Dept. for Speech, Music and Hearing

Quarterly Progress andStatus Report

A comparison of acousticalmeasurements and holograminterferometry measurements

of the vibrations of a guitartop plate

Jansson, E. V.

journal: STL-QPSRvolume: 10number: 2-3year: 1969pages: 036-041

http://www.speech.kth.se/qpsr

STL-QPSR 2-3/1969

B. A COMPARISON OF ACOUSTICAL MEASUREMENTS AND HOLOGRAM INTERFEROMETRY MEASUREMENTS OF THE VIBRATIONS OF A GUITAR TOP PLATE

Introduction

The sound box of string instrumehts and the plates in par t icular offer

intricate physical problems. Careful studies have been ca r r i ed out of

acoustically obtained frequency responses to find correlat ions between the ( 1 ) acoustical properties and the tonal qualities of string instruments .

Experiments have been undertaken to study how changes of the instruments

appear in the frequency responses. By means of gained experience an

acoustical tes t method has been developed and is employed a s guidance in

the building of instruments ('). Recently a technique, hologram interfero- I

metry, has been developed, which gives most accurate and informative

records, holograms, of plate vibrations (3). By means of holog;ams i t is

possible to determine the frequencies and Q-values of a plate 's mode.

The holograms a lso te l l qualitatively how a change of a plate will change

the modes, i. e. i t te l ls the instrument builder what to change for a wanted

result (4). However, the apparatus needed for the holograms i s expensive

and exists only in well equipped optical laboratories.

An opportunity to compare acoustically obtained frequency responses

and vibration patterns, holograms, of a plate is the background of this in-

vestigation. A guitar (5 ) with removed s tr ings and back plate was glued a t

a massive framework. Holograms were made of the f i r s t six modes and

the Q-values were calculated ( 6 ) . The mounting made for the holography

study with the s a m e driving sys tem was also used i n the acoustical mea-

surements.

The a i m of this paper is to present some of the recorded frequency

responses and to compare the results with the resul ts of the holograms.

This gives a bet ter understanding of frequency responses and a lso how to

make these records.

General

The sound produced by a vibrating plate can be divided into th ree pro-

duction steps: 1) the driving, 2) the plate response to the driving, and

3) the sou~id radiation of the vibrating plate.

STL-QPSR 2-3/1969 37.

The driving, the excitation, determines the frequency of the vibrations.

As a mode cannot be driven along i t s nodal lines, the driving points must

be chosen with some care. The d r ive r itself shall ac t upon the plate in-

dependent of frequency and plate vibrations without influencing upon the

properties of the platel The main interest of this investigation is the f re -

quencies and Q-values of the resonance modes. In the holographic study

the driving points were therefore chosen to make the different modes ap-

pear clearly, which led to a special driving point fo r each mode. The

plate response to the driving gives the vibration pattern of the plate.

The third step, i. e. the sound radiation f rom the vibrating plate is

completely determined by the amplitude and the phase of the vibrations.

The radiated sound var ies both with spatial position and frequency and gener-

ally gives ze ro sound p res su re surfaces starting f r o m the nodal lines.

A hologram gives a picture of the plate vibrations, i. e. a recording

af te r step 2. In the frequency responses obtained by a microphone, i. e.

a recording a f t e r s tep 3, the radiation propert ies will introduce extra

maxima and minima which may remove a l l signs of a mode.

Acoustical measurement equipm,ent

A common se t up for acoustical measurements was used ( ~ i g . 111-B-1).

F r o m a n oscil lator a sine wave signal of constant amplitude is fed to a

frequency counter and to the electromagnetic d r ive r exciting the t e s t object.

The d r ive r was assumed to fulfill the requirements ea r l i e r described with-

out a rigora.us test. The sound p res su re produced by the vibrating plate is

picked up by a microphone, B & K type 4131, connected to an amplifier and

sound-level meter. The amplifier output terminal is connected to a n oscil-

loscope and a spectrograph, Rodhe & Schwartz FNA, with a 10 Hz band-

width f i l ter running synchronously with the oscil lator frequency. The

dr iver , the guitar, and the microphone a r e placed in a n anechoic chambe r

and the remaining apparatus outside in the control room.

In Fig. 111-B-2 the ;Irivizig points, D l , D2 etc. a r e marked by numbered

triangles and the numbered rings M2, M3 etc. m a r k the projection of the

microphwne places perpendicular to the top plate plane. The distance

plate - microphone place is called z.

IANECHOIC C H A M B E R i I I

P L A T E

COUNTER D R I V E R

I !

