Abstract

This study shows that a dynamic modal characterization of musical instruments with membrane can be carried out using a low-cost device and that the obtained very informative results can be presented as a movie. The proposed device is based on a digital holography technique using the quasi-Fourier configuration and time-average principle. Its practical realization with a commercial digital camera and large plane mirrors allows relatively simple analyzing of big vibration surfaces. The experimental measurements given for a percussion instrument are supported by the mathematical formulation of the problem.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. R. L. Powel and K. A. Stetson, "Interferometric vibration analysis by wavefront reconstruction," J. Opt. Soc. Am. 55, 1593-1598 (1965).
    [CrossRef]
  2. P. Picart, J. Leval, D. Mounier, and S. Gougeon, "Time-averaged digital holography," Opt. Lett. 28, 1900-1902 (2003).
    [CrossRef] [PubMed]
  3. J. N. Butters and J. A. Leendertz, "Holographic and video techniques applied to engineering measurement," Meas. Control 4, 349-354 (1971).
  4. N. H. Fletcher and T. D. Rossing, The Physics of Musical Instruments (Springer-Verlag, New York, 1999).
  5. E. V. Jansson, "A study of acoustical and hologram interferometric measurements on the top plate vibrations of a guitar,"Acustica 25, 95-100 (1971).
  6. C. M. Hutchins, "The acoustics of violin plates," Scientific American 245, 170-186 (1981).
    [CrossRef]
  7. T. D. Rossing, I. Bork, H. Zhao, and D. Fystrom, "Acoustics of snare drums," J. Acoust. Soc. Am. 92, 84-94 (1992).
    [CrossRef]
  8. O. J. Lokberg and O. K. Ledang, "Vibration of flutes studied by electronic speckle pattern interferometry," Appl. Opt. 23, 3052-3058 (1984).
    [CrossRef] [PubMed]
  9. N. Demoli, J. Meštrovi�?, and I. Sovi�?, "Subtraction digital holography," Appl. Opt. 42, 798-804 (2003).
    [CrossRef] [PubMed]
  10. N. Demoli, D. Vukicevic, and M. Torzynski, "Dynamic digital holographic interferometry with three wavelenths," Opt. Express 11, 767-774 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-7-767">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-7-767</a>
    [CrossRef] [PubMed]
  11. N. Demoli and D. Vukicevic, "Detection of hidden stationary deformations of vibrating surfaces by use of time-averaged digital holographic interferometry," Opt. Lett. 29, 2423-2425 (2004).
    [CrossRef] [PubMed]

Acustica (1)

E. V. Jansson, "A study of acoustical and hologram interferometric measurements on the top plate vibrations of a guitar,"Acustica 25, 95-100 (1971).

Appl. Opt. (2)

J. Acoust. Soc. Am. (1)

T. D. Rossing, I. Bork, H. Zhao, and D. Fystrom, "Acoustics of snare drums," J. Acoust. Soc. Am. 92, 84-94 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

Meas. Control (1)

J. N. Butters and J. A. Leendertz, "Holographic and video techniques applied to engineering measurement," Meas. Control 4, 349-354 (1971).

Opt. Express (1)

Opt. Lett. (2)

Scientific American (1)

C. M. Hutchins, "The acoustics of violin plates," Scientific American 245, 170-186 (1981).
[CrossRef]

Other (1)

N. H. Fletcher and T. D. Rossing, The Physics of Musical Instruments (Springer-Verlag, New York, 1999).

Supplementary Material (2)

» Media 1: AVI (3631 KB)     
» Media 2: AVI (2048 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Experimental setup. M and M’ denote mirrors, L lenses, VBS variable beam splitter, COL collimator, LS loudspeaker, VS vibration surface, Ob object, DC digital camera, and PC personal computer.

Fig. 2.
Fig. 2.

An example of the colored digital hologram (left) and its portion (right).

Fig. 3.
Fig. 3.

A movie composed from experimentally obtained data for modal characteristics of a drum. [Media 1]

Fig. 4.
Fig. 4.

A movie obtained numerically for a membrane analog to the drum. [Media 2]

Tables (2)

Tables Icon

Table 1. Resonant frequencies of the circular membrane used in this work

Tables Icon

Table 2. Resonant frequencies measured experimentally

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

U ( x 1 , y 1 , t ) = δ ( x 1 X , y 1 Y ) + s ( x 1 , y 1 , t ) ,
U ( x 2 , y 2 , t ) exp [ i ( π λ d ) ( x 2 2 + y 2 2 ) ] F { U ( x 1 , y 1 , t ) exp[i(π/λd) ( x 1 2 + y 1 2 ) ] } ,
U ( x 2 , y 2 , t ) exp { i ( π λ d ) [ ( x 2 X ) 2 + ( y 2 Y ) 2 ] } + exp [ i ( π λ d ) ( x 2 2 + y 2 2 ) ]
× F { s ( x 1 , y 1 ) exp [ i ( 4 π λ ) h ( x 1 , y 1 ) sin 2 π ft + i ( π λ d ) ( x 1 2 + y 1 2 ) ] } .
E 1 ( x 2 , y 2 ) exp [ i ( 2 π λ d ) ( x 2 X + y 2 Y ) ]
× F { s ( x 1 , y 1 ) J 0 [ ( 4 π λ ) h ( x 1 , y 1 ) ] exp [ i ( π λ d ) ( x 1 2 + y 1 2 ) ] }
U ( x 1 , y 1 ) s ( x 1 X , y 1 Y ) J 0 [ ( 4 π λ ) h ( x 1 X , y 1 Y ) ] .
[ ( 2 r 2 + 1 r r + 1 r 2 2 φ 2 ) 1 v 2 2 t 2 ] h ( r , φ , t ) = 0
h mn ( r , φ , t ) = A mn J m ( x mn r a ) cos ( m φ φ 0 ) cos ( ω mn t δ ) ,
h ( r , φ , t ) = m = 0 m = 1 h mn ( r , φ , t ) .
d 2 T ( t ) dt 2 + γ dT ( t ) dt + ω mn 2 T ( t ) = F ( t ) ,
T p ( ω ) = P 0 [ ( ω mn 2 ω 2 ) 2 + γ 2 ω 2 ] 1 2 ,
h ( r , φ , ω ) = P 0 m = 0 n = 1 { 1 [ ( ω mn 2 ω 2 ) 2 + γ 2 ω 2 ] 1 2 } J m ( x mn r a ) cos m φ ,

Metrics