The acoustic impedance of the surface coverings used in the laboratory experiments on sound diffraction by topographical ridges was determined. The model, which was developed, takes into account full wave effects and the possibility of surface waves and predicts the sound pressure level at the receiver location relative to what would be expected if the flat surface were not present. The sound pressure level can be regarded as a function of frequency, sound speed in air, heights of source and receiver, and horizontal distance from source to receiver, as well as the real and imaginary parts of the surface impedance

Berthelot, Yves H.

Chen, Pei-Tai

Chisholm, Nathaniel

Kearns, James A.

Main, Geoffrey L.

Pierce, Allan D.

Zhou, Ji-Xun

English

NASA Technical Reports Server

NAG-1-566 Semiannual Report No. 5, page 1 
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SEMIANNUAL STATUS REPORT No. 5 
NASA GRANT NAG1-566 
SOUND PROPAGATION OVER UNEVEN GROUND 
AND IRREGULAR TOPOGRAPHY 
Semiannual Report, February 1987 - July 1987 
by 
Yves H. Berthelot (Co-PI), Allan D. Pierce (Co-PI), Ji-xun Zhou, Geoffrey L. Main (Co-PI), 
Pei-Thi Chen, James A. Kearns, and Nathaniel Chisholm 
Schm! of MechaEica! Engineehg 
Georgia Institute of Technology 
Atlanta, Georgia 30332 
Submitted to 
National Aeronautics and Space Administration 
Langley Rosearch Center 
HTpton,  Virginia 23665 
NASA Technical Officer: 
John S. Preisser 
Mail Stop 460A 
July, 1987 
Obsa-CR-181129) SOUlDC P R C P A 6 A l I O Y  OVER t187-27482 
U B E V E l l  GBGUlPD ALIJD 1.BSLGULALB TCEOGBAPBY 
Semiannual SSatus Bleport Bo- 5 ,  Peb. - JUl. 
7987 (Georgia Iast, of Tecb,) 9 p A v a i l :  Unclaa 
E T I S  BC A O 2 / H F  A01 CSCL 20A 63/71 0082665 
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NAG-1-566 Semiannual Report No. 5, page 2 
TABLE OF CONTENTS 
INTRODUCTION 
PERSONNEL 
MEASUREMENT OF ACOUSTICAL IMPEDANCE 
REFERENCES 
DEVELOPMENT OF CONPUTATIONAL ALGORITHMS 
VIEWGRAPHS USED IN PRESENTATION 
COMPARISON OF EXPERIMENT WiTH THEORY 
DIFFRACTION BY A SMOOTH RIDGE 
VIEWGRAPHS USED IN PRESENTATION 
ECHOES BY HILLS 
Page 
3 
3 
4 
8 
9 
18 
39 
46 
53 
72 
NAG-1-566 Semiannual Report No. 5, page 3 
INTRODUCTION 
The goal of this research is to develop theoretical, computational, and experimental 
techniques for predicting the effects of irregular topography on long range sound propagation 
in the atmosphere. Irregular topography here is understood to imply a ground surface that 
(1) is not idealizable as being perfectly flat or (2) that is not idealizable as having a constant 
specific acoustic impedance. The interest of this study focuses on circumstances where the 
propagation is similar to what might be expected for noise from low-altitude air vehicles 
flying over suburban or rural terrain, such that rays from the source arrive at angles close 
to grazing incidence. 
The objectives of the project, the experimental facility, and the early progress up 
through August 1986 have been described in the four previous semiannual reports [1,2,3,4]. 
The present report discusses those activities and developments that have resulted during 
the period, February 1987 through July 1987. 
PERSONNEL 
In addition to A. D. Pierce and G. L. Main, a third faculty member, Yves H. Berthelot, 
is a now also a -principal investigator on the project. Also involved in activities related 
with the project are three graduate students: James A. Kearns, Nathaniel Chishoim, and 
Pei-Tai Chen. A visiting scholar, Profeseor Ji-xun Zhou of the Acoustics Institute of the 
Academy of Sciences of China (Beijing), has been working on the project since May. Dur- 
ing the past reporting period, Dr. Berthelot, Professor Zhou, and James Kearns have been 
mainly concerned with the the experimental phases of the project, while Allan Pierce and 
