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Submitted on 1 Jan 1979

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EXPERIMENTAL STUDY OF NONLINEARITY INFREE PROGRESSIVE ACOUSTIC WAVES IN AIR

AT 20 kHzDr. Gallego-Juarez, L. Gaete-Garreton

To cite this version:Dr. Gallego-Juarez, L. Gaete-Garreton. EXPERIMENTAL STUDY OF NONLINEARITY IN FREEPROGRESSIVE ACOUSTIC WAVES IN AIR AT 20 kHz. Journal de Physique Colloques, 1979, 40(C8), pp.C8-336-C8-340. �10.1051/jphyscol:1979860�. �jpa-00219566�

EXPERIMENTAL STUDY OF NONLINEARITY IN FREE

PROGRESSIVE ACOUSTIC WAVES IN AIR AT 20 kHz

Dr. J.A. GALLEGO-JUAREZ and L. GAETE-GARRETON

Instituto de Acustica, Laboratorio de Ultrasonidos - Serrano, 144 - Madrid 6 - Spain

Abstract. - This paper describes an experimental investigation of the propagation of periodic waves of finite amplitude in air at 20 kHz.

The acoustic source used in our experimental work is a new high-power ultrasonic transducer for use in air. This transducer, which emits a directive radiation, is able to generate a nearly pure sinusoTdal wave up to sound pressure levels over 160 dB.

The experiments were done in a 7.4 m long, 5.5 m wide and 5.5 m high anechoic chamber, using cw mode. They consisted essentially of measuring the amplitude of the fundamental component of the wave and its first three harmonics for different source pressure levels and at different distances in the farfield. In addition, oscillograms and directivity patterns were recorded.

The obtained results confirm the strong limitations in the transmission of intense waves due to nonlinear distortion. The phenomenon of acoustic saturation at high source levels is clearly observed. Also the evolution of waveforms and the changes in the radiation patterns show the effect of nonlinear behaviour.

1. Introduction. - The experimental studies on pe­

riodic waves of finite amplitude in air have been

enhanced by the interesting researches about their

outdoor propagation carried out recently by Dr.

Blackstock's group at The University of Texas at

Austin /1,2/. These works were undertaken with pe*-

riodic sources (an array of 7 to 10 horn drivers

and a siren) at frequencies in the range 6 to 8

kHz and source levels SPI_lm from 140 dB to 149 dB.

On the other hand, indoor experiments in air were

conducted by C.H. Allen in 1947-195o, but the obtai­

ned results have been reported for the first time

in the former International Symposium on Nonlinear

Acoustics /3/. In C.H. Allen's experiments a sound

field at 14.6 kHz was generated into a 2m long ane­

choic chamber by a St Clair generator which acted

as a baffled piston at a maximum SPL of 161 dB. With

the exception of these studies, very few measurements

have been published on the propagation of periodic

waves of finite amplitude in air. Particularly, the

lack of experiments appears more evident at high

audiofrequencies and at ultrasonic frequencies des­

pite the nonlinear effects are more significant.

This fact may probably be due to difficulties in

disposing adequate high-power sources. In this

paper we present some experiments on the free field

propagation in air of sinusoTdal waves of finite

amplitude at 20 kHz. The acoustic source used is a

new high-power ultrasonic transducer which emits a

high directional radiation at sound pressure levels

greater than 160 dB /4/.

2. Experiments and results. - The experimental

work consisted of measuring the amplitude of the

fundamental component of the wave and its first

three harmonics for different input powers on the

transducer and at different distances in the far

field. In addition, oscillograms and directivity

patterns were recorded. The relative pressure level

of the source was measured by a monitor microphone

mounted off-axis near the source and in such a way

that the sound waves impinged at 90° incidence.

The experiments were performed in a 7.4 m long,

5.5. m wide and 5.5 m high anechoic chamber, using

JOURNAL DE PHYSIQUE Colloque C8, supplément au n°ll, tome 40, novembre 1979, page C8-336

Résumé . - On a étudié expérimentalement la propagation d'ondes d'amplitude finie dans l ' a i r à 20 kHz. La source utilisée est un générateur aérien de puissance d'un type nouveau, capable d'atteindre

avec une grande directivité des niveaux quasi-monochromatiques de l'ordre de 160 dB. Les expériences en ondes entretenues ont été conduites dans une chambre de dimensions 7,4 x 5,5

x 5,5 m3. Les mesures essentielles ont porté sur les amplitudes du fondamental et des trois premiers har­

moniques pour différents niveaux d'émission et à des distances variables dans le champ éloigné. Les formes d'ondes et les diagrammes de directivités correspondants ont été également enregistrés.

Les résultats obtenus confirment la limitation d'amplitude transmissible par propagation non l i ­néaire. On a pu mettre clairement en évidence le phénomène de saturation acoustique.

L'évolution des formes d'ondes et des diagrammes de directivité illustrent également, ce compor­tement non linéaire.

Article published online by EDP Sciences and available at Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979860

JOURNAL DE PHYSIQUE C8-337

cw mode. A block diagram o f the measuring arrange-

ment i s shown i n Fig. 1.

