NASACR-145138BBN Report No. 3379

Measurements of the Reflection Factorof Flat Ground Surfaces

byC. S. VentresM. M. Myles

I. L. Ver

Prepared under Contract No. NAS1-13814by

Bolt Beranek and Newman Inc.Cambridge, Mass. 02138

for

NASANational Aeronautics and

Space AdministrationLangley Research CenterHampton, Virginia 23665

https://ntrs.nasa.gov/search.jsp?R=19770013433 2018-07-17T10:49:45+00:00Z

1. Report No.

NASA CR-1451382. Government Accession No.

4. Title and Subtitle

MEASUREMENTS OF THE REFLECTION FACTOR OFFLAT GROUND SURFACES

3. Recipient's Catalog No.

5. Report DateApril 1977

6. Performing Organization Code

7. Author(s)

C.S. Ventres, M.M. Myles, I.L. Ve>

8. Performing Organization Report No.

3379

10. Work Unit No.9. Performing Organization Name and Address

Bolt Beranek and Newman Inc.50 Moulton Street .Cambridge, Massachusetts 02138

11. Contract or Grant No.

NASI-13814

12. Sponsoring Agency Name and Address'

NASA Langley Research CenterHampton, Virginia 23665

13. Type of Report and Period Covered

Contractor Report

14. Sponsoring Agency Code

15. Supplementary Notes

NASA Langley Technical Monitor: Herbert R. Henderson

16. Abstract

This report discusses measurements made of the reflection factors of asphalt, concrete,and sod at oblique angles of incidence.

Initial measurements were carried out in an anechoic chamber to eliminate the effects ofwind and temperature gradients. These were followed by measurements made outdoors over a widerfrequency range. Data are presented for the magnitudes of the reflection factors of asphalt,concrete, and sod at angles of incidence of 38° and 45°.

17. Key Words (Suggested by Author(s))

Ground Reflection, Ground Impedance,Reflection Factor

18. Distribution Statement

Unclassified

19. Security dassif. (of this report)

Unclassified20. Security Classif. (of this page)

Unclassified

21. No. of Pages 22. Price"

* For sale by the National Technical Information Service, Springfield. Virginia 22161

NASA-C-168 (Rev. 10-75)

TABLE OF CONTENTS

page

SECTION 1: INTRODUCTION- 1 •

SECTION 2: CORRELATION METHOD,...- HARMONIC*INPUT SIGNAL 2

2.1 Description -o"f' Method '•'".•--;"t.•. . . v .. 22 . 2 Instrumentation .-./.•.._.... 8

2.3 Dicsussion of Results ..-"...'..:-. 8

SECTION 3: PHASE-CANCELLATION MEASUREMENTS IH

3.1 Review of Method 14

3. 2 Instrumentation 16

3.3 Results Obtained and Discussion 19

SECTION 4: FILTERED RANDOM NOISE CORRELATION METHOD;OUTDOOR MEASUREMENTS 26

4.1 Measurement Technique 26

4.2 Instrumentation 30

4.3 Discussion of Results 30

SECTION 5: SUMMARY AND CONCLUSIONS 39

LIST OF SYMBOLS 4l

REFERENCES 43

iii

LIST OF FIGURES

Figure page

1. SCHEMATIC OF SINE WAVE CORRELATION METHOD 3

2. GEOMETRY OF EXPERIMENT 5

3. GRAPHICAL SOLUTION FOR AMPLITUDE AND PHASE OFREFLECTED WAVE (PHASOR DIAGRAM) 7

4. INSTRUMENTATION BLOCK DIAGRAM; SINE WAVECORRELATION METHOD 9

5. SOUND SOURCE "T" TERMINATION 10

6. MEASURED MAGNITUDE AND PHASE OF REFLECTION FACTOR ;ALUMINUM PLATE, 6 = 45° . . . •. 11

7. INSTRUMENTATION BLOCK DIAGRAM; PHASE CANCELLATIONMETHOD 17

8. TYPICAL STRIP CHART RECORDING; ASPHALT SAMPLE 18

9. TEST GEOMETRY, SHOWING DIFFRACTED RAY PATHS 21

10. REFLECTION COEFFICIENT; CONCRETE, 6 = 45° 23

11. REFLECTION COEFFICIENT; ASPHALT, 0 = 45° 24

12. INSTRUMENTATION BLOCK DIAGRAM; FILTERED WHITENOISE CORRELATION METHOD 31

13. PHOTOGRAPH OF CYLINDRICAL HORN FITTED TO SOURCEDRIVER 32

14. EXAMPLE OF CORRELATION PLOT: FREQUENCY = 2000 Hz,9 = 45°, CALCULATED |R| = 0.842, ASPHALT 33

15. REFLECTION COEFFICIENT; MOWED GRASS, 6 = 38° 34

16. REFLECTION COEFFICIENT; MOWED GRASS, 0 = 45° 35

17. REFLECTION COEFFICIENT; ASPHALT, 9 = 30° 36

18. REFLECTION COEFFICIENT; ASPHALT, 0 = 45° 37

IV

SECTION 1

INTRODUCTION

In outdoor sound propagation problems, especially in out-door acoustical testing, sound reflected from the ground con-taminates in the direct sound to be measured. This contamina-tion is basically unavoidable. Knowledge of the ground reflec-tion factor is useful in:

(1) Predicting the possible extent of ground contamina-tion in the planning stages of an experiment, and

(2) Reconstructing the direct sound from the measuredsound, that is contaminated by the ground reflec-tion.