I I

* I - I '

L

I I

.c I I I I ,

I 4 I I

Fig. 111-B- 1 . Block diagram of the acoustical measurement equipment.

I I I I I I L,--,,-

A M P L I F I E R

I I I

OSCILLATOR

; 1

M I C R O P H O N E

h

I I d

I

S L - M E T E R

f

. I

i

SPECTROGRAPH

I I I

- *

I I

I I

OSCILLOSCOPE

Fig . 111-B -2 . Driving points ( A ) , microphone places (0).

STL-QPSR 2-3/1969

Frequency responses

Three s e r i e s of experiments should be accounted fo r and discussed.

In the f i r s t s e r i e s of measurements a fixed microphone place was chosen,

M4 with z=100 cm, and the s a m e driving points a s for the holograms were

used. All the frequency responses, Fig. 111-B-3, show peaks a t about

200, 550, and 650 Hz and dips a t about 450, 600, and 700 Hz. A dip is

clear ly shown a t about 300 Hz in the frequency responses a b and e and

a peak a t about 500 Hz in al l the frequency responses except d , where the

dip at about 450 Hz seems to have moved up in frequency and suppressed

the peak. Peak frequencies and -3 dB l imits were accurately measured

by means of the counter and Q-values were calculated, A Q-value was

considered co r rec t although this i s not s t r ic t ly t rue , if the peak was sym-

metr ical with respect to i t s -3 dB limits. The resul ts a r e shown in

Table 111-B-1 under section I. As no peak was found in the vicinity of the

sixth mode f r o m the holograms in any of the acoustical measurements

and the mode most probably is not a simple one, this mode is omitted in

the following.

In the second s e r i e s of measurements different microphone placements

were t r ied, f i r s t M2, M5 and M6, to study the frequency response ' s de-

pendence of microphone place. The distance z was decreased to 10 c m to

improve the signal to noise ratio. The frequency responses, Fig.

111-B-4a, b, c , d show a l l peaks a t about 200 Hz, 300 Hz except c and d,

500 Hz except a. At about 550 Hz a peak i s shown except in Fig. 111-B-4c

where i t shows a dip and at about 650 Hz a peak is shown in Fig. 111-B-4b

and d but a dip in Fig. 111-B-4 a and c. A study of the holograms indicated

that driving point D7 was likely to excite the five "holograln modes". After

a few t r i a l s M7 with z=3 c m was found, where al l the five known modes

were recorded a s peaks (Fig. 111-B-4e). All the frequency responses

show dips o r t r aces of superimposed dips just above 500 Hz, inhibition of

a peak in Fig. 111-B-4a, and a t about 600 and 700 Hz. Note that the five

modes were a l l recorded a s peaks in Fig. 111-B-4b too. The numerical

resul ts a r e listed in Table 111-B-1 under section 11.

Finally the third s e r i e s of measurements were made to obtain more

reliable values of the frequencies and the Q-vaiues in par t icular of the i peaks. The following changes were therefore made to separate the modes:

the s a m e driving points were used a s for the holograms and the micro-

phone was placed a t an antinode for each mode with z decreased to 1 cm.

a 0 0.5 1 kHz b 0 0.5 1 kHz

c 0 0.5 1 kHz d 0 0.5 1 kHz

S'i-bW Fig . 111-B-3. F requency response gu i t a r t o p + t i . G Bolin, Stockholm 9. 9 .63

a ) Dl b) D2 c ) D3 d ) D4 e ) D5

e 0 O,5 1 kHz

The results a r e shown in Fig. III-B-5. Measurements were made with

the most favorable combination of driving point and microphone place for

each mode. The numerical results a r e shown under section 111 in Table

III-B-1.

Under the section holograms in Table III-B-1 the modes' frequencies

and Q-values obtained by holography measurements a r e listed. A com-

parison of the obtained peak frequencies and the mode frequencies agree

within 1 %. When the symmetry cri ter ium i s fulfilled the Q-values agree

within 13 %, Both techniques thus give essentially the same result a s

regards resonance frequencies and Q-values.

TABLE III-B-1. Numerical results of measurements --

- not possible to measure

7 a not symmetrical peak

SECTION I

D F H z Q

2 185.0 34

- 0 0

3 459.9 37

5 509.7 22?

