Dept. for Speech, Music and Hearing

Quarterly Progress andStatus Report

An investigation of a violin bylaser speckle interferometry

and acousticalmeasurements

Jansson, E. V.

journal: STL-QPSRvolume: 13number: 1year: 1972pages: 025-033

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

STL-QPSR 1/1972

111. MUSICAL ACOUSTICS

A. AN INVESTIGATION OF A VIOLIN BY LASER SPECKLE INTER- FEROMETRY AND ACOUSTICAL MEASUREMENTS+:-. Pre l iminary repor t

E . Janoaon

Abstract

This investigation was performed ( I ) to explore how useful a l a s e r speckle interferometer i s in studying the vibrations of a violin, ( 2 ) to study how the holding of the violin influences on the vibrations, and ( 3 ) to tes t a model de- scribing the vibrations. The investigation was limited to the range of the main

I wood resonance.

The experiments proved ( I) that by means of a speckle interferometer nodal l ines could be detected easily and rapidly, but the displacement was difficult to measure , (2 ) that the holding may suppress modes, and (3) that the main wood peak p r i m r i l y der ives f rom the f i r s t top plate mode in agree- ment with the model.

Introduction

In an e a r l i e r investigation resonance propert ies of the top and the back

plate of a violin studied af ter major s teps in making, and shapes, f r e - (1) quencie s , and Q -value s of the normal modes of vibration were reported .

The information collected was transformed into the following hypothetical

model of the wall vibrations of the violin(2' 3). The top plate i s the main

radiator and vibrates under boundary conditions pr imar i ly given by clamped

edges and a f i r m support, the sound post. The r e s t of the sounding box,

the back plate with the r ibs , ac ts a s a considerably differ shell, the vibra-

tions of which a r e limited, mainly by the holding of the violin. Vibrations of

the top plate a r e , however, coupled by sound post, r i b s , neck, arid enclosed

airvolume to the back plate. The a r e a around the bridge and the sound post

works like a rocking lever , with the driving force ( a t the bridge) close to

the fulcrum (the sound post) , which in i t s turn is placed on a slightly springy

support (the back plate).

In electroaco~zstically obtained frequeilcy responses, two prominent peaks

a r e generally found a t about 290 and 460 Hz, the a i r resonance peak and the

"main woodf' o r "principal bodyp' peak, respectively ( 1 , 4 , 5 ,6 ) . The frequen-

cies and the charac ters of these peaks a r c of g rea t importancc for the quality

of the instrument. The resu l t s of(') indicatc that the main wood peak derives

+t The optical investigations were performed a t the Institute of Optical Research, Royal Institute of Technology (KTH), S- 100 44 Stockholm 70

STL-QPSR 1/1972 26.

f rom t h e f i r s t top plate mode. The information collected gave, however, no

opportunity to check this hypothesis by a detailed quantitative comparison of

the acoustically and optically obtained data.

This paper i s a reporc of the work continued after ( I ) . The purpose of

this investigation was, (1) to explore the usefulness of a new tool for optical

real- t ime analysis of vibrating surfaces, 3 l a se r speckle interferometer,

(2) to study how the holding of the violin influences i t s vibrations, and (3) to I tes t the hypothetical model of the vibrations. The investigation was limited

to the frequency range of around the main .,-~ood peak.

Lase r speckle interferometry

One purpose of this investigation was to test the usefulness of a l a se r

speckle interferometer in studying vibrations of a violin in =a1 -time.

When studying vibrations of a surface a real- t ime technique i s of great

advantage. It nlalce s it possible to find normal inode s , i. e. meaningful and

informative pa ramete r s of vibration. In ( a real- t ime hologram -interfero-

meter ( 7 ' 8, was mainly used. This instrument demands, however, high

stability of the object, which i s a serious disadvantage with an object like a

violin. The violin must be arranged with holding and d r ive r s , left to stabilize

for an hour o r two, and not until then the reference hologram can be exposed,

which will be useful for a maximum observxtion time of one hour. No changes

of holding and dr ivers can be done without repeating the whole procedure.

Time-average hologram i n t e r f e ~ o g ~ a m s givc records of highest contrast and

a r e therefore eas ies t to interpret, but can be evaluated only af ter processing.

In l a se r speckle inte rferome try (" lo) the stability demands a r e l e s s severe.

Stability i s necded for a few seconds only, determined by the persis tence time

of the eye and the vizualizing time for evaluation.

