EXPERIMENTAL STUDY OF NONLINEARITY IN FREE PROGRESSIVE ACOUSTIC WAVES IN AIR AT 20 kHz

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EXPERIMENTAL STUDY OF NONLINEARITY IN FREE PROGRESSIVE ACOUSTIC WAVES IN AIR

AT 20 kHz

Dr. Gallego-Juarez, L. Gaete-Garreton

To cite this version:

Dr. Gallego-Juarez, L. Gaete-Garreton. EXPERIMENTAL STUDY OF NONLINEARITY IN FREE

PROGRESSIVE 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�

E X P E R I M E N T A L STUDY OF N O N L I N E A R I T Y IN F R E E P R O G R E S S I V E A C O U S T I C W A V E S IN AIR A T 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 e t des diagrammes de directivité i l l u s t r e n t également, ce compor- tement 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 C 8 - 3 3 7

cw mode. A b l o c k diagram o f the measuring arrange- ment i s shown i n Fig. 1.

TRANSDUCER b ¹¹⁸ ~n MlCROPHMlE

F i g . 1.

-

Block diagram o f the experimental apparatus.

The new transducer, used as a c o u s t i c source, i s a resonant device designed f o r a working f r e quency of about 20 kHz. It c o n s i s t s 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 r a n s d u c t i o n , i n a sandwich c o n f i g u r a t i o n , 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 t h r e e nodal c i r c l e s . The p o i n t s o f maximum s t r e s s i n the mechanical a m p l i f i e r and i n t h e r a d i a t i n g p l a t e a r e water cooled i n order t o avoid f a t i g u e f a i 1 u r e and 1 ocal overheating o f the m a t e r i a l . A view o f t h e transducer, w i t h i t s coo- l i n g system, i s shown i n F i g . 2. The s p e c i a l shape

Fig. 2.

-

Photograph o f t h e transducer w i t h t h e water c o o l i n g system.

o f t h e stepped p l a t e a l l o w s 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 t h e t h e o r e t i c a l p i s t o n o f t h e same r a d i u s /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 p o s s i b l e t o generate a n e a r l y pure sinusoTda1 wave up t o sound pressure l e v e l s over 160 dB. F i g . 3. shows t h e a x i a l pressure d i s t r i - b u t i o n 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, <. " m o w

-~-r--- ^{I - 1 - -} 500 6 6 0 760 8O3 903 I&

DISTANCE FROM THE CENTER OF THE P L A T E ( m m )

F i g . 3.

-

A x i a l sound pressure d i s t r i b u t i o n o f t h e transducer r a d i a t i o n i n t h e 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 - f e r e n t , f i x e d distances from 1.2 m t o 5.7 m. The r e - l a t i v e pressure l e v e l s o f the source, measured by t h e m o n i t o r microphone a t about 12 mm, v a r i e d from 96.5 dB t o 153 dB. I n Figs. 4a, 4b, 4c and 4d f o u r such curves a r e shown. The phenomenon o f a c o u s t i c s a t u r a t i o n a t h i g h source l e v e l s i s c l e a r l y obser- ved. Also t h e changes i n s a t u r a t i o n w i t h d i s t a n c e a r e evidenced. I n fact, i t may e a s i l y be seen t h a t w h i l e t h e e x t r a a t t e n u a t i o n f o r t h e 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 v a l u e represents a power l o s s , due t o n o n l i n e a r effects, as h i g h 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 t h e fun- damental frequency component and i t s f i r s t t h r e e

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 i g . 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 ''}

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2 a cn

:

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E W U W

90 -

A

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95 105 115 125 135 145 155

RELATIVE SOURCE SPL ( d B )

FUNDAMENTAL ^/

A SECONO HARMONIC /

A THlRO /

0 FOURTH / ^/

I A I I

105 115 125 135 145 155

RELATIVE SOURCE SPL ( d B )

F i g . 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 t h e transducer o p e r a t i n g a t h i g h amplitudes.

FUNDAMENTAL A SECOND HARMONIC A THIRD

O F O U R T H s 3

100 1 i - - - 1 - - - 1 - . I

1 2 3 4 5 6

PROPAGATION DISTANCE ( rn )

F i g . 5.