This study was initiated to develop practical, workablemethods by which the reflection factor of representative groundsurfaces could be measured. Interest was centered upon surfacescommonly encountered in aeronautics, such as asphalt and sod(grass-covered soil).

Item (2) above, requires knowledge of the phase as well asthe amplitude of the reflection factor. As a consequence, thefirst phase of this project was aimed at developing methods ofmeasuring the phase as well as the amplitude of the reflectionfactor. A method had already been developed for measuring theamplitude of the reflection factor, one that was demonstratedto work on a specific, highly absorptive surface (Ver and Myles,1973)*- The initial measurements were carried out in an anechoicchamber in order to eliminate the effects of wind and temperaturegradients. In later phases of the program, outdoor measurementswere conducted for the dual purposes of extending the frequencyrange of the data obtained indoors, and estimating, as far aspossible, the effects of meteorological conditions near theground.

*A list of references is provided on page 43.

SECTION 2

CORRELATION METHOD - HARMONIC INPUT SIGNAL

2.1 Description of Method

During the first phase of the program, an attempt was madeto measure both the phase and the amplitude of the reflectionfacotr. The method used is described below.

A schematic drawing of the experimental set up is shownin Pig. 1. (The instrumentation used is discussed in Sec. 2.2.)The basic idea of the method was to create an omnidirectionalsound field at the desired frequency, and to measure the cor-relation between the harmonic input signal supplied to thedriver (sound source) and the output signal from the microphone.This measurement is made once with only the driver and micro-phone in the ariechoic chamber, and then again with the testsurface in place. In the first case, the microphone receivesonly the acoustic signal that travels directly from the driver,whereas in the second case both the direct signal and thesignal reflected off the test surface are present.*

The electrical signal supplied to the driver is a simplesinusoid, which may be written as

e(t) = Re {Ee*ut} (1)

where "Re" is an abbreviation for "the real part of," and 01 isthe radian frequency of the signal. In a free field (no reflect-ing surface present), the sound pressure at a distance, s, fromthe driver may be written as

p (t) = Rei

io)(t-s/c)

EA - (2)

*If the surface being measured is highly absorptive, a barriermust be used in the chamber to attenuate the direct signal sothat it is comparable in amplitude to the reflected signal.Three, rather than two sets of measurements are then required,but the essential features of the method are not altered. Referto Ver and Myles (1973) for details.

ANECHOIC CHAMBER

REFLECTING PLANE

CORRELATOR

AUDIOOSCILLATOR

FIG. 1. SCHEMATIC OF SINE WAVE CORRELATION METHOD.

where A is a complex quantity representing the acoustic outputof the driver at a unit distance, and c is the speed of sound.

With the reflecting plane in place, the pressure at thesame straight-line distance, s, from the source is

P2(t) = Re EA R (3)

In this equation, R is the complex reflection factor of the sur-face under investigation, and r is the length of the reflectedpath (see Pig. 2}.

As mentioned previously, the cross-correlation functionsof the electrical input to the driver (Eq. 1) and the microphoneresponse are measured first with only the driver and microphonein the chamber, and again with the reflecting plane in place.In the first case, the cross-correlation function, obtainedfrom Eqs. (1) and (2), is

I A I • Re <

CD

while in the second case it is

C (T) = |E|2 |A2 i i i Re<

0)

*r . A A(T - — + — + —C CO CO

+ |R|

In these equations, |A|and <j>A are the modulus and phase of A,|R| and <j)pj are the modulus and phase of R, and T is an arbitrarydelay time. It is convenient to re-write these expressions as

C (T) = Re < C ei I i

(5a)

SOURCE

SAMPLE

RECEIVERMICROPHONE

FIG. 2. G E O M E T R Y OF E X P E R I M E N T .

C (T) = Re { C e (5b)

where

C s I E I 2 IAI (6a)i s

C -= (6b)r r

s f

">Tr E f - *A - *R

Prom Eqs. (6a through 6d), the amplitude and phase of the reflection factor can be solved for:

<7a)

*„ = u(T -T ) + £ (r-s) (7b)- T i I X O

However, in the experiment only the amplitudes and phase lagsof the two correlation functions may be measured directly. Theamplitude and phase lag of the. free-field correlation functionCjCr) are the quantities Ct and coTj appearing in Eq . (5a); theamplitude, C2, and phase lag, wT2, of the correlation function,CZ(T), satisfy the complex equation

-iu)TC e 2 = C e 1 + C e r ( 8 )2 i r

which follows from Eq . (5b). Cr and Tr can be determined bysolving this equation (which, being complex, is equivalent totwo real equations). A phasor diagram of this equation is shownin Pig. 3- Once Cr and Tr are known, the amplitude and phaseof the reflection factor can be obtained from Eqs. (7a) and (7b),

C e~lwTr = Cv.re ^2 - C, e'lftMl

FIG. 3. GRAPHICAL SOLUTION FOR AMPLITUDE AND PHASE OFREFLECTED WAVE (PHASOR DIAGRAM).

