Measurements of Acoustic Impedance and Their Data Application to Calculation and Audible Simulation of Sound Propagation

Acoust. Sci. & Tech. 29, 1 (2008) #2008 The Acoustical Society of Japan PAPER

Measurements of acoustic impedance and their data application to calculation and audible simulation of sound propagation

Teruo Iwase1, Yu Murotuka2, Kenichi Ishikawa3 and Koichi Yoshihisa4 1Faculty of Engineering, Niigata University, 8050 Igarashi 2-no-cho Nishi-ku, Niigata, 950–2181 Japan 2Graduate School, Niigata University, 8050 Igarashi 2-no-cho Nishi-ku, Niigata, 950–2181 Japan 3Oriental Consultants Co. Ltd., Shibuya Bldg. 16–28 Shibuya, Shibuya-ku, Tokyo 150–0036 Japan 4Faculty of Science and Technology, Meijo University, 1–501 Shiogamaguchi, Tempaku-ku, Nagoya, 468–8502 Japan ( Received 20 April 2007, Accepted for publication 17 August 2007 )

Abstract: Acoustic impedance determines the boundary condition of each sound field, but collections of actual values to evaluate sound fields are insufficient. Therefore, measurements of acoustic impedance using a particle velocity sensor were taken on different fields. Such measurement results were used for sound propagation calculations. Frequency characteristics of sound propagation on grass, snow-covered, and porous drainage pavement surfaces showed fair correspondence with field measurement results. Subsequently, fine calculations in the frequency domain were converted to impulse responses for each sound field model. Convolution operations based on the impulse response and on voice, music, and other noise sources readily produced an ideal sound field for the audible sound file. Furthermore, simulations of noise from a car running through a paved drainage area, with noise reduction effects, were attempted as advanced applications.

Keywords: Acoustic impedance, Sound propagation, Road traﬃc noise, Snow ﬁeld, Drainage pavement, Impulse response, Convolution PACS number: 43.28.En, 43.58.Bh [doi:10.1250/ast.29.21]

example, the prediction method for traffic noise has 1. INTRODUCTION become a widely known numerical evaluation method Acoustic impedance is a very important parameter for [2]. There is a boundary that has not yet been exceeded determining boundary conditions of sound fields. There- between a numerical evaluation method and an audible one fore, collections and collection projects of the acoustic and there are still some problems to be solved before impedance data for acoustical calculations are desired by widespread adoption of the audible evaluation method. many acoustical researchers and engineers who are To realize audible simulation by acoustical calculation, interested in evaluating and simulating the sound propaga- many acoustic impedance data have been required to have tion in various sound fields. Then, the establishment of an fine and wide continuous frequency values without disorder audible confirmation technique for easy evaluation of the from the point of view of hearing tests for the calculated calculated result using familiar sound signals such as results. Although there has been considerable research and human voice, music and noise signals produced by vehicles developing work on the measurement technique for the or machines is strongly expected by many researchers and impedance of actual materials or actual surface conditions engineers who have researched noise control and architec- of boundaries around us, only the sound tube method or its tural acoustics [1]. However, collections of actual values improved version for computer-aided measurement [3] can are insufficient for calculations and simulations of sound be established as a practical method that produces highly propagation and for evaluation of many sound fields. As for reliable values available to audible applications such as the method of evaluating the acoustical effects, the audible those mentioned above. Many development studies based simulation technique is not yet generalized though; for on the sound tube method using a pair of microphones

21 Acoust. Sci. & Tech. 29, 1 (2008) applied to an actual field have been conducted but effects, we tried many natural methods of correcting the significant success has not been achieved. Such methods measured impedance data. still have the common problem in which unexpected At the last stage of this study, simulations of noise disorder appears in measured results on a highly reflective radiation including noise reduction effects from a car test object or those in some frequency area where high- running through a drainage pavement area were carried out reflectivity characteristics are exhibited by accompany the as advanced applications. test object. For example, Takahashi et al. showed detailed In this paper, we describe a series of studies that starts acoustic impedance data of only fibrous materials and only from the development of methods of measuring acoustic for middle-range and high frequencies higher than several impedance, continues to the execution of measurements hundred Hz, and the method proposed by one of us was and the application of data to sound propagation calcu- limited to the measurement of only sound absorption lations, and finishes with an audible simulation. From our coefficients and was not applicable to the measurement of results, it will be shown that the proposed measuring complex impedance data [4,5]. We found that the main method is effective for the collection of acoustic impe- reason for the lack of collected acoustic impedance data dance data in actual various fields and that not only a was the absence of a practical measurement method and we numerical method but also an audible simulation method were able to conclude that not only collections of acoustic under the condition of a sound source moving in both impedance values but also the establishment of practical methods based on the measured impedance values is measuring methods for field measurement of the acoustic effective as a new way to acoustically evaluate many sound impedance is still greatly needed. fields and provide a virtual experience. At the first stage of our approach towards the goal of 2. METHOD OF MEASURING ACOUSTIC realizing evaluation that includes audible simulation, we IMPEDANCE IN FIELD measured the acoustical surface impedances of various fields. In these measurements, we tested the ordinal A method that employs two-channel microphones is method using a pair of microphones to confirm its often used for measuring acoustic impedance and the sound features and to check the acoustical conditions that could absorption coefficient [4,5]. Figure 1(A) shows that when free the obtained acoustic impedance data from disorder. a pair of microphones with equal sensitivity and a small In addition, we have recently tested a new measuring interval are arranged near a test target surface under the method that uses a hot-wire-type particle velocity sensor assumption of a plane wave sound field, both the sound and a microphone. pressure components of the incident and reflected waves At the second stage of this study, to evaluate measured can be separated from the two microphone outputs pa and ikr impedance data on the basis of the measure of quality pb using the phase delay operation e , corresponding to applicable to numerical calculations including advanced a small interval of r. Thus, the complex sound reflection audible simulations, results from these measurements were ratio r can be obtained from both components. The acoustic applied to some sound propagation calculations focused on impedance ratio z and sound absorption coefficient can the ground with the surface condition varied from being be obtained continuously using the following equations: acoustically very soft to hard. Typical frequency character- P eikr p r ¼ a b ; ð1Þ istics of sound propagation along surfaces of snow, turf, ikr pb pae long grass, and a porous asphalt pavement field were 1 þ r obtained from both measurements and calculations. The z ¼ ; ð2Þ 1 r calculated characteristics showed good agreement with 2 results obtained from inspecting field measurements on the ¼ 1 jrj ; ð3Þ sound propagation. Then, fine calculations in the frequency where i is the imaginary number unit and k is the wave domain were converted to the impulse response for each number. sound field model. Convolution operations based on the impulse response and on voice, music and some noise sources readily produced an ideal sound field for the audible sound file. Loudspeaker Loudspeaker These processes are based on the principle of digital signal processing and very simple, but the obtained impulse response had to be evaluated from other points of view of (A) by a Pair (B) by a Particle Velocity hearing tests on the calculated results. It was confirmed that of Microphones Sensor and a Microphone a little irregularity in the impulse response signal brought a strange and unrelenting tone. To avoid such unexpected Fig. 1 Two measurement models for sound reflection.