For vibration detection by l a s e r speclcle interferometry, the object i s

illuminated by l a s c r light. When viewed tllrough a sufficiently small aperture,

the object appears covered with a granular intensity s t ructure, the so-called

speckles. In the viewing instrument, a uniform reference field derived f rom

the same l a se r i s superimposed onto the image of the object. The speckles

resulting froin the interference of the two fields on the retina change shape

wher, the object surface moves to o r f rom the observer by about a quarter of

a waveleilgth, they regain their shape after a displacement of about half a

wavelength. F o r vibration periods of the surface shor ter than the persis tance

Fig. 111-A-1. The optical system used; Abbreviations: laser (L), beam- splitter s (BS , and BS3), beam expanders (LP I , LP2, and LP ), (CL), aperture (A), hologram holder &I), and object violin (0) clamped to jig (J) .

STL-QPSR 1/1972

The vibrations of an object can be described by a combination of i t s normal

modes. These modes a r e determined by the object itself and how it i s held,

i. c . by the propert ies of the object and tlie boundary conditions. Therefore,

an object should preferably be tested under holding conditions matching those

in actual use. Here some difficulties a r i s e with an object like the violin.

When played i t i s held in a weakly defined way: both place and way of holding

vary due to different placc of chin and shoulder r e s t s , varying damping by

the chin and different fingering. A straight forward approach i s to study the

violin under siinple and physically well-defined conditions, then to make a

reasonable, real is t ic approximation of the r ea l boundary conditions and

finally to estimate the perturbations encountered in actual playing. Conse - quently a suitable s ta r t is to study the normal modes under boundary condi-

tions type clamped and f r ee edges. These boundary conditions a r e physically

well-defined and give the eas ies t interprcted lnodcs. It should be noticed,

however, that these holdings may add, suppress o r cause quite misleaciihg

modes. Thereafter introduce boundary conditions approximating those in

r e a l u se , rcgis ter the modes, and compare these with those ea r l i e r obtained.

F r o m the comparison the perturbations ellcountered in actual playing can be

derived.

It should be noticed that a l l normal modes a r e excited when an object i s

s e t into vibration, more o r l e s s , depending on the coupling of each mode to

the driving. The normal mode close s t to the driving frequency ( sinewave

excitation) i s , however, often excited most effectively. The modes can, if

necessary, be separated by driving a t different points.

The model described in the introduction makes modes of vibration possible,

that were not sought for in ( I). Be sides vibration modes of the plates with

little coupling to the r e s t of the instrument, type modes of clamped plate at

edges, modes of the whole s t ructure, body modes, a r e possible. The la t te r

type of modes may be of two kinds. F i r s t the violin may vibrate a s a unit,

like a bar o r plate. Sceondly the whole surface enclosing the a i r volume may

split up into vibration modes. Therefore special ca re i s necessary , when

deciding which clamping i s accurate. This may be part icular ly important in

fu tu re quality tes t s of violins.

STL-QPSR

Experiments

Experiments were performed to find answers to the questions sketched

above, viz. :

I. 5ow useful is a l a s e r speckle interferometer in studying the vibration modes of a violin,

2. how doe s the holding influence the vibration modes of the violin, and

3 . how good i s the hypothetical model of the violin?

The study was limited to the range around the main wood 'resonance.

The ea r l i e r used holding jig for the violin was modified allowing the jig

with violin to be moved without changing the driving. Thus the top and back

plate of the assembled violin could be studied with the same driving - the

back plate through the hole of the jig. Fur thermore the jig with violin could

be moved f rom a n anechoic chamber providing acoustically well-defined con-

ditions to the hologram table without changing the driving. In this way d i rec t

comparisons of acoustical and optical measurements were possible.

The experiments proved, a s expected, that nodal l ines could be detected

by means of the speckle interferometer with no delay af ter setting up the ob-

ject for te sting. This means that holding and driving could be changed during

the experiments without loosing any time for stabilization. It was, however,

hardly possi ble to detect equal displa.cement fringes but in few exceptions.

No significant ilnprovelnent was acco~~zplished by inserting polaroids in the

beams a s in(9). The frequency of lnaximum displacement by a mode could

still be estimated by keeping constant driving amplitude and changing the

frequency to maximum broadness of the antinodal a r e a o r a reas . This ;rave

not very accurate frequency measurements , though.

A typical speckled image, interferogram, i s shown in Fig. 111-A-2 (com-

pare Fig. 111-A-4. c). One zero motion line starts f rom the left f-hole, goes

close to the r ibs to the bottom of the tailpiece and another passes in a bend on

top of the sound post. Equal displacement fr inges can not be detected. The

speckle pat terns a r e eas i e r to watch directly because automatic optimizing of

watching conditions a r e made by the eye.