2.2 Instrumentation

The heart of the measurement system, as shown in Fig. 4, isa digital correlator in parallel with a phase meter. The sourceoscillator is tuned to a fixed freuqency, and the correlator andphase meter receive as inputs the output signal of the sourceamplifier and the microphone signal; the latter is filtered forbetter signal-to-noise ratio. The amplitude of the calculatedcorrelation function (a sine wave) and the indicated phaseangle serve as inputs into a computer program to evaluate Eqs.(7a) and (7b) for the amplitude and phase of the reflectionfactor.

Because a level difference between the direct and reflectedpath directions of even a few decibels could result in a signi-"ficant error in computing the reflection factor, the sound sourcemust be omnidirectional. The source arrangement used consistedof an electrostatic horn driver and an acoustic transmissionline made up of flexible plastic tubing and ordinary 1/2 in.iron pipe. The driver, described in Ver and Myles (1973), re-mained outside the chamber. That portion of the pipe withinthe chamber was lagged to minimize spurious sound radiation.The pipe was terminated by a pipe "T" fitting oriented hori-zontally, as shown in Fig. 5- The source had a radiation patternwhich was cylindrically symmetric about the axis of the "T",and so radiated equally in the directions of both the directand reflected paths. Measurements made at several angles indi-cated that the source was indeed cylindrically non-directionalto within ±1.0 dB. By plugging the openings of the "T", it wasalso established that the intensity of the sound radiated bythe pipe walls was at least 28 dB lower than that of the soundradiated from the pipe termination at all frequencies of interest,

2.3 Discussion of Results

Results typical of those obtained by this method are shownin Fig. 6. The reflecting surface is an aluminum sheet 5/16inch thick and about four feet square. The sheet was placedon glass fiber pads to minimize resonant oscillations. Alsoshown in the same figure is the magnitude of the reflectionfactor as determined by the phase cancellation method (Verand Myles, 1973).

The two methods provide comparable values for the amplitudeof the reflection factor except at low and high frequencies.More important is the behavior of the phase angle <J>TDJ which isn

QO

oo

LU

I/O

Q

O_JCO

PIPE LAGGINGTREATMENT

OPENING2cm I.D.

MICROPHONE

FIG. 5. SOUND SOURCE "T" TERMINATION,

10

Of.Oi—u

ZOI—uUJ

Of.

1.2

1.0

0.8

0.6

0.4

0.2

00

-60

-120

•- sU Q)"J S» "ISOu_ q>

ocu_

OUJOID

O

^\x

—

S r*/ \iv / y

fr

CORRELATION METHODPHASE CANCELLATIONMETHOD

A^

QC.

2u

o:u_OUJto

Xo.

-240

-300

-3601000 2000 3000 4000 5000

FREQUENCY ( H z )

FIG. 6. MEASURED MAGNITUDE AND PHASE OF REFLECTION FACTOR;ALUMINUM PLATE, 9 = 45°.

11

not as expected. Because the aluminum plate is a hard surface,the phase angle should be small except near the coincidencefrequency, which for this plate and angle of incidence is about42000 Hz. When the experiment was repeated at the same reflec-tion angle but with a slightly different relative placement ofsource, reflecting plane, and receiver microphone, the measuredvalues of the magnitude of the reflection factor were found tobe repeatable with a precision of ±10%. However, the measuredvalues of the phase angle could not be repeated.

The phase angle <(>R is determined by comparing the phasesof the direct and reflected signals. Refering to Eq. (7b), andnoting that u>/c = 2ir/A, (X E wavelength),

= 2ir f -277 (9)

Let Ars be the error incurred in measuring the path length dif-ference (r-s). The concommitant error in 4>R is

A<J>y A_ rs2ir A

In this equation, the error A<J>R has been normalized by 2ir radians,or 360°. The allowable error in the path length measurement isrelated to the wavelength of the acoustic signal, rather. thanto the lengths of the propagation paths. This fact imposes astringent requirement on the dimensional accuracy of the testarrangement, particularly at the high frequencies.

At lower frequencies, where this requirement is less severe,diffraction from the edges of the sample can contaminate theresults. We sought to minimize this source of error by usingsamples whose lateral dimensions were 4 to 6 times the longestwavelengths involved, and by arranging the sound source, sample,and receiver microphone so that the acoustic image point wascentered on the sample. (The image point is that point on thesample where a ray extending from the sound source to the sampleand from there to the microphone forms equal angles, 6, of inci-dence and reflection.) Despite these precautions, spurioussignals believed to be caused by edge diffraction were encounteredat all frequencies (see Sec. 3-3).