22 T. IWASE et al.: MEASUREMENTS AND APPLICATIONS OF ACOUSTIC IMPEDANCE

(A) for Acoustic Impedance and Sound Absorption Coefficient Loudspeaker: for White Noise

Amplifire DAT Pair microphones B&K 3519 1.0m Power Supply DAT 50mm, 12mm ∆r Amplifire Sony TCD-D5 Snow Layer

Fig. 2 Block diagram for ﬁeld measurements on acoustic impedance of snow surface and sound propagation on the snow ﬁeld.

If acoustic particle velocity can be measured by any istics above the same field were also carried out to confirm method [6] with the sound pressure measured using a the simulation calculation of sound propagation character- microphone, we can obtain the acoustic impedance in istics [8]. For this study, we updated the already measured accordance with the definition. parts of data by reanalyzing the original recorded data and The following new method, which uses a set of sensors by recalculation. In these measurements, as shown in consisting of a particle velocity sensor and a microphone, Fig. 2(A), the previously described methods based on a is used in our measurements of acoustical impedance closed pair of microphones were used to obtain sound for many sound fields. Figure 1(B) shows that a particle absorption characteristics for snowy surfaces. The reason velocity sensor and a microphone are arranged close to for the use of the ordinal method, the only method for each other. Acoustic admittance and acoustic impedance acoustic impedance measurement at the time, was to ratio z can be obtained directly using the definitions confirm its usefulness under the low reflectance condition. presented below. A block diagram for the measurement of sound propagation characteristics above the snow field is shown ¼ u=p; ð4Þ in Fig. 2(B) for measurements in 1999. The sound source z ¼ 1=: ð5Þ heights were set respectively as 0.3 m, 1.5 m, 4.4 m, and This method is superior because it yields stable results 6 m, and white noise or frequency-limited band noise for for low-sound-absorption materials and those for the long-distance propagation was emitted from a loudspeaker. frequency region in which high-reflectivity characteristics The receiving points of sound propagation were set at a are expected. As introduced later, it can be used to solve constant height of 1.5 m; the distances from the sound the difficult problem that accompanies the ordinal two- source were 1 m, 10 m, 20 m, 40 m and additionally 100 m microphone method introduced above. for long distance. Each output signal from the sound level meter arranged at each receiving point was recorded on a 3. FIELD MEASUREMENTS 16-channel data recorder. Each sound propagation charac- For the most recent decade or so, field measurements teristics was obtained as the relative sound pressure level have been carried out to investigate sound propagation on and the frequency response function using transfer function various ground surfaces. For each of those measurements, analysis with reference to the signal at the point 1 m away acoustical impedances or sound absorption coefficients from the sound source. The tested snow surface conditions were measured simultaneously where possible. Some were of two types: natural and trod by snowshoes. examples are shown below. 3.1.2. Measured results Examples of frequency characteristics of sound ab- 3.1. Snow-Covered Field sorption for natural snow and for compressed snow trod by 3.1.1. Outline of measurements snowshoes are shown in Fig. 3; they show that the snow Field measurements of basic acoustical properties of a field, even at a 50 cm depth, had high sound absorption snowy field were carried out for acoustic impedance and beyond 0.9 in a wide frequency range higher than 50 Hz for sound absorption coefficients on two snow fields with natural snow and beyond 0.6 for compressed snow. In these respective snow depths of 50 cm in 1998 and 100 cm in measurements, the small interval between two micro- 1999 [7]. Measurements of sound propagation character- phones r was select to be 50 mm for the lower frequency

