Abstract

Two main aims of our investigation are to show differences in natural vibrations between two violins that differ in the thickness of the back plate and to determine whether they are linear systems. Two experiments were performed on the top and back plates. The first experiment was a mechanical modal analysis in a version with a fixed response point. In the second experiment optical measurements of the plate’s velocities in modal frequencies obtained from the first experiment were performed by use of laser Doppler vibrometry. The second experiment was a simplified modal analysis experiment with a fixed excitation point. Changes in the thickness of the back plate caused changes in certain modal frequencies of both plates. However, no important differences in mode shapes were found in both experiments. Thus, violins can be treated as linear systems but with great care.

© 2009 Optical Society of America

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References

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  1. E. B. Arnold and G. Weinreich, “Acoustical spectroscopy of violins,” J. Acoust. Soc. Am. 72, 1739-1746 (1982).
    [CrossRef]
  2. P. Gren, K. Tatar, J. Grandström, N.-E. Molin, and E.V. Jansson, “Laser vibrometry measurements of vibration and sound fields of a bowed violin,” Meas. Sci. Technol. 17, 635-644 (2006).
    [CrossRef]
  3. A. Runnemalm, N.-E. Molin, and E. Jansson, “On operating deflection shapes of the violin body including in-plane motions,” J. Acoust. Soc. Am. 107, 3452-3459 (2000).
    [CrossRef] [PubMed]
  4. E. Jansson, N.-E. Molin, and H. Sundin, “Resonances of a violin body studied by hologram interferometry and acoustical methods,” Phys. Scr. 2, 243-256 (1970).
    [CrossRef]
  5. E. V. Jansson and N.-E. Molin, “On deviating results of optical hologram interferometry and modal analysis of a violin,” Speech Transm. Lab. Q. Prog. Status Rep. 30 (4), 45-52 (1989), http://www.speech.kth.se/qpsr.
  6. J. A. Moral and E. V. Jansson, “Eigenmodes, input admittance, and the function of the violin,” Acustica 50, 329-337 (1982).
  7. H. O. Saldner, N.-E. Molin, and E. V. Jansson, “Vibration modes of the violin forced via the bridge and action of the soundpost,” J. Acoust. Soc. Am. 100, 1168-1177 (1996).
    [CrossRef]
  8. G. Bissinger and J. Keiffer, “Radiation damping, efficiency, and directivity for violin normal modes below 4 kHz,” ARLO 4 (1), 7-12 (2003).
    [CrossRef]
  9. K. D. Marshall, “Modal analysis of a violin,” J. Acoust. Soc. Am. 77, 695-709 (1985).
    [CrossRef]
  10. G. Bissinger, “Some mechanical and acoustical consequences of the violin soundpost,” J. Acoust. Soc. Am. 97, 3154-3164 (1995).
    [CrossRef]
  11. G. Bissinger, “Modal analysis of a violin octet,” J. Acoust. Soc. Am. 113, 2105-2113 (2003).
    [CrossRef] [PubMed]
  12. G. Weinreich, C. Holmes, and M. Mellody, “Air-wood coupling and the Swiss-cheese violin,” J. Acoust. Soc. Am. 108, 2389-2402 (2000).
    [CrossRef] [PubMed]
  13. G. Bissinger, “Wall compliance and violin cavity modes,” J. Acoust. Soc. Am. 113, 1718-1723 (2003).
    [CrossRef] [PubMed]
  14. C. M. Hutchins, “A 30-year experiment in the acoustical and musical development of violin-family instruments,” J. Acoust. Soc. Am. 92, 639-650 (1992).
    [CrossRef]
  15. C. M. Hutchins, “A study of the cavity resonances of a violin and their effect on its tone and playing qualities,” J. Acoust. Soc. Am. 87, 392-397 (1990).
    [CrossRef]
  16. E. A. G. Shaw, “Cavity resonance in the violin: network representation and the effect of damped and undamped rib holes,” J. Acoust. Soc. Am. 87, 398-410 (1990).
    [CrossRef]
  17. G. Bissinger, “A0 and A1 coupling, arching, rib height, and f-hole geometry dependence in the 2 degree-of-freedom network model of violin cavity modes,” J. Acoust. Soc. Am. 104, 3608-3615 (1998).
    [CrossRef]
  18. J. Bretos Linaza, C. Santamaria, and J. Alonso Moral, “Vibrational patterns and frequency responses of the free plates and box of a violin obtained by finite element analysis,” J. Acoust. Soc. Am. 105, 1942-1950 (1999).
    [CrossRef]
  19. H. Meinel, “On the frequency curves of violin,” Akust. Zh. 2, 22-33 (1937).
  20. N. E. Molin, L.-E. Lindgren, and E. V. Jansson, “Parameters of violin plates and their influence on the plate modes,” J. Acoust. Soc. Am. 83, 281-291 (1988).
    [CrossRef]
  21. D. J. Ewins, Modal Testing: Theory, Practice, and Application (Wiley, 1998).
  22. H. G. Natke, Einfuehrung in Theorie und Praxis der Zeitreihen-und Modalalalyse (Vieweg, 1992).
  23. The STAR system version 3.02 D. Theory and application. User's Manual (SMS, 1990).
  24. STAR. The STAR system. Advanced Curve Fitting reference manual (SMS, 1992).
  25. M. H. Richardson, “Is it a Mode Shape, or an Operating deflection shape,” Sound Vib. Mag. 30th Anniversary Issue (March 1997), pp.1 -11.
  26. L. E. Drain, The Laser Doppler Technique (Wiley, 1980).