12

Our inability to achieve repeatable results in the anechoicchamber using the correlation method led us to revert to thephase cancellation method for all subsequent indoor measurements

13

SECTION 3

PHASE-CANCELLATION MEASUREMENTS

3.1 Review of Method

The phase-cancellation method (Ver and Myles, 1973) wasused for all subsequent indoor measurements. With this method,the sound pressure level created by an omnidirectional pointsource in an empty anechoic chamber was recorded on a stripchart as the frequency was varied. These measurements wererepeated with the sample reflecting surface in place (recorded,for convenience, on the same strip chart). The second tracedisplays pronounced maxima and minima at those frequencies forwhich the direct and reflected acoustic signals interfered con-structively and destructively. By comparing the sound levelsrecorded with and without the sample in place, the magnitudeof the reflection factor can be inferred. In principle, thefrequencies at which the constructive or destructive inter-ference occurs can be used to determine the phase angle of thereflection factor as well. However, our measurements of thephase angle displayed the same scatter as encountered in thesine wave correlation measurements discussed in Section 2. Thisscatter can be attributed to diffraction from the edges of thesample (see Section 3.2).

Referring to Fig. 2 and Eq. (3)5 the pressure at the re-ceiver microphone at a frequency for which destructive inter-ference (pressure minimum) occurs is

|p I = |E A | i - -LEU- (10)I rnn yi ' ' ' I o TO I x 'min'

while at a frequency at which constructive interference (pres-sure maximum) occurs,

|P | = |EA | - + -"- (11)1 max' ' ' \ s ^ '

In the absence of the sample, the pressure is given by the firstterm in each of these expressions:

'Pfree'

The ratios of the pressure minima and maxima to the free-fieldlevels at the same frequency can be used to determine the re-flection coefficient (amplitude of the reflection factor) at therespective frequencies. Specifically, at a frequency for whichdestructive interference occurs,

I RI =1 i 1- Ipmin/Pfreel

while at a frequency for which constructive interference occurs,

|R| = - (|P /P. | -1 1 s \ ' m a x free1

Two sources of error inherent in this method of measurementmust be mentioned. First, if the free field pressure (P in

Eqs. [13] and [14] above) varies rapidly with frequency, it isdifficult to judge precisely the extreme values of the pressureratios by inspecting the strip chart recording (a sample ofwhich is shown in Fig. 8). In our experiments, this variationwas reduced by using a feedback arrangement to minimize thevariation of the free field output of the sound source withfrequency (see Section 3-2). Second, when destructive inter-ference occurs, the sound pressure levels being measured maybe quite small. For example, at a grazing angle of incidenceof 30°, and in a situation where the source and receiver areequidistant from the surface, the ratio of direct to reflectedpath lengths is s/r = cos (30°) = 0.866. If the surface isvery hard so that |R| = 1, then, from Eqs. (10) and (12)

P . /P- = (l - - |R|] = 0.134 (15)mm free \ r ' '/ J

In this case, the minimum pressure is about 17 dB lower thanthe free field value. The background noise level, as well asextraneous emissions from the point source (casing radiation orharmonics of the driver frequency) must be reduced to at least10 dB below this level, or 27 dB below the free-field level.This places stringent requirements upon both the performancecharacteristics of the noise source, and the environment inwhich the measurements are made. These requirements are moresevere for highly reflective surfaces and for grazing angles ofincidence (which correspond to R - 1 and s/r = 1 in Eq . [15]).

15

3.2 Instrumentation

The phase cancellation method, which is essentially thesame as that described by Ver and Myles (1973), employs a sweptoscillator/tracking filter arrangement, as shown in Pig. 7.

The omnidirectional source exposes the sample to a pure toneacoustic signal generated by an oscillator whose frequency isvaried continuously. The tracking narrow band filter, gangedto the oscillator, is always centered on the frequency of theswept sine wave and filters the output from the measurementmicrophone. The filtered microphone output level is recordedas a function of frequency on the graphic level recorded. Twofrequency sweeps are made, one. with the sample surface in thechamber, and one with the chamber empty. A sample recording isshown in Fig. 8.

As mentioned previously, a refinement was made in the tech-nique which reduced the measurement error caused by the non-flatfrequency response of the source. An automatic level recorder,or compressor, was used to regulate the output of the soundsource as the frequency of the oscillator was swept upward. Thecontrolling feedback was provided by a microphone placed near tothe source. In order to eliminate low frequency ambient noisethat would have disturbed the feedback signal, the control micro-phone output was A-weighted before the control input of the com-pressor. As a result of this level regulation procedure, theon-axis response of the source-receiver system was nearly flatwith frequency, so that the difference between the two graphiclevel recorder traces could be read directly, without the errorsintroduced by variations in the frequency response A(u).

The BBN anechoic chamber in which these measurements weremade is 2.4 m high and has a floor measuring about 2.4 m by 3 m.The lower cut-off frequency of the chamber is about 400 Hz.