23 Acoust. Sci. & Tech. 29, 1 (2008)

(A) Acoustic Impedance sound source is as low as 0.3 m, attenuations spread and 4 increase on the lower frequency side and the deep dips in Real Part 3 the higher frequency side disappear, which may be the 2 reason why they shift towards the higher frequency side. When the surface of the snow field is compressed, the 1 Natural Snow attenuations at each dip slightly weaken compared with 0 those under natural snow conditions. -1 Compressed In other words, for these common large attenuations -2 Snow in the low frequency range, human voices are difficult to transmit along the snowfield. On the other hand, these -3 Acoustic Impedance Ratio Imaginary Part characteristics also produce easy and noisy transmission -4 for sound sources that include high-frequency spectra, 50 100 1000 5000 e.g., instrumental music. For a higher sound source point Frequency : Hz such as 4.4 m or 6 m, attenuations at lower frequencies (B)Sound Absorption Coefficient are weakened. 1 0.9 3.2. Measurement of Acoustic Impedance on a Turf 100 cm 0.8 Field and a Grass Field 0.7 3.2.1. Outline of measurements 50 cm 0.6 Some studies similar to those described in Sect. 3.1 0.5 were carried out on a turf field that had been prepared in a Natural Snow 0.4 football stadium in 2003. Moreover, studies of a field with 0.3 Compressed Snow long grass were conducted near a runway at the multi- 0.2 purpose air park in Taiki town, Hokkaido in 2005.

Acoustic Impedance Ratio 0.1 In these studies, a pair of a small microphone and an 0 old-type Micro Flown sound particle velocity sensor was 50 100 1000 5000 used to measure acoustic impedance as introduced in Frequency : Hz Sect. 2. A block diagram of the measurements is shown in Fig. 5. Both received signals were recorded on a digital Fig. 3 Measured acoustic absorptive properties for each audio tape (DAT) recorder. The play-back signals were snow-field surface condition. input to a fast-Fourier transform analyzer or to a PC through a sound card; then transfer function analyses were range or to be 12 mm for the higher frequency range, both performed for the frequency response function. These analysis results based on both r values were combined analyzed results of sound particle velocity against sound together in these figures. The boarder frequency was pressure directly indicate acoustic admittances. Their chosen to be between 1 kHz and 2 kHz for smooth reciprocal values show acoustic impedances as defined by connection and on the basis of Nyquist frequency theory. Eqs. (4) and (5). These results show that the ordinal two-microphone 3.2.2. Measured results method is sufficiently available for highly absorptive Analyzed examples of acoustic impedance are shown objects such as deep snow fields in these measurements. in Fig. 6 for the turf and in Fig. 7 for the grass field. Frequency characteristics related to sound propagation Respective sound absorption coefficients are shown in are shown in Fig. 4. In these figures, the reference value Figs. 8 and 9. Both datasets commonly have typical 0 dB corresponds to the measured value at the reference characteristics of porous materials: acoustic impedance point 1 m away from the sound source when the height of data have a high value at low frequency and decrease as the sound source is 1.5 m. In the similar figures showing the they reach the value in the air at higher frequency. As an measured results of sound propagation such as Figs. 9 and overview of these results, we can conclude that these sound 10 shown later, 0 dB has the same meaning. In the results at absorption coefficients are increased by increasing fre- points 20 m or 40 m, large attenuations appear in the low- quency. Although object surfaces have high reflectance frequency range below several hundred Hz. As for natural characteristics in the low frequency region as mentioned snow, they reach 10 and several dB or 20 dB. Frequency just above, the results obtained by the new method indicate characteristics in a higher frequency range have deep sharp very gentle tendencies. These results show the effective- comb-teeth-type dips, but the averaged attenuations are not ness of the new method of measuring acoustic impedance large in the higher frequency range. When the height of the based on the definitions of sound pressure and particle

24 T. IWASE et al.: MEASUREMENTS AND APPLICATIONS OF ACOUSTIC IMPEDANCE

(A) Hs=1.5m Hr=1.5m Natural Snow (B) Hs=1.5m Hr=1.5m Compressed Snow -10 -10 Distance=10m Distance=10m -20 -20 20m -30 -30 20m -40 40m -40 40m -50 -50 100m Relative Level : dB Relative Level : dB -60 -60 100m -70 -70 50 100 1000 5000 50 100 1000 5000 Frequency : Hz Frequency : Hz (C) Hs=0.3m Hr=1.5m Natural Snow (D) Hs=0.3m Hr=1.5m Compressed Snow -10 -10 Distance=10m Distance=10m -20 -20 20m -30 20m -30

-40 -40 40m 40m -50 -50 Relative Level : dB Relative Level : dB -60 -60 100m 100m -70 -70 50 100 1000 5000 50 100 1000 5000 Frequency : Hz Frequency : Hz

Fig. 4 Comparisons of sound propagation frequency characteristics of natural and compressed snow surfaces. Hs and Hr represent both the height of the sound source and that of the receiving points, respectively, and D represents the distance from the sound source to each receiving point. In these ﬁgures, 0 dB is the ideally received sound pressure level at the referent point with a distance of 1 m from a point sound source.

Amplifier DAT/MD Loudspeaker 5 on Turf Field Corrected Source signal: Real Part White noise 0 Microflown 1-1.5m Particle velocity sensor Amplifier DAT Imaginary Part -5 Sony Impedance Ratio Corrected Microphone TCD-D100 Measurement object -10 100 1000 5000 Frequency : Hz Fig. 5 Block diagram for field measurements of acoustic impedance on wide turf field and grass field. Fig. 6 Obtained acoustic impedance ratio on a turf surface.

