a comparison of acoustical measurements and hologram
TRANSCRIPT
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