2006

P. Gren, K. Tatar, J. Grandström, N.-E. Molin, and E.V. Jansson, “Laser vibrometry measurements of vibration and sound fields of a bowed violin,” Meas. Sci. Technol. 17, 635-644 (2006).
[CrossRef]

2003

G. Bissinger and J. Keiffer, “Radiation damping, efficiency, and directivity for violin normal modes below 4 kHz,” ARLO 4 (1), 7-12 (2003).
[CrossRef]

G. Bissinger, “Wall compliance and violin cavity modes,” J. Acoust. Soc. Am. 113, 1718-1723 (2003).
[CrossRef] [PubMed]

G. Bissinger, “Modal analysis of a violin octet,” J. Acoust. Soc. Am. 113, 2105-2113 (2003).
[CrossRef] [PubMed]

2000

G. Weinreich, C. Holmes, and M. Mellody, “Air-wood coupling and the Swiss-cheese violin,” J. Acoust. Soc. Am. 108, 2389-2402 (2000).
[CrossRef] [PubMed]

A. Runnemalm, N.-E. Molin, and E. Jansson, “On operating deflection shapes of the violin body including in-plane motions,” J. Acoust. Soc. Am. 107, 3452-3459 (2000).
[CrossRef] [PubMed]

1999

J. Bretos Linaza, C. Santamaria, and J. Alonso Moral, “Vibrational patterns and frequency responses of the free plates and box of a violin obtained by finite element analysis,” J. Acoust. Soc. Am. 105, 1942-1950 (1999).
[CrossRef]

1998

G. Bissinger, “A0 and A1 coupling, arching, rib height, and f-hole geometry dependence in the 2 degree-of-freedom network model of violin cavity modes,” J. Acoust. Soc. Am. 104, 3608-3615 (1998).
[CrossRef]

1996

H. O. Saldner, N.-E. Molin, and E. V. Jansson, “Vibration modes of the violin forced via the bridge and action of the soundpost,” J. Acoust. Soc. Am. 100, 1168-1177 (1996).
[CrossRef]

1995

G. Bissinger, “Some mechanical and acoustical consequences of the violin soundpost,” J. Acoust. Soc. Am. 97, 3154-3164 (1995).
[CrossRef]

1992

C. M. Hutchins, “A 30-year experiment in the acoustical and musical development of violin-family instruments,” J. Acoust. Soc. Am. 92, 639-650 (1992).
[CrossRef]

1990

C. M. Hutchins, “A study of the cavity resonances of a violin and their effect on its tone and playing qualities,” J. Acoust. Soc. Am. 87, 392-397 (1990).
[CrossRef]

E. A. G. Shaw, “Cavity resonance in the violin: network representation and the effect of damped and undamped rib holes,” J. Acoust. Soc. Am. 87, 398-410 (1990).
[CrossRef]

1989

E. V. Jansson and N.-E. Molin, “On deviating results of optical hologram interferometry and modal analysis of a violin,” Speech Transm. Lab. Q. Prog. Status Rep. 30 (4), 45-52 (1989), http://www.speech.kth.se/qpsr.