25 Acoust. Sci. & Tech. 29, 1 (2008)

25 -10 (A) Hs=1.5m 20 Distance=10m on Deep grass field 15 -20 10 20m Real Part 5 -30 0 40m -5 -40 -10

Imaginary Part Relative Level : dB -15 -50 60m Acoustic Impedance Ratio -20 80m -25 -60 100 1000 6000 100 1000 5000 Frequency : Hz Frequency : Hz

Fig. 7 Obtained acoustic impedance ratio on a grass surface. Fig. 10 Example of frequency characteristics of sound propagation on a turf field. 1 0 on Thin Grass Field 0.8 Distance= 5 m -10 0.6 10m -20 Corrected 0.4 20m Effective -30 0.2 FlowResistance 40m -40 σ =300 kPas/m2 Sound Absorption Coefficient 0 Relative Level : dB 100 1000 5000 -50 Frequency : Hz -60 Fig. 8 Measured sound absorption coefficient on a turf surface. 100 1000 6000 Frequency : Hz 1 0.9 Fig. 11 Example of frequency characteristics of sound 0.8 propagation on a grass field. 0.7 0.6 calculation results as described later, we corrected the 0.5 measured impedance values on basis of the most simple 0.4 linear correction theory for such a frequency region. For 0.3 example, the corrected values are shown in Fig. 6 by the 0.2 dotted lines. It seems that these problems were caused by 0.1 the sensitivity limitation of the old-type Micro Flown Sound Absorption Coefficient 0 acoustic velocity sensor used. 100 1000 6000 Examples of measured frequency characteristics of Frequency : Hz sound propagation are shown in Fig. 10 for the turf field and in Fig. 11 for the grass field. In both figures, commonly Fig. 9 Measured sound absorption coefficient on a grass surface. wide and deep dips are shown clearly at low and middle- range frequencies. Even though only dips are described, velocity. However, unexpected large fluctuations appeared they are narrower and sharper than those in the results for such as unable to be disregarded negative values of the real the acoustically very soft snow surface as shown in Fig. 4. part of the acoustic impedance in a partial frequency region between 250 Hz and 400 Hz for only reflective objects. To 3.3. Porous Asphalt Pavement avoid unnatural frequency characteristics in the numerical The use of porous asphalt pavements for drainage is an

26 T. IWASE et al.: MEASUREMENTS AND APPLICATIONS OF ACOUSTIC IMPEDANCE important measure to the reduction of road traffic noise by Loudspeaker suppressing the effects of air pumping noise and by sound Amplifier White Noise absorption due to the porosity of the pavement [9–14]. 3.3.1. Outline of measurements There are two methods of investigating these acoustical properties of porous asphalt pavements. One is the widely On Site Measurement Amplifier known standing wave method using a sound tube and a cut- Microphone DAT out test material [12–14]. Another is the method described Parsonal Computer above for sound absorption or acoustic impedance in a DAT Sound field. Particle Velocity Power Supply Card Sensor & Amplifire Both methods were used. For the first method, several circular test materials with a 100 mm diameter were cut out Off Site Analyzing from actual roads; then their acoustic impedance, propagation constant, and characteristic acoustical impedance Fig. 12 Sample setup for measurements of sound were obtained. Using the second method, acoustical absorption characteristics of porous asphalt. impedance and sound absorption coefficients were obtained for actual roads in use and a test course with a dense asphalt pavement and some types of porous drainage tions. The acoustic impedance of one of the porous asphalt pavement. In Fig. 12, the sample setup for the measure- pavements with a double layer [10,11,15] is shown in ment of the sound absorption coefficient using a micro- Fig. 13(B). phone and a particle velocity sensor is shown. The imaginary part of acoustic impedance has a zero 3.3.2. Measured results crossing from negative to positive values at a frequency Measured examples are shown in Fig. 13(A) for many below or of about 1 kHz. This is clear evidence of the types of porous pavement constructed in the test course. excitation of acoustic resonance in porous asphalt pave- The selected porous pavement types were a typical ments in accordance with their designed thickness. pavement with a single layer and two pavements with Other results for sand, a layer of fallen leaves, and so two layers of smaller-size gravel for the surface side and on were measured using the second method. of normal-size gravel for the base side. They had been 4. APPLICATIONS TO CALCULATION accurately controlled to have a common thickness of OF SOUND PROPAGATION 40 mm. In addition, one of the new-type porous elastic pavements [11] with unknown thickness was selected. The obtained acoustical impedance of the field surface Every result except that of the porous elastic pavement is a very important value that determines boundary shows the typical characteristics in which the peak value of conditions for each sound field. Therefore, the measured sound absorption is shown at a frequency of about 1 kHz, acoustic impedance data were applied to some calculations or lower to be exact, for a pavement thickness of about of sound propagation above various ground surfaces. 40 mm. These narrow and high peaks at the same frequency Figure 14 shows the sound propagation model for calcu- show the exactness of control at the pavement construc- lations consisting of the direct sound path and the reflected

1 20 Porous Asphalt (A) (B) Double Layler-2 0.8 10 Porous Single Porous Real Part Layler Elastic 0.6 Porous Double 0 Layler-1 0.4 Dense Asphalt -10 Imaginary Part 0.2 -20 Porous Asphalt Double Layler-2 Acoustic Impedance Ratio

Sound Absorption Coefficient 0 -30 100 1000 5000 100 1000 5000 Frequency : Hz Frequency : Hz

Fig. 13 Sound absorption coeﬃcients obtained using particle velocity sensor for many actual road pavement surfaces and an example of acoustic impedance of porous pavement with double layer.

