Sound Attenuation Through Absorption by Vegeta- Tion

J. Acoust. Soc. Jpn.(E)17, 4(1996)

Sound attenuation through absorption by vegetation

Toshio Watanabe* and Shinji Yamada** *Fukushima National College of Technology, 30, Nagao, Kamiarakawa, Taira, Iwaki, 970 Japan ** Yamanashi University, 4-37 4-chome, Takeda, Kofu, 400 Japan

(Received 5 July 1995)

The sound absorption coefficient(ƒ¿)of trees was theoretically derived and expressed as ƒ¿= G•Ef1/2, where f is frequency and G is a constant; since the value of G cannot be calculated directly, absorption coefficients of four kinds of trees were experimentally measured by the reverberation-chamber method. It was found that sound energy was absorbed mainly by the leaves of trees and not their trunks. The values of G were determined by comparing theoretical and experimental results, and were found to be between 0.001 and 0.002. The attenuation in vegetation was theoretically expressed by G. To check the accuracy of this, experiments were carried out using two kinds of trees. The sound energy absorbed by tree leaves was measured. The theoretical values agreed approximately with experimental results, indicating that the attenuation through absorption can be predicted.

Keywords: Attenuation, Sound energy, Sound absorption, Vegetation, Rectangular plate

PACS number: 43. 20. Fn

refraction by scatterers (i.e. trees). The mechanisms 1. INTRODUCTION of sound attenuation in vegetation are still obscure. Belts of trees and hedges are frequently used as The aim of this paper is to investigate the mecha- noise barriers. Sound propagation through vegeta- nism of sound absorption by trees and to predict the tion has been investigated in order to determine the attenuation by trees through absorption. effectiveness of its application and also to predict the 2. SOUND ABSORPTION BY attenuation of sound.1-9) Other investigations with VEGETATION vegetation models8'13) have been conducted to ana- lyze the factors which affect sound transmission. 2.1 Theoretical Sound Absorption of a Plate Sound propagation through vegetation includes Sound energy decreases through absorption when several acoustic phenomena: scattering, absorption sound waves progress through vegetation. Sound and reflection. It is supposed that sound attenua- energy can be considered to be dissipated by friction tion is mainly caused by scattering and absorption with the surfaces of leaves and converted into ther- in the stems, branches and leaves of trees. There- mal energy. A leaf can be regarded as a rectangular fore, the studies concerning absorptionl10,11) and flat plate. When a sound wave with a particle scattering12,13) have been presented. It was recently velocity V contacts this flat plate, its components of revealed that refraction is also important for sound velocity in the three directions(x-axis, y-axis and propagation in vegetation.14) A sound wave does z-axis)are as shown in Fig. 1. The dissipation not diverge spherically and bends as it is focused in energy of sound wave per unit time on the surface of the reverse side in some frequency ranges due to the plate is given by15)

175 J. Acoust. Soc. Jpn.(E)17, 4(1996)

(4)

Dissipation energy on the surface of the plate is given by

It is apparently impossible to integrate this equation by a singular point at the edge of the plate. As many leaves have similar shapes, the value of total dissipation energy will be finite. The integral can be expressed by

Fig. 1 Components of particle velocity of an where A is a constant which is determined by the incident wave to a plate. dimension and the shape of the plate. Therefore, the dissipation energy is given by

(1) (5) where n is the coefficient of the viscosity of air, p is By combining equations(2),(3)and(5), the total the density of air, w is the angular frequency, S is dissipation energy is given by the area of one side of the plate and Vs is the particle (6) velocity on the surface of the plate.

As the sound wave is considered to be a random where incident, the mean value of the particle velocity is (7) determined by averaging the velocity in angles of and ƒÆ. Using the components of the particle veloc- The random incident energy per unit time on the ity in the axial directions, the dissipation energy is area S is given by given as follows. (8) (a) x axial component The dissipation energy on the x axis is given by where c is the velocity of sound. Accordingly, the absorption coefficient is given by

(9) where f is the frequency. Regarding G as

(10) (2) one obtains (b) y axial component The dissipation energy on the y axis is given by (11) The absorption coefficient of a plate is proportional to the square root of the frequency of the sound. Here, G is called the frequency-absorption factor.