Figs. 111-A -2 and 111-A-4. c also show the advantage of making records of

relevant modes by time-average hologranls for la te r detailed studies, this in

agreement with expectations.

Fig. 111-A-2. Speckle interferogram of the top plate obtained by a camera looking

. . through the aperture (compare time-average interferogram in Fig. 111-A-4. c obtained with three times higher driving amplitude).

Fig . 111-A-3. In te r fe rograms a t 465 Hz of s e r i e s a , clamping a t r ibs . - 3 a. top plate Us = 0. 14 x m /set.

-4 3 b. back plate Us = 0.085 x 10 m /sec.

STL-QPSR 1/1972 30.

Three s e r i e s of experiments with different boundary conditions should be

accounted for in this report : s e r i e s 5 - type clamped edges, s e r i e s - b - type f ree edges, and ser ie s - c - holding apprmilnately a s in playing. The

( 6 ) place of driving was chosen according to . The source strength U of antinodal a r e a s a r e estimated by the product

S

of angular frequency, displacement amplitude, and a r e a of more than half-

amplitude displacement. This measure in r m s of the source strength i s given

in the figure captions.

In s e r i e s - a the studies were car r ied out under the same conditions a s in

the l a s t step of (1): clamping a t the chin r e s t and the upper corner blocks,

i. e. type clamped edges. The interferograms sIlow the same vibration pat-

t e rns a s were obtained ea r l i e r . In the meantime, the violin had been varnished,

adjusted, and fitted with new strings. The resu l t indicates no substantial in-

fluence f rom these change s and adjustments. The interferograms were r e - corded at the main wood peak, hence follows the frequency discrepancy corn-

pared to( ') (cornpare a l so Table 111-A-I). I Table 111-A-I. Frequcncie s of maximum antinodal a r e a s

and maximum acoustical output.

Clamping Optical I Optical I1 Acoustical

Clamping I according to Fig. 111-A-3 I I I1 I I " Fig. 111-A-4

I 1 1 1 1 " " Fig. 111-A-5

Optical I and 11: the same measurements before and af ter a dismounting and reinounting with a tuning of the violin. A c o ~ s t i c a l nearfield ~ n e a s u r e m e n t s , compare Fig. 111-A- 6.

A comparison of Figs . 111-A-3. a and 111-A-3, b shows clear ly that the top

place i s the main radiator. Est imated source strengths give a difference of 1

5 dB. The interference fringes shown the same displacement of both p l a t e s

a t the sound post and a t the r ibs . This shows that the lower p a r t of the violin

moves in phase, i. e. vibrations in a body inode of the f i r s t type a r e superim-

posed on the top plate vibrations.

STL-OPSR 1/1972 3 1.

The acoust ical output in an anechoic chamber with the same driving was

riieasured to 65 dB SPL at a distance of 35 crn (Fig. 111-A-6. a ) (playing t e s t s

Gave that this co r re sponds to the fundamental of a pianissimo note with this

fundamental frequency). A f i r s t o rder est imate, the top plate, approximated

by a simple source and a stiff back plate gives 55 dB SPL. By adding a 3 dB

correct ion because of not spherical radiation (equivale nt to the radiation f r o m

a cylindrical piston, with a radius of laixbda/6 in the end of a long tube), a

discrepancy of 7 dB i s obtained. Theoretical es t imates , without and with

radiation frorc the f-holes give a discrepancy of 5 dB(''). The close agree-

ment i s a further support for regarding the top plate a s main radiator. It

must , however, be pointed out that the c s t i z a t e i s ra ther crude as the radia-

tion of the back plate and the baffle effect of the jig has been neglected.

In s e r i e s - b the clan.ping of the violin vras moved to nodal a r e a s estimated

f rom s e r i e s - a (Fig. 111-A-3. a ) , thus giving boundary conditions type f r e e

edges ( r i g . 111-A-4, clamping a t the left f-hole, a t the right foot of the bridge

and a t the finger board). The vibrations \-?ere studied a t f req~rencie s of modes

found a t 370, 455, a:id 515 Hz (sane modes with different clamping a t 340,

430, and 505 Hz in(')). In the interferogram (Fig. 111-A-4), obtained with

constant driving, the following can be observed. The top plate vibrates in i t s

i i r s t mode at a l l frequencies. At 455 Hz a distorted version of the "370 Hz"

