beam velocity sensitivity is expressed in terms of the transfer function between the measured beam velocity and air particle velocity. Thus, the measured transfer function 𝐻1 is: 𝐻1=𝑉𝑏𝑒𝑎𝑚_𝑐𝑎𝑙𝑖 𝑉𝑎𝑖𝑟_𝑐𝑎𝑙𝑖 (3.2.2 ) Where 𝑉𝑏𝑒𝑎𝑚_𝑐𝑎𝑙𝑖 is the velocity measured with the laser vibrometer during the calibration process, and 𝑉𝑎𝑖𝑟_𝑐𝑎𝑙𝑖 is the air particle velocity in a plane wave . When performing an air particle velocity measurement, the micro beam is placed at the desired location with the laser focused on the beam. The measured air particle velocity can be calculated as: measuring velocity on the sample. The first sample is a strand of tension free spider silk drag line. The second sample is a silicon based compliant cantilever beam. The setup is used to acquire data for Fig. 9(b) and Fig. 10. (b) Measured velocity response to plane wave sound across the frequency range of 100Hz to 10kHz. 24 𝑉𝑎𝑖𝑟=𝑉𝑏𝑒𝑎𝑚/𝐻1=𝑉𝑏𝑒𝑎𝑚⋅𝑉𝑎𝑖𝑟_𝑐𝑎𝑙𝑖 𝑉𝑏𝑒𝑎𝑚_𝑐𝑎𝑙𝑖 (3.2.3 ) Where𝑉𝑎𝑖𝑟 is the air particle velocity at the location under investigation, 𝑉𝑏𝑒𝑎𝑚 is the corresponding beam velocity response measured by the laser vibrometer. As shown in figure 9. 4 Conclusion It is often preferred to perform an acoustic response measurement in an anechoic chamber due to its performance like ultra -low noise, minimal air flow, and minimal influence from acoustic reflections . Although when attempting to detect faint fluctuations o f acoustic pressure or trying to measure acoustic particle velocity, the result ing data are sensitive to low level s reflections Fig. 10 Measured velocity of the silicon beam response to plane wave sound compared with spider silk response. The solid line is measured velocity of the beam. The dotted line is the velocity measured from Fig. 9 (b). Getting rid of the reflection helps to get a clean velocity measurement . 25 such as those from the chamber wall or the equipment in the experimental setup. The consequences are considerable frequency depe ndent variations in the final frequency response. These variations are misleading at times, and thus need to be eliminated. A time-domain window incorporated with human interactions was created to help modify the data acquisition process in order to contro l the imposed sound and signal receiving duration. Instead of physically removing the reflection source, since it is not always feasible, it filtered the effect of the reflection from the measured data . And since the imposed pure tone is used as a sound so urce, it is easier to employ narrow band least square s to fit the data for every section of the sent tone for different frequencies, in which process the noise from all other irrelevant frequencies is filtered out. Results showed the smoothness of data com paring before and after the method was applied. After getting rid of the reflection and noise, the data variation across the wide frequency band from 100Hz to 10kHz has dropped from 12dB to less than 3dB , shown in Fig. 8(a). Since the sound wave can be co nsidered as a uniform plane wave, a better pressure measurement leads to a more accurate measure of air particle velocity. This can be helpful when characterizing the response of a structure that is intended to be driven by air particle velocity. This meth od offered a n approach to characterize the sound pressure as well as the media particle velocity without being affected by reflection wave and noise. The time -domain approach described here can be an effective alternative to frequency -domain analyses that employ the FFT algorithm . Not all acoustic characterization can be done in an anechoic chamber and acoustic reflections can have an adverse effect on the measured results . We showed that even if the experiment is conducted in an anechoic chamber, there cou ld still be reflections from the wall s that significantly impact the results . The approach presented here can lead to clean results with the measurement conducted in a relatively quiet conventional room without anechoic surfaces. 26 Acknowledgements : This wor k was supported in part by the National Institute on Deafness and Other Communication Disorders of the National Institutes of Health under award number R01DC017720 (to R.N.M). 27 5