Dr. Main have been working primarily on the theoretical aspects. Pei-lsi Chen has been as- 
sisting Dr. Pierce on some theoretical questions involving echoes, while Nathaniel Chisholm 
has been assisting with the computational aspects of the project. 
Allan Pierce, Geoffrey Main, and Yves Berthelot visited NASA Langley Research Cen- 
ter on February 23,1987, and discussed complementary NASA and Georgia Tech research 
activities with the NASA technical officer, Dr. John Preiseer, with William Willshire, and 
with their colleagues. 
1 
I e 
NAG-1-566 Semiannual Report No. 5, page 4 
MEASUREMENT OF ACOUSTIC IMPEDANCE 
During the past few months a special effort has been made to determine experimentally 
the acoustic impedance of the surface coverings used in the laboratory experiments on 
sound diffraction by topographical ridges. As was discussed during the group’s visit to 
NASA Langley on February 23, it wae initially hoped that acoustic impedance could be 
determined simply by taking the ratio of the complex Fourier transform of a direct signal 
and the subsequent signal that corresponds to a reflected wave from the surface of unknown 
impedance. Further refinement of the data processing technique and altering some incorrect 
procedures showed that such a method is indeed adequate to measure the magnitude of the 
reflection coefficient, but the technique was too crude to measure the phase of the reflection 
coefficient (especially at high frequencies). This indicated that a different technique was 
needed to achieve a reliable measurement of acoustic impedance. 
After discussions at various scientific conferencea with other groups engaged or experi- 
enced in acoustic propagation experiEents, it was decided to use FI technique described by 
E d l e t o n ,  Piercy, and Psigle [SI. They use n re!ntive!y highly accurate theoretical solution 
(better than a plane wave reflection model) for the sound pressure level at a moderate to 
large distance caused by a point harmonic source at a specified height above a flat surface 
with given impedance. The model takes into account full wave effects and the possibiity 
of surface waves and predicts the sound pressure level at the receiver location relative to 
what would be expected if the flat surface were not present. Thia sound pressure level can 
be regarded as a function of frequency, sound sped in air, heights of source and receiver, 
and horizontal distance from source to receiver, tu well as the real and imaginary parts of 
the surface impedance. The latter quantitiw are presumed to depend on frequency and 
flow-resistivity u in a semi-impirical manner predicted by Delany and Bazley [6], such that 
R f -0.76 - = 1 + 9.08( -) 
PC U 
X f -0.79 - = 11.9(-) 
PC U 
Here the left sides are dimensionless and the flow resistivity u has the customary units of 
cgs Rayls (so the coefficients 9.08 and 11.9 have correspondingly awkward units). 
The consequence of Eqs. (1) is that, for given source and receiver locations, there 
is a unique graph of sound pressure level (re open environment expected values) versus 
NAG-1-566 Semiannual Report No. 5, page 5 
frequency for any given value of Q. Consequently, given that the theoretical model and the 
general forma of Eqs. (1) are correct, one can infer the value of u from a plot of sound 
pressure level versus frequency. Once such a value of u hss been determined, one can then 
use Eqs. (1) to compute the real and imaginary values of surface impedance for any value 
of frequency. 
Our implementation of this technique is to experimentally determine (using our spark 
source and taking ratios of Fourier transforms) the sound pressure level (which here, strictly 
speaking, is an excess attenuation in dB) versus frequency and also plot simultaneously 