1988

N. E. Molin, L.-E. Lindgren, and E. V. Jansson, “Parameters of violin plates and their influence on the plate modes,” J. Acoust. Soc. Am. 83, 281-291 (1988).
[CrossRef]

1985

K. D. Marshall, “Modal analysis of a violin,” J. Acoust. Soc. Am. 77, 695-709 (1985).
[CrossRef]

1982

E. B. Arnold and G. Weinreich, “Acoustical spectroscopy of violins,” J. Acoust. Soc. Am. 72, 1739-1746 (1982).
[CrossRef]

J. A. Moral and E. V. Jansson, “Eigenmodes, input admittance, and the function of the violin,” Acustica 50, 329-337 (1982).

1970

E. Jansson, N.-E. Molin, and H. Sundin, “Resonances of a violin body studied by hologram interferometry and acoustical methods,” Phys. Scr. 2, 243-256 (1970).
[CrossRef]

1937

H. Meinel, “On the frequency curves of violin,” Akust. Zh. 2, 22-33 (1937).

Arnold, E. B.

E. B. Arnold and G. Weinreich, “Acoustical spectroscopy of violins,” J. Acoust. Soc. Am. 72, 1739-1746 (1982).
[CrossRef]

Bissinger, G.

G. Bissinger and J. Keiffer, “Radiation damping, efficiency, and directivity for violin normal modes below 4 kHz,” ARLO 4 (1), 7-12 (2003).
[CrossRef]

G. Bissinger, “Modal analysis of a violin octet,” J. Acoust. Soc. Am. 113, 2105-2113 (2003).
[CrossRef] [PubMed]

G. Bissinger, “Wall compliance and violin cavity modes,” J. Acoust. Soc. Am. 113, 1718-1723 (2003).
[CrossRef] [PubMed]

G. Bissinger, “A0 and A1 coupling, arching, rib height, and f-hole geometry dependence in the 2 degree-of-freedom network model of violin cavity modes,” J. Acoust. Soc. Am. 104, 3608-3615 (1998).
[CrossRef]

G. Bissinger, “Some mechanical and acoustical consequences of the violin soundpost,” J. Acoust. Soc. Am. 97, 3154-3164 (1995).
[CrossRef]

Drain, L. E.

L. E. Drain, The Laser Doppler Technique (Wiley, 1980).

Ewins, D. J.

D. J. Ewins, Modal Testing: Theory, Practice, and Application (Wiley, 1998).

Grandström, J.

P. Gren, K. Tatar, J. Grandström, N.-E. Molin, and E.V. Jansson, “Laser vibrometry measurements of vibration and sound fields of a bowed violin,” Meas. Sci. Technol. 17, 635-644 (2006).
[CrossRef]

Gren, P.

P. Gren, K. Tatar, J. Grandström, N.-E. Molin, and E.V. Jansson, “Laser vibrometry measurements of vibration and sound fields of a bowed violin,” Meas. Sci. Technol. 17, 635-644 (2006).
[CrossRef]

Holmes, C.

G. Weinreich, C. Holmes, and M. Mellody, “Air-wood coupling and the Swiss-cheese violin,” J. Acoust. Soc. Am. 108, 2389-2402 (2000).
[CrossRef] [PubMed]

Hutchins, C. M.

C. M. Hutchins, “A 30-year experiment in the acoustical and musical development of violin-family instruments,” J. Acoust. Soc. Am. 92, 639-650 (1992).
[CrossRef]

C. M. Hutchins, “A study of the cavity resonances of a violin and their effect on its tone and playing qualities,” J. Acoust. Soc. Am. 87, 392-397 (1990).
[CrossRef]

Jansson, E.

A. Runnemalm, N.-E. Molin, and E. Jansson, “On operating deflection shapes of the violin body including in-plane motions,” J. Acoust. Soc. Am. 107, 3452-3459 (2000).
[CrossRef] [PubMed]

E. Jansson, N.-E. Molin, and H. Sundin, “Resonances of a violin body studied by hologram interferometry and acoustical methods,” Phys. Scr. 2, 243-256 (1970).
[CrossRef]

Jansson, E. V.