2.2 Measurement of Sound Absorption Coeffi- (3) cients of Leaves (c) z axial component The theoretical absorption coefficient for flat When a sound wave goes into a flat plate perpen- plates was obtained as described above. The shape dicularly the particle velocity in the direction along of a leaf is similar to that of a flat plate, so Eq.(11) the plate is expressed by16) can be considered as giving the absorption

176 T. WATANABE and S. YAMADA: SOUND ATTENUATION THROUGH ABSORPTION BY VEGETATION coefficient of tree leaves. In order to determine the placed in the room. value of G, an experiment was carried out in a The absorption coefficient of trees am can be reverberation room using trees. Several trees, calculated as follows: whose roots had been cut away, were put into the reverberation room and the reverberation times with (12) and without the trees were measured. One loud- where V is the volume of the reverberation room, speaker and four microphones were used. The Sm is the surface area of the leaves, Tin is the rever- sound source signal was 1/3 oct. band noise. The beration time with trees and To is the reverberation range of the center frequencies was from 125 Hz to 8 time without trees. kHz. The measurement system is shown in Fig. 2. The absorption coefficient of trees does not The reverberation time was measured seven times at depend theoretically on the total leaf surface area. frequencies of 125-315 Hz, five times at frequencies It may be assumed that the passage of the sound of 400-800 Hz and three times at frequencies of 1 wave is interfered with by trees and that the wave kHz-8 kHz with each microphone. The average of does not diffuse uniformly in the reverberation these reverberation times was adopted as the repre- room; consequently the absorption coefficient sentative value for each frequency. The species of changes depending on the total leaf surface area trees and the surface areas of the leaves used in the present. The absorption coefficients of sawara experiments are shown in Table 1. The reverbera- cypress were measured for different total surface tion times were measured for each species and for all areas and the results are shown in Fig. 3. Three species combined. The reverberation time for groups with leaf surface areas of 2.80 m2, 4.78 m2 sawara cypress was also measured when only tree and 8.70 m2 were used. The values of the absorp- skeletons(stems and branches without leaves)were tion coefficient for the small total leaf area of 2.80 m2 vary widely with frequency. As the amount of leaf area increases, the values become smoother in some

Fig. 2 Experimental setup. The reverberation Fig.3 The sound absorption coefHcient fbr room; the surface area is 203 m2 and the sawara cypress with differing total leaf surface volume is 198m3. areas.○:2.80 m2,□:4.78 m2,△:8.70 m2.

Table 1 Trees used for the measurement of sound absorption .

177 J. Acoust. Soc. Jpn.(E)17, 4(1996) frequency ranges and smaller in others. However The absorption coefficients of other species are all are nearly the same. Therefore the measurement shown in Fig. 5(a)and(b). The values of the values for the absorption coefficient can be consid- broadleaf trees are comparatively greater than those ered as being independent of the leaf surface area. of the conifers. Broken lines show theoretical val- The absorption power of sawara cypress with and ues by Eq.(11)in Fig. 5. The values of G were without leaves(skeleton)is shown in Fig. 4. The determined in such a way as to fit with the experi- absorption power of the skeleton is much smaller mental results. The experimental result for each than that of the entire trees. So it is obvious that species agrees approximately with theoretical results the sound is mainly absorbed by leaves. when the value of G is between 0.0008 and 0.002 for frequencies greater than 500 Hz. This incidentally agrees well with the theoretical result G=0.001 at all frequencies for the case in which all species of trees were mixed(Fig. 5(c)). This illustrates that the absorption coefficient for tree leaves can be expressed by Eq.(11).

3. ATTENUATION OF SOUND TRAVELING THROUGH VEGETATION

3.1 Calculation of the Attenuation When a sound wave travels through vegetation, the sound energy is attenuated by absorption on the Fig.4 The absorption power by sawara cypress with leaves(○)and without leaves(skeleton) surface of tree leaves. The attenuation can be cal-

(●). The surface area of leaf is 8.70 m2. culated from the absorption coefficient. The

(a) (c)

Fig.5 The sound absorption coemcient by several kinds of trees. ●: Japanese Aucuba, ▽: spindle tree, △: sawara cypress, ◇: Japanese cedar, ×: all trees listed in Table 1. Dotted lines show the theoretical curve by Eq.(11).

(b)

178 T. WATANABE and S. YAMADA: SOUND ATTENUATION THROUGH ABSORPTION BY VEGETATION

yields

(18) In the practical application of the equation, the minimum values of L and f are about 0.3 m and Fig.6 Components of sound intensityof a 100 Hz. As long as the values of L and f are sound wave propagating through vegetation. greater than these, the attenuation can be expressed Ii: incident sound intensity,It: transmitted with sufficient accuracy by sound intensity,Ia: absorbed sound intensity, Ir: refiectedsound intensity. (19) absorption energy dI by vegetation per unit time 3.2 Measurement of Attenuation and per unit area in the short distance dx is express- Sound attenuation through absorption can be ed by Ea.(6)as follows. predicted by Eq.(19). In order to verify the equation, sound attenuation by plant leaves was mea- (13) sured. Two kinds of tree leaves, shown in Table 2, where Vo is the particle velocity, k is the wave length were used. Some branches with leaves were prepar- constant and F is the surface area density(i.e. the ed and uniformly put in the space of a rectangular total surface area of leaves per unit volume). The parallelepiped frame as shown in Fig. 7. A loud- absorption energy of a sound wave transmitted speaker was placed in front of this. The experiment through vegetation is given by was carried out in an anechoic room with white noise as the source sound signal. Sound intensity in the normal direction of the six planes which form the rectangular parallelepiped was measured and the (14) sound energy on each plane was calculated by the following equation. where L is the depth of trees. As shown in Fig. 6, when sound waves pass through Table 2 Tree leaves used for the measurement of trees, the sound attenuation through absorption is sound attenuation. given by