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the snow field as introduced in Sect. 3.1 are shown in Observation Fig. 15. In these and similar figures showing the calculated Point results, the reference level 0 dB corresponds to the level of at each frequency defined by only the first term on the Point right-hand side of Eq. (6) at the ideal reference receiving Source point with a distance of 1 m from an ideal point sound Admittance: β source in a free field. These results are almost consistent with the measured frequency characteristics. For example, the lowest levels at low and midrange frequencies at the points with propagation distances of 20 m and 40 m are lower than ten and several or twenty dB from the peak Fig. 14 Calculation model for sound propagation along value at a high frequency such as 3 kHz or 4 kHz, and the ground with finite acoustic impedance value. they are slightly raised by the compression of the snow surface. For another example, the deep dip with a level of 37 dB is shown in the measure results at the point with a sound path via the ground surface. Calculations were 20 m propagation distance at 1.7 kHz; on the other hand, carried out using Kawai’s formulations [16]: the deep dip with a level of 39 dB is shown at 1.5 kHz in eikR1 eikR2 ¼ þ the calculated results. It seems that other deep dips match R1 R2 in regions between each nearby frequency. The calculation 2ð1 þ cos Þa pffiffiffiffiffiffiffiffiffiffiffi of sound propagation can reproduce similar frequency VðÞþf1 VðÞg Fð ikR2aÞ ; ð6Þ ðcos þ Þ2 characteristics, which have very wide and deep depth in low and middle frequency range around the frequency VðÞ¼ðcos Þ=ðcos þ Þ; ð7Þ pffiffiffiffiffiffiffiffiffiffiffiffiffi range of the main spectra of the human voice. Such a ¼ 1 þ cos 1 2 sin ; ð8Þ characteristics make it difficult to hear and have conversa- pffiffiffiffiffiffiffiffiffiffiffiffiffi tions on the snow field. 2 Reð 1 Þ > 0; ð9Þ Regarding the turf field and grass field, calculated pffiffiffi pffiffiffiffiffiffi pffiffiffi Fð Þ¼1 þ i wð Þ; ð10Þ results obtained using data of measured acoustical impe- pffiffiffi dance are shown in Figs. 16 and 17. Figure 17(C) shows wð Þ : error function: ð11Þ four pairs of comparisons between measured and calculated In these equations, R1 is the distance from a point source S, frequency characteristics for propagation distances of 5 m, 0 R2 is the distance from an imaginary point source S 10 m, 20 m and 40 m. The frequencies of each pair of sharp reflected by a boundary, is the angle of sound incident deep dips are almost the same, and the depth profiles are to the boundary and denotes the admittance of the also in good agreement as that they are shallow at near boundary. receiving points and deep at far points. As for matches of Examples of calculated frequency characteristics along level values, they are not so good at higher frequencies. the snow field using measured acoustic impedance data of It can be thought that the reasons for disagreement are

(A) Height of sound source= 0.3 m (B) Height of sound source = 1.5 m -10 -10 D=10m D=10m -20 -20 20m -30 -30 20m 40m -40 -40 80m 40m 100m -50 80m -50 100m Soft Compressed -60 -60 Natural Snow Natural Snow Soft Compressed Relative Level : dB (Ref. at 1m point)

Relative Level : dB (Ref. at 1m point) -70 -70 40 100 1000 6000 40 100 1000 6000 Frequency : Hz Frequency : Hz

Fig. 15 Frequency characteristics of sound propagation on snow ﬁeld calculated using each measured acoustic impedance value shown in Fig. 3.

28 T. IWASE et al.: MEASUREMENTS AND APPLICATIONS OF ACOUSTIC IMPEDANCE

-10 -10 (A)Hs=1.5m Distance=10m (B)Hs=0.3m Distance=10m -20 -20 20m 20m -30 -30 40m

-40 40m -40 60m Relative Level : dB

Relative Level : dB 80m -50 -50 60m 80m -60 -60 100 1000 5000 100 1000 5000 Frequency : Hz Frequency : Hz

Fig. 16 Frequency characteristics of sound propagation on the turf surface calculated using the measured acoustic impedance value shown in Fig. 6.

0 0 (A) on Thin Grass Field Distance= 5m Distance (B) on Deep Grass Field -10 -10 = 5m 10m 10m -20 -20

-30 -30

-40 -40 20m 20m Relative Level : dB Relative Level : dB 40m 40m Measured -50 -50 Calculated -60 -60 100 1000 6000 100 1000 6000 Frequency : Hz Frequency : Hz

0 (C) on Run Way Distance= 5 m -10

-20

-30 10m -40 20m Relative Level : dB -50 Flow Resistance 2 40m 1,000,000kPas/m -60 100 1000 6000 Frequency : Hz

Fig. 17 Frequency characteristics of sound propagation calculated using the measured acoustic impedance value shown in Fig. 7 and using the ideal high flow resistance value [17,18] for very highly reflective surface of a runway. The height of the sound source is 1.5 m for all cases. the lowering of coherency in transfer function analyses results and similar to the calculated and measured results between the source signal and the actually received signals for the snow field. However, dips for the turf and grass field affected by air turbulence, which make random phase shifts are not very wide and their dip frequencies are higher than on the propagating sound, and sound absorption in the that for the snow field. atmosphere [19]. From overall comparisons, it seems that As for the porous drainage pavement, the sound these calculated results are consistent with measured propagation calculations even for numerical evaluation

29 Acoust. Sci. & Tech. 29, 1 (2008)

0.015 These processes are very simple from the point of view of the principle of digital signal processing, but the obtained 0.01 Distance 40m impulse response had to be evaluated from other point of 0.005 view of the audible simulation that is based on hearing tests on the calculated results. Figure 19(A) shows calculated 0 frequency characteristics obtained using the measured Amplitude acoustic impedance data of a porous asphalt pavement with -0.005 a double layer as shown in Fig. 13(B). In this calculated -0.01 result, there are only several components with high values, 0.11 0.12 0.13 at frequency about several hundred or over one thousand Time : sec. Hz, among many frequency components from low frequen- 0.015 cy to high, which will hardly cause any numerical diﬀer- 0.01 ence. On the other hand, as shown in Fig. 19(B), they will Distance 80m make a slightly continuous response in the impulse response 0.005 signal and will bring a strange and unrelenting tone, which is weak but audible. We can tell that the cause of this 0