The floor of the chamber is constructed of wire mesh. Inorder to preserve the dimensional integrity of the experimentwith workers moving about in the chamber, the pipe that formedthe point noise source was cantilevered from one wall, whilethe sample reflecting surfaces and the receiver microphone weresuspended from the ceiling. The samples themselves consistedof plywood trays 7-5 cm deep and 1.22 m square, into which theconcrete, asphalt, etc. were poured. The asphalt was heatedwith a blow torch and tamped down to compact it.

16

QO

UJo

Q

o_iCQ

oo

17

<c3:o.

•a:

Oo;oi_>LUa:

o

D_l—io:l—oo

CO

18

The 1.22 m square samples were the largest reflectingsurfaces that could be accommodated within the chamber. Itwas not anticipated therefore, that meaningful measurementsof the reflection factor could be made much below 1000 Hz.The actual limit turned out to be higher than this — about2000 to 3000 Hz.

3.3 Results Obtained and Discussion

The strip chart recording diplayed in Fig. 8 is typicalof the results obtained. In this case, the reflecting surfacewas asphalt; the sound source and receiver microphone were bothelevated 123.2 cm above the surface, and were spaced 150.3 cmapart. The length of the direct path was 150.3 cm while thereflected path length was 288.3 cm.

The frequency increment between successive maxima or minimacan be found by taking the absolute value of both sides of

Eq. (3), and introducing R = JR| e"R

P =EAs

- - 4>R1 + -

rR

The pressure maxima occur when

^ (r-s) - <{>R = 0, 2TT , ITT,

and the minima when

- <J)R = TT, 3TT, 57T,

The frequency increment between successive maxima (or minima)is then (assuming that the phase of the reflection factor <j> ,does not vary too rapidly with frequency),

2TT — (r-s) = 2rrc

19

or

Af =r-s

Using c = 3/J2 m/sec and r-s = 288.3 - 150.3 = 1?8 cm, we obtainAf = 247 Hz, which agrees reasonably well with the spacing be-tween the extremes shown in Pig. 8.

However, the envelope of the solid line in the figure(measured with the asphalt sample in place) is itself modulated.The modulation is more pronounced at low frequencies, and theinterval between the peaks in the modulation envelope is be-tween 1200 and 1300 Hz.

One way to explain this modulation is to assume that sounddiffracted from the edges of the sample nearest the sound sourceand receiver microphone interfered with the direct and reflectedfields (see Fig. 9). Because of the symmetry of the locationsof the noise source and receiver microphone, the lengths of thetwo diffracted paths are equal. In this situation the magnitudeof the pressure at the microphone would be

P| = |EA|

icod

+ R + De (16)

In this equation, d is the path length from the source to eitherof the fore and aft edges, and from there to the receiver micro-phone. D is the complex amplitude of the diffracted signal.The most pronounced maxima and minima will occur when the lasttwo terms in Eq. (16) agree in phase, while the weakest willoccur when they are out of phase. When they are in phase,

- (d-r) = 0, 2fT, ITT, . . .C

while when they are out of phase,

^ (d-r) = TT,

20

SOURCERECEIVERMICROPHONE

SAMPLE SURFACE d=d'+d

FIG. 9. TEST GEOMETRY, SHOWING DIFFRACTED RAY PATHS.

21

The frequency increment between any two successive phase additionsor cancellations is

2Tr — (d-r) = 2?rc

so that

cAf =(d-r)

In the situation being discussed here, the distance d (to eitheredge) is 314.6 cm while r is 288.3 cm. Using c = 3*12 m/sec, weget

Af = 1303 Hz ,

which agrees well with the period of the modulation in Fig. 8.

Once the importance of edge diffraction was realized, anattempt was made to diminish it by supporting two layers of1/2 in. thick glass fiber mat above the edges of the sample soas to break the line of sight between source, edge, and receivermicrophone. This reduced the amplitude of the modulation about50% above 3000 Hz, but had little effect at lower frequencies.

Edge diffraction remains, therefore, a major limitationon the precision that could be realized in the indoor measure-ments of the reflection coefficient. This limitation appliesas well to the sine wave correlation measurements discussedin Section 2.

The reflection coefficients (magnitude of the reflectionfactor) measured for concrete and asphalt are displayed inFigs. 10 and 11, respectively. Most of the scatter in thedata, as well as the measured reflection coefficients exceedingunity in Fig. 10, may be attributed to edge diffraction, asdiscussed above. No results are shown for frequencies lessthan 2000 Hz for the same reason. The driver was unable toattain an adequate signal-to-noise ratio above 7000 Hz. Despitethe spread in the data, the measured reflection coefficients forthe asphalt sample are significantly lower than those for theconcrete.

22

£* 1.5

onO

1.0

DC.

OID

O

0.5

CONCRETE 0 =45

I2000 4000

FREQUENCY (Hz)8000

FIG. 10. REFLECTION COEFFICIENT; CONCRETE, 8 =45°.