TRANSDUCER b 118 ~n MlCROPHMlE

F ig . 1. - Block diagram o f the experimental apparatus.

The new transducer, used as acoust ic source,

i s a resonant device designed f o r a working f r e

quency of about 20 kHz. It cons is ts e s s e n t i a l l y

o f a p i e z o e l e c t r i c element o f t ransduct ion, i n a

sandwich con f igu ra t ion , a s o l i d horn, which acts

as a v i b r a t i o n a m p l i f i e r , and a r a d i a t o r consis-

t i n g o f a stepped c i r c u l a r p l a t e which o s c i l l a t e s

f l e x u r a l l y w i t h th ree nodal c i r c l e s . The po in ts o f

maximum s t ress i n the mechanical a m p l i f i e r and i n

the r a d i a t i n g p l a t e a re water cooled i n order t o

avoid f a t i g u e f a i 1 ure and 1 ocal overheating o f the

mate r ia l . A view o f the transducer, w i t h i t s coo-

l i n g system, i s shown i n F ig. 2. The specia l shape

Fig. 2. - Photograph o f the transducer w i t h the water coo l ing system.

o f the stepped p l a t e a l lows one t o generate an acous-

t i c f i e l d q u i t e s i m i l a r t o t h a t o f the t h e o r e t i c a l

p i s t o n o f t h e same rad ius /5,6/. I n a d d i t i o n w i t h

t h i s transducer i t i s poss ib le t o generate a near l y

pure sinusoTda1 wave up t o sound pressure l e v e l s

over 160 dB. F ig. 3. shows the a x i a l pressure d i s t r i -

bu t ion f o r the transducer w i t h e l e c t r i c a l i n p u t po-

wers o f 1 W, 100 W, and 200 W. The resonant frequen

cy i s o f 20.4 kHz.

1. INPUT POWER 1 W g, .. 100 W 3, <. " mow

-~-r--- I - 1 - -

500 6 6 0 760 8O3 903 I&

DISTANCE FROM THE CENTER OF THE PLATE (mm)

Fig. 3. - Ax ia l sound pressure d i s t r i b u t i o n o f the transducer r a d i a t i o n i n the near f i e l d .

Amplitude response curves f o r fundamental, se-

cond, t h i r d and f o u r t h harmonics were taken a t d i f -

fe ren t , f i x e d distances from 1.2 m t o 5.7 m. The re -

l a t i v e pressure l e v e l s o f the source, measured by

the moni tor microphone a t about 12 mm, var ied from

96.5 dB t o 153 dB. I n Figs. 4a, 4b, 4c and 4d f o u r

such curves a re shown. The phenomenon o f acoust ic

sa tu ra t ion a t h igh source l e v e l s i s c l e a r l y obser-

ved. Also the changes i n sa tu ra t ion w i t h d is tance

are evidenced. I n fact, i t may e a s i l y be seen t h a t

w h i l e the ex t ra a t tenua t ion f o r the fundamental

frequency a t 1.2 m i s about 11 dB, a t 5.7 m i t i s

20 dB. The l a t e r va lue represents a power loss,

due t o nonl inear effects, as h igh as 99%.

Propagation measures were made i n the d i s -

tance range 0.9 t o 5.7 m ( f a r f i e l d ) f o r the fun-

damental frequency component and i t s f i r s t th ree

J.A. Gal lego-Juarez and a1 .

OISTANCE = 1 2 rn

A SECONO HARMONIC A THIRD 0 FOURTH "

i A

i / 1 . . L . - L - . L i

95 105 115 125 135 145 155

RELATIVE SOURCE SPL ( d B )

F ig . 4a - Amplitude response curves a t 1.2 m.

Fig. 4b. - Amplitude response curves a t 2 m.

/

/ DISTANCE = 3.2 rn /

FUNOAMENTAL /

/ A SECOND HARMONIC /

140

I I I 1

95 105 115 125 135 145 155

RELATIVE SOURCE SPL ( d B )

DISTANCE = 2 rn /

- FUNOAMENTAL /

/ A SECOND HARMONIC /

~ j g . 4c. - Amplitude response curves a t 3.2 m.

A THIRD

130 - 0 FOURTH ''

,-. m 2 120 - 2 a cn

: 110- E W U W

90 -

A 80 - I . I

95 105 115 125 135 145 155

RELATIVE SOURCE SPL ( d B )

FUNDAMENTAL /

A SECONO HARMONIC /

A THlRO /

0 FOURTH /

/

A I I I

105 115 125 135 145 155 RELATIVE SOURCE SPL ( d B )

Fig. 4d. - Amplitude response curves a t 5.7 m.

harmonics. Fig. 5. shows propagation curves o b t a i -

n d w i t h the transducer operat ing a t h igh amplitudes.

FUNDAMENTAL A SECOND HARMONIC A THIRD O F O U R T H s3

100 1 i - - - 1 - - - 1 - .I 1 2 3 4 5 6

PROPAGATION DISTANCE ( rn )

F ig . 5. - Propagation curves

It i s a lso o f great i n t e r e s t t o observe the

evo lu t ion o f the waveforms through the recorded

osci l lograms and t h e i r spectra. Figures 6a. and 6b.

i l l u s t r a t e the successive changes i n the shape o f

the wave o r i g i n a t e d along the propagation d is tance

for two f i x e d source l e v e l s . The waveforms and

spectra o f received s ignal a t a constant d is tance

fo r var ious source l e v e l s a re shown i n F ig . 6c.