P. Gren, K. Tatar, J. Grandström, N.-E. Molin, and E.V. Jansson, “Laser vibrometry measurements of vibration and sound fields of a bowed violin,” Meas. Sci. Technol. 17, 635-644 (2006).
[CrossRef]

H. O. Saldner, N.-E. Molin, and E. V. Jansson, “Vibration modes of the violin forced via the bridge and action of the soundpost,” J. Acoust. Soc. Am. 100, 1168-1177 (1996).
[CrossRef]

E. V. Jansson and N.-E. Molin, “On deviating results of optical hologram interferometry and modal analysis of a violin,” Speech Transm. Lab. Q. Prog. Status Rep. 30 (4), 45-52 (1989), http://www.speech.kth.se/qpsr.

N. E. Molin, L.-E. Lindgren, and E. V. Jansson, “Parameters of violin plates and their influence on the plate modes,” J. Acoust. Soc. Am. 83, 281-291 (1988).
[CrossRef]

J. A. Moral and E. V. Jansson, “Eigenmodes, input admittance, and the function of the violin,” Acustica 50, 329-337 (1982).

Keiffer, J.

G. Bissinger and J. Keiffer, “Radiation damping, efficiency, and directivity for violin normal modes below 4 kHz,” ARLO 4 (1), 7-12 (2003).
[CrossRef]

Linaza, J. Bretos

J. Bretos Linaza, C. Santamaria, and J. Alonso Moral, “Vibrational patterns and frequency responses of the free plates and box of a violin obtained by finite element analysis,” J. Acoust. Soc. Am. 105, 1942-1950 (1999).
[CrossRef]

Lindgren, L.-E.

N. E. Molin, L.-E. Lindgren, and E. V. Jansson, “Parameters of violin plates and their influence on the plate modes,” J. Acoust. Soc. Am. 83, 281-291 (1988).
[CrossRef]

Marshall, K. D.

K. D. Marshall, “Modal analysis of a violin,” J. Acoust. Soc. Am. 77, 695-709 (1985).
[CrossRef]

Meinel, H.

H. Meinel, “On the frequency curves of violin,” Akust. Zh. 2, 22-33 (1937).

Mellody, M.

G. Weinreich, C. Holmes, and M. Mellody, “Air-wood coupling and the Swiss-cheese violin,” J. Acoust. Soc. Am. 108, 2389-2402 (2000).
[CrossRef] [PubMed]

Molin, N. E.

N. E. Molin, L.-E. Lindgren, and E. V. Jansson, “Parameters of violin plates and their influence on the plate modes,” J. Acoust. Soc. Am. 83, 281-291 (1988).
[CrossRef]

Molin, N.-E.

P. Gren, K. Tatar, J. Grandström, N.-E. Molin, and E.V. Jansson, “Laser vibrometry measurements of vibration and sound fields of a bowed violin,” Meas. Sci. Technol. 17, 635-644 (2006).
[CrossRef]

A. Runnemalm, N.-E. Molin, and E. Jansson, “On operating deflection shapes of the violin body including in-plane motions,” J. Acoust. Soc. Am. 107, 3452-3459 (2000).
[CrossRef] [PubMed]

H. O. Saldner, N.-E. Molin, and E. V. Jansson, “Vibration modes of the violin forced via the bridge and action of the soundpost,” J. Acoust. Soc. Am. 100, 1168-1177 (1996).
[CrossRef]

E. V. Jansson and N.-E. Molin, “On deviating results of optical hologram interferometry and modal analysis of a violin,” Speech Transm. Lab. Q. Prog. Status Rep. 30 (4), 45-52 (1989), http://www.speech.kth.se/qpsr.

E. Jansson, N.-E. Molin, and H. Sundin, “Resonances of a violin body studied by hologram interferometry and acoustical methods,” Phys. Scr. 2, 243-256 (1970).
[CrossRef]

Moral, J. A.

J. A. Moral and E. V. Jansson, “Eigenmodes, input admittance, and the function of the violin,” Acustica 50, 329-337 (1982).

Moral, J. Alonso

J. Bretos Linaza, C. Santamaria, and J. Alonso Moral, “Vibrational patterns and frequency responses of the free plates and box of a violin obtained by finite element analysis,” J. Acoust. Soc. Am. 105, 1942-1950 (1999).
[CrossRef]

Natke, H. G.

H. G. Natke, Einfuehrung in Theorie und Praxis der Zeitreihen-und Modalalalyse (Vieweg, 1992).

Richardson, M. H.