23

Q£ 1.3

1

OC

OU

u_

z i.oOt—UUJ

IIi M

UJOC

0 OS

UJ

1—

zO< 0< 2C

\ \ \

A A A

A A A A A ^

A A* AV- A A ^

ASPHALT 6 = 45°

1 1 1)00 4000 80(

FREQUENCY ( H z )

FIG. 11. R E F L E C T I O N C O E F F I C I E N T ; A S P H A L T , 8 = 45'

Becuase of the limitations of the data obtained in theanechoic chamber for asphalt and concrete, no further indoormeasurements were carried out. All subsequent tests wereconducted outdoors.

SECTION 4

FILTERED RANDOM NOISE CORRELATION METHOD; OUTDOOR MEASUREMENTS

This method, which was employed to measure the reflectioncoefficient outdoors, avoids the gross sensitivity to geometryinherent in the sine wave correlation method, and the sensitivityto ambient noise that exists with the sine wave phase cancella-tion technique. It cannot, however, be used to measure thephase of the reflection factor.

4.1 Measurement Technique

The geometry of the experimental setup is the same as thatdepicted in Pig. 2. In this case, the source is fed with bandlimited random noise, whose Power Spectral Density is given by

tG(o))=G ; o)0 < to < 0)x, — — u

= 0 ; otherwise (17)

(jJ0 = band lower limit, w = band upper limit.A/ U.

A "source microphone" is placed close to the source, the outputof which is correlated with the signal measured at the receivermicrophone position. Using the nomenclature presented pre-viously, the cross-correlation function is thus

ssi

r~s

(18)sr

where s = distance from source to source microphone,i

26

We assume that R(w) is constant over the frequency band^<J>R

and represent it as |R| e . By noting that we can change thelimits of integration to those of the passband and that G isconstant over the band, we obtain:

C(T) =_ _

2 IT

u

/ s~s \iw IT - I

\ c /G e

W,ss

+ G|R| e

\

r / r-s \tw (T - -1 + i

[_ \ c / R

rs

,dco (19)

By defining = t + —- ; we obtainO

1TT

W

f U

J }

U£

G cos w(£ - — ) G R cos w (C - — IL \ c / J , L \ c / J

ss rsi i

da>

(20)

For convenience, we define Aw = w - w,, andu £

2_IT

G

ssCOSO)

W + W

u)c = 2 U • Thus,

G|R| si

rs - t) cosw - I + *R)

27

This function consists of two sin x/x envelopes centered attimes £j = £ - s/c and £ = 5 - r/c, with corresponding amplitudes, G/SSJ and GJRl/rSj.

We can see, by inspection, that the first envelope hascoefficients related only to the direct path, and the secondhas coefficients related only to the reflected path. The re-flection coefficient is thus obtained by the ratio of themagnitudes of the maxima of the two envelopes. Hence,

where

C - ; the measured magnitude of the maximum of the1 ssi first envelope

; the measured magnitude of the maximum of thesecond envelope

Note that Eq. (22) is valid only when the two envelopesare separated widely enough in time that the respective maximaare practically determined only by that sin x/x envelope whichis centered at the specific time delay.

The argument of the envelope of the function in Eq. (21),is proportional to the signal bandwidth Aw. Consequently,the narrower the bandwidth, the broader the envelopes will bein delay time, and the greater the path-length difference thatmust exist to avoid superposition of the two. This require-ment creates an inverse relationship between frequency resolu-tion and the physical size of the experiment. This situationis most acute for near-grazing incidence and low frequencybands (if proportional bandwidths, such as octave or one-thirdoctave bandwidths, are used).

We found that a relative bandwidth of one octave representeda reasonable compromise solution to the size-frequency dilemmafor the angles and frequencies we wished to measure. We wereable to measure down to the 250 Hz octave band at an incidenceangle of ^5° with source-receiver separations of about 10 m.

28

(Our primary physical limitation was the height at which wecould support the 10 kg.driver, using a structure that waseasy to erect and transport.)

Using a band of frequencies rather than a single tone givesa reflection factor averaged over the band. However, measure-ments made using single-frequency techniques (such as by Embleton,et al.3 1976) indicate that the reflection factor magnitudes forgrass and asphalt are not strong functions of frequency, and sofine frequency resolution may not be a significant advantage.Moreover, measuring octave-band average reflection coefficientsusing the filtered white noise correlation technique is com-patible with established methods of measuring acoustic absorp-tion, notably the Reverberation Room Method (ASTM Standard C423[1972]).

Lack of severe sensitivity to ambient noise, distance meas-surement errors, and phase made the filtered while noise cor-relation technique the most attractive for outdoor measure-ments, where conditions are much less controllable than in thelaboratory. The results obtained using this technique weredecidedly more consistent and repeatable than were data obtainedusing the methods described earlier.

The insensitivity of this method to ambient noise stemsfrom the use of the cross-correlation function, which "ignores"extraneous noise that is not correlated with the source signal.This insensitivity to ambient noise is a distinct advantage,because finding suitable measurement sites at very quiet loca-tions is often difficult. The technique can therefore be usedwhen the reflection coefficient must be measured at a specificlocation where a high ambient noise is unavoidable.