Note the s t rong d i s t o r t i o n s a t ta ined and i r r e g u l a -

r i t i e s such as the asymmetry o f the wave shapes

and pu lsa t ions a t the middle o f the wave. It seems

t h a t d ispers ion i s responsib le f o r the formations

of these two e f fec ts /7,8/.

JOURNAL DE PHYSIQUE

WAVE F O R M S I SPECTRA WAVE FORMS SPECTRA

DISTANCE 0.012m DISTANCE

0.012 rn.

DISTANCE 2.1 m

DISTANCE 2.1 m

DISTANCE 3.2 m.

DISTANCE L rn

5.5 m.

9 5 f 2f 3f Lf

TIME S C A L E . 2 0 p s I d l v .

- 1201

DISTANCE - 5.5 m

l o o 8 0 1 7 L f 2 f 3f L f

TlME SCALE . 2Opsldiv .

Fig. 6a. - Evolut ion o f waveforms and spectra w i t h propagation distance.

Fig. 6b. - Evo lu t ion o f waveforms and spectra w i t h propagation distance.

F i n a l l y , we present the d i r e c t i o n a l characte-

r i s t i c s o f the fundamental, second, t h i r d and

f o u r t h harmonics a t two distances i n the f a r f i e l d

and f o r two d i f f e r e n t source l e v e l s (Fig. 7 ) . I n

these pat terns, the broadening o f the major lobe

and the growing o f minor lobes w i t h increasing

amplitude can be observed. Also t h e e f f e c t s o f

f i n i t e - a m p l i t u d e a t tenua t ion on major lobes g ive

r i s e t o a r e l a t i v e increase o f minor lobes w i t h

propagation distance.

c i e n t l y h igh amplitudes and the sa tu ra t ion l e v e l

decreases w i t h propagation distance. Power losses

induced by n o n l i n e a r i t y can be as h igh as 99 % a t

r e l a t i v e l y s h o r t distances. The evo lu t ion o f wave-

forms and the changes i n the r a d i a t i o n pa t te rns

a lso show the e f f e c t s o f the nonl inear behaviour.

I n conclusion, the experimental data here

presented o f f e r s a c o n t r i b u t i o n t o the knowledge o f

high-ampli tude wave propagation and they can be

very use fu l i n examining the d i f f e r e n t es tab l i shed

t h e o r e t i c a l models. 3. Conclusion. - The propagation o f f i n i te-ampli-

tude waves i n a i r generated s i n u s o i d a l l y a t 20 kHz

by a d i r e c t i v e source, has been considered. Acknowledgements. The authors wish t o thank Dr.

D.T. Blackstock f o r h i s encouragement and sugges-

t i o n s t o i n i t i a t e t h i s work..

The obtained r e s u l t s conf i rm the strong l i m i -

t a t i o n s i n the transmission o f in tense waves due t o

nonl inear d i s t o r t i o n . The wave saturates a t s u f f i -

J.A. Gallego-Juarez, and a1 . SECQND THIRD FOURTH

FUNDAMENTAL HARMONIC HARMONIC HARMONC

2.1 rn. WAVE FORMS SPECTRA

0 0

- 5 - 5

- 10 -10 I

Pi /\ SOURCE LEVEL 3 - 15 -15

130.5dB

/I , -20 -20

80 -25 -23 1 I f 2f 3f hf

I A SOURCE LEVEL 2

142.5dE a120 V)

11° f 2 f 3 f I . f

Fig. 7. - D i r e c t i v i t y pat terns.

SOURCE LEVEL; 143.5dB

REFERENCES

TIME SCALE 2Opsldiv.

/1/ Webster, D.A., Theobald, M.A. and Blackstock, D.T., 9 ICA Contr ibuted papers I 1 (1977) 740.

Fig- 6c. - waveforms and 'pectra for various 'Our- /2/ Theobald, M.A., Technical Report ARL-TR-77-5, ce leve ls . Appl ied Research Laborator ies, The U n i v e r s i t y

o f Texas a t Aus t in (1977)

/3/ A l len, C.H., 7 th ISNLA Abstracts (1976) 226

/4/ Gallego-Juarez, J.A., Rodriguez-Corral, G. and Gaete-Garreton, L., U l t rason ics 16 (1878) 267

/5/ Barone, A., and Gallego-Juarez, J.A., J. Acoust. Soc. Am. 51 (1972) 953.

/6/ Gallego-Juarez, J.A., J. Sound Vib. 26 (1973) 411.

/7/ Webster, D.A., Technical Report ARL-TR-77-4, Appl ied Research Laborator ies, The U n i v e r s i t y o f Texas a t Aust in (1977)

/8/ Rudenko, O.V., and Soluyan, S.I., Theoret ica l Foundations o f Nonl inear Acoustics, Plenum Publ ish ing Corporation, New York, 1977.