-

Propagation curves

I t i s a l s o o f g r e a t i n t e r e s t t o observe t h e e v o l u t i o n o f t h e waveforms through t h e recorded oscillograms 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 t h e shape o f the wave o r i g i n a t e d along t h e propagation d i s t a n c e f o r two f i x e d source l e v e l s . The waveforms and spectra o f r e c e i v e d s i g n a l a t a c o n s t a n t d i s t a n c e f o r v a r i o u s source l e v e l s a r e shown i n F i g . 6c.

Note t h e s t r o n g d i s t o r t i o n s a t t a i n e d and i r r e g u l a - r i t i e s such as t h e asymmetry o f t h e wave shapes and p u l s a t i o n s a t the m i d d l e o f t h e wave. I t seems t h a t d i s p e r s i o n i s r e s p o n s i b l e f o r t h e formations of these two e f f e c t s /7,8/.

JOURNAL DE PHYSIQUE

WAVE F O R M S

I

S P E C T R A WAVE FORMS S P E C T R A

D I S T A N C E

0.012m DISTANCE

0.012 rn.

DISTANCE 2.1 m

DISTANCE 2.1 m

DISTANCE 3.2 m.

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DISTANCE

-

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l 8 0 o o

1 7

^L

f 2 f 3f L f TlME S C A L E . 2 O p s l d i v .

Fig. 6a.

-

E v o l u t i o n o f waveforms and spectra w i t h propagation distance.

Fig. 6b.

-

E v o l u t i o n o f waveforms and spectra w i t h propagation distance.

F i n a l l y , we present t h e d i r e c t i o n a l characte- r i s t i c s o f t h e fundamental, second, t h i r d and f o u r t h harmonics a t two distances i n t h e 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 p a t t e r n s , the broadening o f t h e major lobe and the growing o f minor lobes w i t h i n c r e a s i n g 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 t e n u a t i o n on major lobes g i v e 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 i g h amplitudes and t h e s a t u r a t i o n l e v e l decreases w i t h propagation distance. Power l o s s e s induced by n o n l i n e a r i t y can be as h i g h as 99 % a t r e l a t i v e l y s h o r t distances. The e v o l u t i o n o f wave- forms and the changes i n t h e r a d i a t i o n p a t t e r n s a l s o show t h e e f f e c t s o f t h e n o n l i n e a r behaviour.

I n conclusion, t h e experimental d a t a here presented o f f e r s a c o n t r i b u t i o n t o t h e knowledge o f high-amplitude wave propagation and they can be very u s e f u l i n examining t h e d i f f e r e n t e s t a b l i s h e d 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 c o n f i r m the strong l i m i - t a t i o n s i n the transmission o f i n t e n s e waves due t o n o n l i n e a r d i s t o r t i o n . The wave s a t u r a t e s a t s u f f i -

J.A. Gallego-Juarez, and a1

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SECQND THIRD FOURTH

FUNDAMENTAL HARMONIC HARMONIC HARMONC

2.1 rn.

WAVE FORMS SPECTRA ^{0 0}

- 5 - 5

- 10 -10

I

Pi /\

^SOURCE 130.5dB ^{LEVEL 3 - 1 5 -15}

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REFERENCES

TIME S C A L E 2 O p s l d i v .

/1/ Webster, D.A., Theobald, M.A. and

Blackstock, D.T., 9 ICA Contributed papers I 1 (1977) 740.

Fig- 6c.

-

^waveforms and 'pectra for various 'Our- /2/ Theobald, M.A., Technical Report ARL-TR-77-5, ce l e v e l s .

Applied Research Laboratories, The U n i v e r s i t y o f Texas a t A u s t i n (1977)

/3/ A l l e n , C.H., 7 t h ISNLA Abstracts (1976) 226 /4/ Gallego-Juarez, J.A., Rodriguez-Corral, G. and

Gaete-Garreton, L., U l t r a s o n i c s 16 (1878) 267

/5/ Barone, A., and Gallego-Juarez, J.A., J.

Acoust. Soc. Am. 5 1 (1972) 953.

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

/7/ Webster, D.A., Technical Report ARL-TR-77-4, Applied Research Laboratories, The U n i v e r s i t y o f Texas a t A u s t i n (1977)

/8/ Rudenko, O.V., and Soluyan, S.I., T h e o r e t i c a l Foundations o f Nonlinear Acoustics, Plenum P u b l i s h i n g Corporation, New York, 1977.