The technique is insensitive to phase disturbances becausethe calculation of the reflection factor has no phase term.This, too, is indeed a great advantage for outdoor measure-ments because the need for precision distance measuring devicesand time consuming procedure is eliminated, as are measurementambiguities — e.g., to what depth of a layer of grass shouldthe source-to-ground measurement be made? The only geometricfunction is the need for adequate path length differences, asdiscussed above.

Thus, although the technique cannot be used to measure thephase of the reflection factor, the simplicity of the setup,the ease with which the measurements are made, and the accuracyof the method make it a useful procedure.

29

4.2 Instrumentation

Figure 12 is a block diagram of the system as it was em-ployed in the field. As with the sine wave correlation method,a digital correlator was the heart of the system. Both thenoise source and the receiver microphone signals were filteredin a bandwidth of one octave using a tunable filter that couldbe centered at any arbitrary frequency (i.e., not only atstandard octave band frequencies).

A special horn with a cylindrically symmetric radiationpattern, was fitted on the source driver. As seen in the photo-graph of Fig. 13, the horn is an exponential flare of revolu-tion; i.e., it is a cylinder, any radial section of which is ahorn-shaped flare.

Figure 1^ shows a typical correlation plot. Two distinctsin x/x envelopes are visible; the one on the left correspondsto the direct path, while the one on the right corresponds tothe reflected path.

4.3 Discussion of Results

The results of the outdoor measurements using the filteredwhite noise correlation technique are graphed in Figs. 15through 18. These data are for the reflection factor averagedover a bandwidth of one octave centered at the frequency in-dicated. The method was used to measure the magnitude of thereflection factor for mowed grass and asphalt, at two anglesof incidence for each surface.

The data were, in almost all cases, consistently repeatableto within the limits of experimental accuracy. At frequencieswhere repeat measurements were made, more than one measurementvalue is plotted in the graphs.

The data for grass (Figs. 15 and 16) gave a reflectionfactor well below 1.0 at all frequencies. The indicated trendof decreasing reflection (increasing absorption) with increasingfrequency is to be expected, as wavelengths become smaller andapproach the length of the blades of grass.

The asphalt data (Figs. 17 and 18) are consistently near1.0 for all frequencies, as expected for a hard surface. Notethat the ^5° asphalt data agrees quite well with that measuredwith the phase cancellation method (see Fig. 11). The reflec-tion coefficient at 45° decreased slightly with increasing

30

OCJ

UJa:

cc.ID

oo

ICO

•z.ot—II—<c

rD ao: o

CM

31

FIG. 13. PHOTOGRAPH OF C Y L I N D R I C A L HORN FITTED TOSOURCE D R I V E R .

32

II

CD

Oooc\j

UJ

\— CL.o on—letO-

•*Z CMO 1-I-H 00I— •< O

O OLCJ -

LL OO UJ

1 <_>

33

Ioe.Ou

oNO

I1D

UJOf.u_oUJO

-z.O<

I.U

0.6

0.2

02^

''

'-•

• "

GRASS 0 = 38°

•'

50 500 1000 2000 4000 8000

FREQUENCY (Hz)

FIG. 15. REFLECTION COEFFICIENT; MOWED GRASS, 6 = 38'

Ioceo

»—uUJ

u.UJ

UJO

•z.O

0.8

0.6

0.4

0.2

02!

...

""

GRASS 0=45°

•

••m

SO 500 1000 2000 4000 8000

FREQUENCY (Hz)

FIG. 16. REFLECTION COEFFICIENT; MOWED GRASS, 9 = 45°.

35

1.6

-.4O£.

o

^ 1 9o '-zI—UJ

u_UJQC

* 1.0

zo< 0.8

0.6

ASPHALT 0 = 30°

250 500 1000 2000 4000 8000

FREQUENCY (Hz)

FIG. 17. REFLECTION COEFFICIENT; ASPHALT, 6 = 30(

36

IOf.

eu2

t—uUJ_iu.UJOf.

UJOZ>^-

Zo<5

10.8

0.6

0.4

0.2

02i

' -\<

ASPHALTB = 45°

1 .. ,,

SO 500 1000 2000 4000 80(

FREQUENCY (Hz)

FIG. 18. R E F L E C T I O N C O E F F I C I E N T ; A S P H A L T , 6 = 4 5 ° .

37

frequency — a trend not seen in the 30° data. We did notundertake any investigation of this phenomenon, and thereforedo not know its cause. Theory (Morse and Ingard, 1968) pre-dicts, however, that the reflection coefficient at a givenfrequency should increase for incident angles near grazing.

At one frequency band, (the 8000 Hz octave band) (for9 = 30°), the measured reflection coefficient was slightly,greater than 1.0. This result would indicate that moreacoustic energy is reflected from the asphalt surface thanwas incident upon it — an impossible result. One explanationfor the observed data is that small surface irregularities,with dimensions comparable to shorter wavelengths, createda slight focusing effect that caused a reflected ray of greateramplitude than that reflected from a true plane surface.