Amplitude problem is the negative value of the real part of the -0.005 measured acoustic impedance. The negative value of the real part corresponds to ‘‘negative resistance’’ in electric -0.01 0.22 0.23 0.24 circuit theory; then, it corresponds to a signal enhancer Time : sec. or signal oscillator as shown by calculation, which is impossible to obtain from normal sound propagation Fig. 18 Calculated impulse response from frequency phenomenon. However, these unexpected data are often characteristics shown in Fig. 17(B). produced by avoidable or unavoidable causes accompany- ing measurement sensors, their geometrical setting con- are very effective in determining noise reduction effects, dition and other factors. To avoid such unexpected audible called excess attenuation, on road traffic noise brought problems, we carried out many trials of the correction of about by the replacement of ordinary dense asphalt the measured impedance data. Figures 19(C) and 19(D) pavement with porous pavement. show recalculated examples obtained by the very simple correction that partial real parts with large negative values 5. APPLICATIONS TO AUDIBLE such as less than 0:25 in the higher frequency region SIMULATIONS around 3 kHz and 4 kHz were replaced with 0. These 5.1. Method Based on Impulse Response and Convo- figures show very normal frequency characteristics and an lution Operations impulse response signal. There will be more reasonable Audible sound data and information for ideal propaga- correction methods in terms of physical meaning. tion in a sound field are obtainable if the frequency characteristic data related to sound propagation in a sound 5.2. Method of Direct Conversion from Frequency field can be obtained through measurement or calculation. A Data to Time-Series Signals very simple method for this purpose is described as follows. If the sound source is moving, the impulse response First, measured or calculated fine sound propagation changes rapidly from each varying position of the sound characteristics in the frequency domain are converted to source to an observation point; at every fine sampling time, impulse response data in the time domain. The Fourier calculation of sound propagation from varying sound transform operation allows us to easily execute this source points and a convolution operation to convert to a conversion. Then, the convolution operation between the time signal are necessary. impulse response and any sound source produces an Many calculations and very long calculation times are audible sound signal similar to the sound source signal basically required for a great number of periodic Fourier and is recorded in the target sound field. Figure 18 shows operations included in such convolution operations even if examples of obtained impulse responses for long-distance we use FFT to shorten Fourier transform calculation. For propagation on a deep grass field. Then, the sound data this reason, we introduce a slightly simplified calculation created by performing convolution operations between the method. As shown in Fig. 20, summation of sound impulse response and the voice, music or noise source in propagation characteristics in the frequency domain multi- the wave file format can be played back easily using a PC plied by the amplitude of a sampled source signal with sound system [20]. compensation of the time delay for each sampling time are

30 T. IWASE et al.: MEASUREMENTS AND APPLICATIONS OF ACOUSTIC IMPEDANCE

(A) Original Frequency characteristics (B) Original Impulse Response

10 0.02 on Double Lyer Porous Asphalt 0 Hs=0.3m Distance=20m 0.01 -10

-20 0

-30 Amplitude 50 60 70 Hr=1.5m Relative Level : dB -0.01 Time : ms -40

-50 -0.02 100 1000 6400 Frequency : Hz

(C) Corrected Frequency characteristics (C) Corrected impulse Response 10 on Double Lyer Porous Asphalt 0.02 0 Hs=0.3m Distance=20m 0.01 -10

-20 0 50 60 -30 Amplitude 70 Hr=1.5m Time : ms Relative Level : dB -0.01 -40

-50 -0.02 100 1000 6400 Frequency : Hz

Fig. 19 Sound propagation characteristics and impulse response obtained from measured impedance data shown in Fig. 13 and those corrected by the correction on partial negative values of real part of original measured impedance data. Original characteristics have a sharp peak at higher frequencies and an impulse response is added as an unexpected response in the form of sine wave signals. made. The summed up result is converted eventually to of the calculation system. There will be other techniques time series signal data using a very simple inverse Fourier for shortening these calculation procedures. The calculated transform calculation once. These calculations are executed time signal data, which are formatted as a wave-type ﬁle, by following Eqs. (12) and (13) as can be played back easily for review.

XN1 One example is the simulated passage of noise signals ð!kÞ¼ fSðlÞ expði!kltÞgTrf ðl;!kÞ; ð12Þ of a passenger car running on an ideal road with a dense l¼0 asphalt pavement surface or porous drainage asphalt. For 1 XN! these examples, sound propagation calculations, described AmpðntÞ¼ ð!kÞ expði!knttÞ; ð13Þ previously in Sect. 4, were performed for every sampling 2N! k¼N! time using acoustic impedance data of the porous asphalt where ð!kÞ is the total summation at the angular and the hard dense asphalt. For ideal simulation of the frequency of !k, SðlÞ is the amplitude of the sound source mutual pavement road of dense asphalt and porous drain- signal at the l-th position, Trf ðl;!kÞ is the transfer function age, as shown in Fig. 21(A), the waveform of noise signals on the sound propagation from the l-th sound source from a running car shown in Fig. 21(B) and simulated road position to the ideal receiving point and AmpðntÞ is the traﬃc noise signals shown in Fig. 21(C) are created merely amplitude of the simulated sound signal at the nt-th by time-sharing the mixing of both audible sound signals time point from the start of simulation. This calculation for the dense asphalt pavement and for the drainage procedure can be separated into several time blocks in pavement to recognize the noise-reduction eﬀect. The accordance with the permissible memory storage capacity reason for using such a simple mixing technique is that