4 640.2 503

- - - L

Driving points and microphone places

1 The bright and dark fringes of the time-average holograms ( ~ i g . III-B-6)

map the points of equal amplitude within 15 % of a wavelength of the used

light (6328 A). F r o m zero amplitude, the brightest region surrounding the

fringes, to maximum darkness of the f i rs t fringe the amplitude has grown

to approx. 0.14- 1 0 ' ~ c m (7). Hereafter the growth of amplitude between -4 maximum darkness and maximum brightness i s approx. 0.09- 10 cm.

i The holograms give an amplitude vibration pattern of the plate of good re-

solution. This information will here be used to 1) to study the influence 1

SECTION I1

D F H z Q

- 7 186.1 26

7 280.9 443

7 458.1 251

7 507 163

7 640 43

1 SECTION 111 I HOLOGRAM

D F H z C

1 184.2 30

2 282.5 52

3 458.0 267

4 509 25

5 640 46

- - - 2 - -

D F H z Q

1 185 30

2 287 46

3 460 45

4 508 2 1

5 645 - 2 685 -

a o 0.5 1 kHz b 0 0.5 1 kHz

c 0 O,5 1 kHz d 0 0.5 1 kHz

dB

Fig . 111-B-5. F requency response gu i t a r top plate. G Bolin, Stockholm 9 .9 .63 0 dB w 80 dB SL z = l c m

a ) D l , M4 b) D2, M2 c ) D3, M3 d ) D4, M 2 e ) D5, M5

e 0 0,5 1 kHz

Normal ized driving point ampl i tude

Fig. 111-B-7. Sound p r e s s u r e a s function driving point amplitude/ antinode amplitude.

F i g . 111-B-6. T i m e a v e r a g e ho log rams of a g u i t a r t op p la te ( G Bolin, S tockholm 9 .9 .63 ) a t r e sonance (by K A S te t son and N - E Molin, Ins t i tu te of Opt ica l R e s e a r c h , KTH, s tockholm) . Dr iv ing points ( A )

a ) 185 Hz Q = 30 b ) 287 Hz Q = 46 c ) 460 Hz Q = 45 d ) 508 Hz Q = 21 e ) 645 Hz f ) 685 Hz, probably a cornbination mode

STL-QPSR 2-3/1969

Summary

In this paper i t has been possible to interpret in detail acoustically

obtained frequency responses of a plate with complicated f o r m and s truc-

t u r e by comparisons with accurate vibration patterns, holograms. It

has been shown that the frequencies and (2-values of resonance modes of

the plate can b e acoustically measured. It has a l so been shown that one

and the same frequency response can give a good record of the plate 's

resonance properties if the driving point and the microphone place i s ca re -

fully chosen. Finally simple qualitative studies have been made of how

the driving point and microphone place influence on the frequency response;

Acknowledgments - G. Bolin has lent his guitar with framework made fo r the holographic

studies to the acoustical measurements. N-E. Molin and K.A. Stetson

have provided the resul ts of their holographic studies of the plate and have

supported the acoustical investigations with valuable suggestions. J.

Sundberg has read the manuscript and has suggested many improvements.

The author wants to thank these persons and for the help given by others.

References and footnotes

(1) See fo r instance Index of J. Acoust, Soc. Am.

(2) Hutchins, C. M. : "The Physics of Violins ", Scientific American I

(Nov. 1962), pp. 78-93. Huber, J. : "The Application of Acoustical Testing Methods to the

Guitar", Catgut Acoust. Soc. Newsletter No. 11 (1 969), pp. 15-19.

( 3 ) Powell, R. L. and Stetson, K. A. : "Interferometric Vibration Analysis by Wavefront Reconstruction", J. Opt. Soc. Am. 55 (1 965), pb. - 1593-1598.

Stetson, K. A. and Powell, R. L, : "Interferomet r ic Hologram Evalua- tion and Real-Time Analysis of Diffuse Objects", J. Opt. Soc, Am. 55 (1965), pp. 1694-1695.

Molin, and Stets on, K. A. : "Measuring Combination Mode Vibration Pat te rns by Hologram Interferometry", J. Sci. Inst. (J. Phys. E.) - 2 (1969), pp. 609-612.

(4) Agren, C -H. and Stetson., K. A. : "Measuring the Resonances of Treble Viol Plates by Hologram Interferometry and Designing an Im- proved Instrument", submitted fo r publ. in J. Acoust. Soc. Am.

(5) Bolin, G. , Stockholm, September 9, 1963.

(6) This study was done by N-E. Molin and K.A. Stetson, the Institute of Optical Research, KTH, Stockholm.

( 7 ) See ref. ( z ) , and Brown, G, M., Grant, R. h4., and Stroke, G. W.: "Theory of Holographic Interferometry", J. Acoust. Soc, Am. 45 (1969), pp. 1172-1177. - I