38

SECTION 5

SUMMARY AND CONCLUSIONS

Measurements of the reflection factor were made in an ane-choic chamber using two different techniques. The first methodused a correlator and a point source emitting a pure tone, andwas intended to determine both the amplitude and phase of thereflection factor. The measured values of the phase were erraticand could not be repeated, despite extensive efforts to refinethe technique.

The second method used for the indoor measurements was thephase cancellation method — a variation of the technique usedpreviously by Ver and Myles (1973). Data obtained over a limitedrange of frequencies for two surfaces, concrete and asphalt,showed considerable scatter. This scatter is attributed to thedisturbing effects of sound diffracted from the edges of thesamples, whose size was limited by the dimensions of the anechoicchamber. The reflection coefficient for concrete was found tobe about 1.0, while that of asphalt was lower, about 0.8 between2000 and 6000 Hz.

Outdoor measurements of the reflection coefficients of as-phalt and grass-covered soil were made using the filtered ran-dom noise correlation method because of its insentisivity toambient noise. Here again, a correlator was used, but thistime in conjunction with a noise source emitting white noisefiltered in bandwidths of one octave. The technique thusmeasured the reflection coefficient averaged over an octave,rather than at a single frequency. The averaging ability ofthe correlator made the techniques much less sensitive to ambientnoise, allowing its use in outdoor environments. •

Between 500 and 4000 Hz, the reflection coefficient of grassdrops off considerably with increasing frequency, while that ofasphalt does not. The data obtained outdoors for asphalt com-pares well with that measured in the anechoic chamber, althoughthere is considerable scatter in the latter data.

Only a small variation in the wind velocity and surfacetemperature was encountered during the course of the measure-ments made outdoors, and it had no noticeable effect on theresults obtained. This is not surprising, however, since onlythe magnitude and not the phase of the reflection factor wasmeasured. The primary effect of wind and temperature gradientsis to change the length of the propagation paths. This change

39

is usually small In comparison with the length of the propaga-tion paths themselves, but may be comparable to a wavelength.The phase of the wave reflected off the surface is thus affectedmuch more than its amplitude. Hence, measurements of the phaseangle and the reflection factor may be expected to be verysensitive to local meteorological conditions, whereas measure-ments of the magnitude would be less effected by these factors.

LIST OF SYMBOLS

A = Acoustic transfer function of sound source (Eq. 2).

C(T) = Cross-correlation function.

C = Amplitude of cross-correlation function between soundsource input and receiver microphone output (no reflect-ing plane present), (Eq. 5a).

C = Amplitude of cross-correlation function between the2 sound source input signal and the receiver micropho

output signal (reflecting plane in place).

C = Amplitude of the cross-correlation function between ther input signal to the sound source and that portion of the

receiver microphone output which is due to the reflectedsignal (Eq. 5b).

c = Speed of sound.

D = Complex amplitude of diffracted wave (Eq. 16).

d = Path length of diffracted wave (Eq. 16).

E = Complex amplitude of voltage supplied to sound source.

•e(t') = Voltage supplied to sound source.

f = Frequency.

G(w) = Power spectral density of input to sound source (Eq. 17).

P = Complex amplitude of pressure.

p(t) = Sound pressure.

R = Complex reflection factor.

Re{ } = Real part of quantity in brackets { }.•

r = Length of reflected path (Fig. 2).

LIST OF SYMBOLS (Continued)

s = Distance from sound source to receiver microphone (Pig. 2)

s = Distance from noise source to source microphone.

T = Time delay (Eq. 6c) .

Time delay (Eq. 8).

T = Time delay (Eq. 6d).

t = Time.

Greek Letters

A c = Error in measuring path length difference r-s.rlo

Af = Frequency increment.

Aw = Radian frequency bandwidth.

9 = Sound wave incidence angle (Fig. 2).

A = Wavelength.

5 = Delay time (Eq. 20) .

T = Delay time.

4>. = Phase angle of complex transfer function A (Eq.

4>R = Phase angle of complex reflection factor R.

(jj = Radian frequency .

CD = Upper limit of frequency band (Eq. 19).

w = Lower limit of frequency band (Eq. 19).A*

o) = Radian center frequency of filter band (Eq. 21)

REFERENCES

American Society for the Testing of Materials, (1972), "StandardMethod of Test for Sound Absorption of Acoustical Materials inReverberation Rooms," designation C*J23-66 (Reapproved 1972),1975 Annual Book of ASTM Standards, Philadelphia.

Embleton, T.F.W., et al., (197*0. "Outdoor Sound PropagationOver Ground of Finite Impedance," J. Acoust. Soc. Amer. 59(2)267-277.

Morse, P. and Ingard, K.U. (1968). Theoretical Acoustics,McGraw-Hill, New York.

Ver, I.L. and Myles, M.M. (1973). "Acoustical Modeling Studyof the Proposed NASA Langley Outdoor Anechoic Test Apparatus,"BBN Report No. 26l4, prepared under contract NAS1-9559-