theoretical curves that correspond to different values of u. The inferred experimental value 
of cr corresponds to that of the theoretical curve which best matches the experimental sound 
pressure level versus frequency curve. acoustical preperties of fibrous aborbent materials 
Some typical results are shown in Figs. 1 and 2, which depict the predicted and the 
measured SPLversus-f curves for sound propagating over carpet and plywood, respectively. 
For both sets of data, the source height is two centimeters and the receiver height is 0.3 
cm. For the data shown in Fig. 1 (carpet), the horizontal separation distance between 
source and receiver is 80 cm. For the data shown in Fig. 2 (plywood), it is 100 cm. It is 
inferred from these figures that for plywood u is approximately equal to 80,000 cgs Rayls. 
For carpet , Q is approximatey 1500 Rayla cgs. These values, when inserted into Eqs. (1) 
predict values of R and X at the characteristic laboratory experiment frequency of 20,000 
Hz which are about the same as the values of R and X for asphalt covered ground and gram 
covered ground, respectively, at the characteristic field experiment (outdoors) frequency of 
loo0 Ha. 
NAG-1-566 Semiannual Report No. 5, page 6 
Figure 1. Typical results for determination of flow resistivity u of carpet material on 
plywood. Shown are predicted and the measured SPGvereus-f curves for sound propagating 
over carpet; the source height is two centimeters and the receiver height k 0.3 cm; the 
horizontal separation distance between source and receiver is 80 cm. F’rom the data shown 
it is inferred that o is approximatey 1500 Rayls cgs. 
b , 
NAG-1-566 Semiannual Report No. 5 ,  page 7 
Figure 2. Typical results for determination of flow resistivity Q of plywood. Shown are 
predicted and the measured SPL-versus-f curves for Bound propagating over carpet; the 
source height is two centimeters and the receiver height ie 0.3 cm; the horizontal separation 
distance between source and receiver is 100 cm. From the data shown it is inferred that Q 
is approximatey 80,000 Rayls cgs. 
NAG-1-566 Semiannual Report No. 5, page 8 
REFERENCES 
[l] Semiannual Status Report No. 1, NASA Grant NAG-1-566, Georgia Institute of Tech- 
nology, Atlanta, September 1985. 
[2] Semiannual Status Report No. 2, NASA Grant NAG-1-566, Georgia Institute of Tech- 
nology, Atlanta, February 1986. 
(31 Semiannual Status Report No. 3, NASA Grant NAG-1-566, Georgia Institute of Tech- 
nology, Atlanta, August 1986. 
[4] Semiannual Status Report No. 4, NASA Grant NAG-1-566, Georgia Institute of Tech- 
nology, Atlanta, February 1987. 
[5] T. F. W. Embleton, J. Piercy, and G. Daigle, “Effective flow resistivity of ground 
surfaces determined by acoustical measurements: J. Acoust. Soc. Am. 74(4), 1239- 
1244 (1983). 
[6] M. E. Delany and E. N. Bazley, “Acoustical preperties ef fibrous aborbent meterials, 
Applied Acoustics 3, 105-116 (1970). 
NAG-1-566 Semiannual Report No. 5, page 9 
DEVELOPMENT OF COMPUTATIONAL ALGORITHMS 
The following pages reprint a paper written and published by Allan Piere and Geoffrey 
Main during the subject reporting period. The proper citation for this paper is as follows: 
Allan D. Pierce and Geoffrey L. Main, "Computational algorithms for the matched asymp 
totic expansion solution of high frequency acoustic wave diffraction by curved surfaces of 
finite impedance," in Advance8 in Computer Methods for Partial Differentid Equation8 e VI 
(R. Vichnevetsky amd R. S. Stepleman, editors), International Aseociation for Mathemat- 
ics and Computers in Simulation (IMACS), Rutgers University, Department of Computer 
Science, New Brunswick, New Jersey 08903, 1987, pp. 187-194. 


Sound propagation over uneven ground and irregular topography

Sound propagation over uneven ground and irregular topography

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