=ode and the f i r s t back plate rr-ode ( 5 15 I-iz) a r e superimposed. The source

strength of the f i r s t top plate mode i s al\-!;rays dominant, about 6 dB compared

to the distorted a t 455 Hz and 2 dB conpared to the f i r s t back plate

mode a t 515 Hz. Note that in Figs . 111-fl-4. c and d , the same number of

f r inges a r e cutting the r i b s in both plates z:~d a t the sa=e places, i. c. a

body rzode of the f i r s t kind. The distortcd mode a c t s a s a dipdle, which

rz2eans the maximum acoustical output, colxpared to the simple source, i s 2n & i ~ o d i f i e d by a factor - (Z 0. 05) wherc & i s the distance separating the h

two vibrating a r e a s and h i s the wave length of the radiated sound.

In s e r i e s - c , finally, the vibration pat terns were recorded a t 465 Hz using

a c lanping a t the lower bouts and the neck, thus approximating the holding

used in playing. The violin vibrates , a s in s e r i e s a and b =airily in the f i r s t - - top plate mode (Fig. 111-A-5). Note that the clam-ping has suppre ssed one

rr=ode observed ir, se r i e s b and that the f i r st back plate mode has appeared, - i t s source strength being about 17 dB lower than that of the top plate.

Fig. 111-A-5. Interferograms a t 465 Hz of se r i e s c, an approximate - violin - holding clamping.

- 4 3 a. The top plate Us = 0.078 x 10 m /sec

- 4 3 b. The back plate Us = 0.01 1 x 10 m /sec

dB SPL

Fig. 111-A-6. Frequency responses obtained with the microphone close to left lower bout. a. clamping according to ser ies a , b. clamping according to ser i e s 'iS, and c. clamping according to ser ies c.

STL-QPSR 1/1972 33.

playing. It i s suggested that, in future experiments, the violin should be

clamped a t the chinrest in the f irst place and a t nodal lines a s far a s possible.

The model introduced earl ier indicates that the rr-ain wood resonance

derives principally from the fir st top platc mode, since the top plate i s

easiest to set into vibration. This washund to be in agreement with the ex-

perimental results. The fir s t top plate node was always the most outstand-

ing. But both the interfcrometric and t l ~ c acoustical studies show, that sev-

e ra l modes a r e building up the main wood peak. I rr,ust be said that only

one violin has been investigated. It is , however, believed, that the con-

clusions made so far a r e qualitatively true for most violins.

The experiments a r e carried on to study all the vibration modes up to

about 1200 Hz with the experience gained from this investigation.

Aclcnowledgment o

This investigation vras made possible by optical equipKent, which was

put a t the disposal of the author hy the Institute of Optical Research. The

author gratefully aclaol-rledge the support and help given by Prof. Eri!:

Ingelstam, Klaus 3iedermann, and Leif E:: of that institute. Grateful ad-

lmowledpent s hocld also be given to Harry Sundin for preparing the violin

for the tests and to Nils-Erik Molin for technical advice.

This work was supported by the Swedish Humanistic Research Council

and the Swedish Natural Science Re search Council,

References

( 1) Jansson, E. , Molin, N-E. , and Sundin, H. , Physica Scripta - 2 ,

243 (1970).

(2) Jansson, E . , Molin, N-E., and Sundin, H . , 7th Internat. Congr. on

Acoustics, paper 19 S 3 (197 1).

(3 ) Jansson, E . , hlolin, N-E., and Sundiiz, H., Sldjd och Ton, No. 6 (1971) and No. 1 (1172).

(4) Saunders, F., Sound - I, No. 4(1962).

(5) Hutchins, C. IX., Scientific Arrier. - 207, No. 5 (1962).

(6) Hutchins, C. ivl. and Fielding, F. L. , Physics Today - 2 1, KO. 7 (196C).

(7) Powell, R. L. and Stetson, K.A. , J. Opt. Soc.Amer. 55 - , 1694 1955).

(c) Biedermann, I<. and Molin, N. E. , J . Phys. E. :Sci. Instrum. 3, 669 (1970). - (9) El c , L. and Molin, N-E., Optics Co~:ll=unications 2, 419 (1971). -

(10) Stetson, M.A., 0pt .Laser Technol. - 2 , 179 (1970).

( l i ) Molin, N-E. afid Stetson, K.A. , J . Phy5.E. : Sci. Instrum. 2, 509 (1969). - (12) Schelleng, J . C . , J .Acoust .Soc.A~cr . 35, 326 and 1291 (1963). -

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