(15) where ht is the sound intensity absorbed by vegetation and Ie=Ii-Ir, Ii is the sound intensity incident on vegetation, Ir is the sound intensity reflected by vegetation. Substituting Eq.(14)and

(16) into Eq.(15), the attenuation is given by

(17) Fig. 7 A view of the apparatus for the experiment to measure the sound energy passed Furthermore, substitution of Eq.(10)into Eq.(17) through plant leaves.

179 J. Acoust. Soc. Jpn.(E)17, 4(1996)

shown in Fig. 8 should be zero in free space when (20) nothing is placed within inside the planes; some where E is the sound energy and Ii is the sound values resulted due to the difference in the phases of intensity in the normal direction on the small sur- the output signals from the paired microphones. face which has the area Sj. The sound energy was measured in six planes when The planes which fbrm the rectangular parallele- plant leaves were absent and in five planes(exclud- piped were named as shown in Fig.8. The number ing the -X plane) with plant leaves present. In of measurement points was eighty on the plane order to eliminate error from the measurement val- +X,-Y,+Y and -Y, and one hundred on the ue, the sound energy transmitted through plant plane +Z and -Z. The sound energy was trans- leaves was obtained by subtracting the first from the mitted into the -X plane and passed through the second. other planes. The sound energy transmitted The experimental results of sound attenuation through plant leaves is given by through absorption by plant leaves for 1/3 oct. bands each from 315 Hz to 4 kHz are shown in Fig. (21) 9. The sound attenuation theoretically given by where E+x, E+y, E-y, E+z, E-z is the sound energy on Eq.(19)is shown in the same figure, where the value each plane. The sound energy input into the plant of G is 0.0015 for Japanese cedar and 0.002 for leaves is Sudajii. The value of G for Sudajii was not measured. But Sudajii is a broadleaf tree, so the shape of (22) the leaf is similar to that of spindle tree or Japanese The sound attenuation is given by Aucuba. Therefore, 0.002 was adopted as the value of G for sudajii. The theoretical values of attenua- (23) tion agree approximately with the experimental The sound intensity was measured by paired micro- results for both species of trees. There are discrep- phones. The total sound energy in the six planes ancies at some frequencies. These can be considered to have been caused by external factors; for example, the number of measurement points was too small, the acoustical conditions of the measurement room were insufficient, and there were other measurement errors. The same attenuation should be obtained if rectangular plates were used instead of plant leaves since the rectangular plate was considered in the

Fig. 8 The coordinate axes and the name of theory. The sound attenuation by rectangular each plane which forms the rectangular paral- plates made of steel was measured. The size of the lelepiped. plates-which were 490 in number-was 10 cm

(a) (b) Fig. 9 Sound attenuation through absorption by plant leaves. Continuous lines showthe theoretical curve by Eq.(19).(a)Japanese cedar(FL=5.45, G=0.0015),(b)sudajii(FL=6.53, G=0.002).

180 T. WATANABE and S. YAMADA: SOUND ATTENUATION THROUGH ABSORPTION BY VEGETATION

in some frequency ranges. The mechanism and the property of refraction should be investigated in order to predict attenuation more accurately.

ACKNOWLEDGEMENTS

The authors would like to thank Professor H. Tachibana and the staff members in the laboratory of Institute of Industrial Science, University of Tokyo for their help and the use of the reverberation chamber and equipment.

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181 J. Acoust. Soc. Jpn.(E)17, 4(1996)

99 (in Japanese). Shinji Yamada received the D.Eng. 16) B. Fujimoto, Fluid Mechanics-revised edition (Yo- degree from Tokyo University in 1977. kendo, Tokyo, 1965), p.45 (in Japanese). He is now a professor and the dean of student affaires bureau of Yamanashi Toshio Watanabe received the M. University. His research interests E. degree from Yamanashi University in include low frequency noise, acitve con- 1976. He is now an associate professor trol and neural network. of Fukushima National College of Technology. His research interests include noise reduction by vegetation and low frequency noise.

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