31 Acoust. Sci. & Tech. 29, 1 (2008)

Sound Source Signal S(n) 1 0.5 0

Amplitude -0.5 -1 2250 2750ω∆ 3250 Time S(l) exp(-ilk t) Summation + + + + + + + + +

:Angular Frequency ω 5000 5000 5000 0.15 0.15 0.15 Amplitude 0.1 1000 0.1 at ωk 1000 0.1 1000 y : Hz

0.05 0.05 0.05 Amplitude

Amplitude Frequency : Hz Amplitude Frequenc Frequency : Hz 0 0 0 100 100 100 l-th Transfer ω Function Trf ’ (l. ) Inverse Fourier Transform Produced Sound Signal 0.1 0.05 0 -0.05 Amplitude -0.1 1750 2250 2750 3250 Time

Fig. 20 Simplified calculation for sound propagation simulation from moving sound source in frequency domain. exact calculation methods are not established at this time pavement conditions at a time in the observation period for for sound propagation above a surface with different simulated results and for actually recorded noise signals. acoustic impedance conditions. The spectral difference for recorded noise signals between Noise reduction effects are clearly discernible as shown both pavement conditions is larger than that for simulated by the silence brought on the porous pavement parts. ones. The large spectral difference was brought about by However, these effects and differences are not clearly the fact that the actual porous pavement had been exactly recognized from only the observation of the calculated controlled; thus, it is called a very silent road. On the other waveform as shown in Fig. 21(B). Figure 22 shows the hand, simulation models have typical spectra of the sound calculated waveform with A-weighting correction on the source for the road traffic noise prediction on the porous other calculated results at the other point with a 7.5 m pavement [2] and typical acoustic impedance. Thus, it distance from the lane and shows its simulated level produces typical noise reduction effects brought about by recording waveform. A clear difference or the effect of each the typical porous pavement. It can be thought that audible factor on both pavements is shown in this figure. As an simulation will effectively assist the easer reorganization example for reference, this simulated result was compared of acoustical effects of many countermeasures for noise with the recorded running noise of a passenger car on both reduction and for acoustical comparisons between different actual dense asphalt and porous asphalt pavements with a sound field conditions. single layer in the test course as introduced in Sect. 3.3. 6. CONCLUSION See Fig. 13 for their sound absorption coefficients. Figure 23 shows comparisons between level recording Methods of measuring acoustic impedance using two waveforms of simulated passage noise and actual ones. microphones and using set of sensors consisting of a Figure 24 also shows spectral comparisons between both microphone and a sound particle velocity sensor were

32 T. IWASE et al.: MEASUREMENTS AND APPLICATIONS OF ACOUSTIC IMPEDANCE

(A) Ideal stereophonic recording model for running vehicle noise on the mutual pavement road.

(B) Produced ideal waveform of (C) Produced ideal waveform for traffic vehicle noise. flow noise.

Fig. 21 Example of simulated running vehicle noise on a pavement road of dense asphalt and porous drainage and an ideal model for this simulation.

(B) Actual Vehicle Noise on (A) Simulated Running Vehicle Noise Each Different Pavement 70 on Dense Asphalt on Dense 10dB Asphalt 60

40 on Drainage on Drainage Pavement Pavement A-Weighted Level Difference 30

0 5 10 15 20 25 A-weighted Sound Pressure Level : dB 0 5 10 15 Time : s Time : s

Fig. 23 Changes of A-weighted sound pressure level of simulated running vehicle noise on mutual road with two kinds of pavement and comparison with sound Fig. 22 Another example of simulated running vehicle pressure level of actual vehicle noise recorded on a test noise ideally recorded at a point with shorter distance course. of 7.5 m from a running lane; waveform and level recording with A-weighting correction. Changes/differences between both pavements are clearly shown. snow, turf, and grass fields are commonly similar to that of a fibrous or porous material such as glass wool. Sound propagation characteristics obtained from field measure- introduced. Then, measurements were executed for the ments on the snow, turf, and grass fields have a wide dip at acoustic impedances of various ground surfaces. Many low or middle-range frequencies and calculation of sound measurements showed that the acoustic impedances of propagation based on the measured acoustic impedance

33 Acoust. Sci. & Tech. 29, 1 (2008)

0 0 (A) Simulated Sound (B) Actually Recorded Sound -10 -10 on Dense Asphalt on Dense Asphalt Pavement -20 -20 Pavement

-30 -30 on Porous Drainage on Porous -40 -40 Pavement Drainage Pavement Relative Level : dB Relative Level : dB -50 -50 0dB : Over All on Dense Asphalt 0dB : Over All on Dense Asphalt -60 -60 50 100 1000 5000 50 100 1000 5000 Frequency : Hz Frequency : Hz

Fig. 24 Spectral comparisons of vehicle noise running on both dense asphalt and porous drainage pavements for each simulated signal and actually recorded signal. Both figures show clear spectral differences in the frequency range from 300 Hz to 2 kHz. These are evidence of the different hearing impressions of vehicle noise on each pavement. was carried out. Even though correction of impedance data [5] T. Iwase, ‘‘Measuring method for sound reflection or absorp- is required when needed, calculated sound propagation tion coefficient by using two closed microphones with different sensitivities,’’ Proc. Internoise 94, pp. 1951–1954 (1994). characteristics are in good agreement with actual propaga- [6] T. Iwase, ‘‘Measurements of particle velocity in sound field tion characteristics. In addition, the calculated results can and their applications,’’ J. INCE/J, 24, 339–343 (2000). be converted easily to impulse responses for convolution [7] T. Iwase, T. Sakuma and K. Yoshihisa, ‘‘Measurements on operations to obtain audible sound signals. To give a more sound propagation characteristics in snow layer,’’ Proc. in CD- Rom of ICA 2001 (2001). complex example, simulations of noise propagation from [8] T. Iwase, T. Sakuma and K. Yoshihisa, ‘‘Measurements and a car running through a drainage pavement area were simulations on sound propagation above snow field,’’ Proc. in executed as advanced applications. Our acoustic impe- CD-ROM of internoise-2001 (2001). dance measurement method is useful. Calculated sound [9] U. Sandberg, The Tyre/Road Noise Reference Book (Informex, propagation characteristics based on the measured acoustic Kisa, 2002). [10] U. Sandberg, ‘‘Low noise road surface —A state-of-the-art impedance correspond to actual propagation character- review,’’ J. Acoust. Soc. Jpn. (E), 20, 1–17 (1999). istics. Audible simulations will be effective for future [11] S. Meiarashi, ‘‘Research on low noise pavement in Japan,’’ J. evaluations of sound fields. Acoust. Soc. Jpn. (E), 20, 19–27 (1999). [12] H. Hatanaka and K. Yamamoto, ‘‘Measurements and analysis ACKNOWLEDGMENTS of acoustic properties of drainage asphalt,’’ J. Acoust. Soc. Jpn. (E), 20, 55–62 (1999). This study was carried out as part of the research [13] T. Iwase and R. Kawabata, ‘‘Measurements of basic acoustical project supported by the Grants-in-Aid for Scientific properties of the porous pavement and their applications to the Research ‘‘KAKENHI’’ with the help of many students of estimation of road traffic noise reduction,’’ J. Acoust. Soc. Jpn. (E), 20, 63–74 (1999). Niigata University. We appreciate their assistance. [14] M. Yanaguchi, H. Nakagawa and T. Mizuno, ‘‘Sound absorp- REFERENCES tion mechanism of porous asphalt pavement,’’ J. Acoust. Soc. Jpn. (E), 20, 29–43 (1999). [1] Many papers in Proc. ASVA 97;‘‘International Symposium on [15] T. Iwase, ‘‘Acoustic properties of porous pavement with double Simulation, Visualization and Auralization for Acoustic Re- layers and its reduction effects for road traffic noise,’’ Proc. in search and Education’’ (1997). CD-ROM of internoise-2000, France (2000). [2] H. Tachibana and Research Committee of Road Traffic Noise [16] T. Kawai, ‘‘On sound propagation above a locally reacting in the Acoustical Society of Japan, ‘‘Road traffic noise boundary,’’ J. Acoust. Soc. Jpn. (J), 39, 374–379 (1983). prediction model ‘‘ASJ RTN-Model 2003’’ proposed by the [17] Y. Miki, ‘‘Acoustical propertes of porous materials —Model- Acoustical Society of Japan,’’ J. Acoust. Soc. Jpn. (J), 60, 192– ing of Delany Bazley models,’’ J. Acoust. Soc. Jpn. (E), 11, 241 (2004). 15–24 (1990). [3] J. Y. Chung and D. A. Blaser, ‘‘Transfer function method of [18] M. E. Delany and E. N. Bazley, ‘‘Acoustical properties of measuring in-duct acoustic properties,’’ J. Acoust. Soc. Am., fibrous absorbent materials,’’ Appl. Acoust., 3, 105–116 (1970). 68, 907–913 (1980). [19] ISO 9613-1, ‘‘Acoustics-Attenuation of Sound during prop- [4] Y. Takahashi, T. Otsuru and R. Tomiku, ‘‘In site measurements agation outdoor-Part1; Calculation of the absorption of sound of surface impedance and absorption coefficients and porous by the Atmosphere’’ (1993). materials using two microphones and ambient noise,’’ Appl. [20] Architectural Institute of Japan, Sound Material in Living and Acoust., 66, 845–865 (2005). Environment, DVD version (Gihodoshuppan, Tokyo, 2004).

34 T. IWASE et al.: MEASUREMENTS AND APPLICATIONS OF ACOUSTIC IMPEDANCE

Teruo Iwase was born in 1948. He received Kenichi Ishikawa was born in 1960. He his B.Eng., M.Eng. and Dr. degrees from received his B.Eng. degree from The Open University of Tokyo. He was given the Sato University of Japan in 1987. Now, he belongs to Prize Paper Award from A. S. J. in 2000. He Oriental Consultants Co. Ltd. and to Graduate is Professor of Department of Architecture, School of Science and Technology, Niigata Niigata University. His research interests are University. His research interests are road traffic acoustic properties of sound material, such as noise, especially noise reduction effect by absorption and insulation, recently more wide as porous drainage asphalt. porous asphalt, audible simulation and acoustical diagnosis. Koichi Yoshihisa was born in Tokyo, Japan Yuu Muroduka was born in 1983. He re- in 1952. He received his degree Dr. Eng. from ceived his B.Eng. degree from Niigata Univer- Tokyo University in 1981. He worked at sity in 2006. Now, he belongs to Graduate Institute Industrial Science, Tokyo University School of Science and Technology, Niigata form 1982 to 1984 as a research assistant. He University. His research interests are acoustic has been working at Meijo University since properties of sound materials, such as sound 1984 and is currently a Professor of Dept. of absorption and sound insulation. Architecture. His fields of interest include acoustic design of buildings, environmental noise assessment and education in acoustics.