M. H. Richardson, “Is it a Mode Shape, or an Operating deflection shape,” Sound Vib. Mag. 30th Anniversary Issue (March 1997), pp.1 -11.

Runnemalm, A.

A. Runnemalm, N.-E. Molin, and E. Jansson, “On operating deflection shapes of the violin body including in-plane motions,” J. Acoust. Soc. Am. 107, 3452-3459 (2000).
[CrossRef] [PubMed]

Saldner, H. O.

H. O. Saldner, N.-E. Molin, and E. V. Jansson, “Vibration modes of the violin forced via the bridge and action of the soundpost,” J. Acoust. Soc. Am. 100, 1168-1177 (1996).
[CrossRef]

Santamaria, C.

J. Bretos Linaza, C. Santamaria, and J. Alonso Moral, “Vibrational patterns and frequency responses of the free plates and box of a violin obtained by finite element analysis,” J. Acoust. Soc. Am. 105, 1942-1950 (1999).
[CrossRef]

Shaw, E. A. G.

E. A. G. Shaw, “Cavity resonance in the violin: network representation and the effect of damped and undamped rib holes,” J. Acoust. Soc. Am. 87, 398-410 (1990).
[CrossRef]

Sundin, H.

E. Jansson, N.-E. Molin, and H. Sundin, “Resonances of a violin body studied by hologram interferometry and acoustical methods,” Phys. Scr. 2, 243-256 (1970).
[CrossRef]

Tatar, K.

P. Gren, K. Tatar, J. Grandström, N.-E. Molin, and E.V. Jansson, “Laser vibrometry measurements of vibration and sound fields of a bowed violin,” Meas. Sci. Technol. 17, 635-644 (2006).
[CrossRef]

Weinreich, G.

G. Weinreich, C. Holmes, and M. Mellody, “Air-wood coupling and the Swiss-cheese violin,” J. Acoust. Soc. Am. 108, 2389-2402 (2000).
[CrossRef] [PubMed]

E. B. Arnold and G. Weinreich, “Acoustical spectroscopy of violins,” J. Acoust. Soc. Am. 72, 1739-1746 (1982).
[CrossRef]

Acustica

J. A. Moral and E. V. Jansson, “Eigenmodes, input admittance, and the function of the violin,” Acustica 50, 329-337 (1982).

Akust. Zh.

H. Meinel, “On the frequency curves of violin,” Akust. Zh. 2, 22-33 (1937).

ARLO

G. Bissinger and J. Keiffer, “Radiation damping, efficiency, and directivity for violin normal modes below 4 kHz,” ARLO 4 (1), 7-12 (2003).
[CrossRef]

J. Acoust. Soc. Am.

K. D. Marshall, “Modal analysis of a violin,” J. Acoust. Soc. Am. 77, 695-709 (1985).
[CrossRef]

G. Bissinger, “Some mechanical and acoustical consequences of the violin soundpost,” J. Acoust. Soc. Am. 97, 3154-3164 (1995).
[CrossRef]

G. Bissinger, “Modal analysis of a violin octet,” J. Acoust. Soc. Am. 113, 2105-2113 (2003).
[CrossRef] [PubMed]

G. Weinreich, C. Holmes, and M. Mellody, “Air-wood coupling and the Swiss-cheese violin,” J. Acoust. Soc. Am. 108, 2389-2402 (2000).
[CrossRef] [PubMed]

G. Bissinger, “Wall compliance and violin cavity modes,” J. Acoust. Soc. Am. 113, 1718-1723 (2003).
[CrossRef] [PubMed]

C. M. Hutchins, “A 30-year experiment in the acoustical and musical development of violin-family instruments,” J. Acoust. Soc. Am. 92, 639-650 (1992).
[CrossRef]

C. M. Hutchins, “A study of the cavity resonances of a violin and their effect on its tone and playing qualities,” J. Acoust. Soc. Am. 87, 392-397 (1990).
[CrossRef]

E. A. G. Shaw, “Cavity resonance in the violin: network representation and the effect of damped and undamped rib holes,” J. Acoust. Soc. Am. 87, 398-410 (1990).
[CrossRef]

G. Bissinger, “A0 and A1 coupling, arching, rib height, and f-hole geometry dependence in the 2 degree-of-freedom network model of violin cavity modes,” J. Acoust. Soc. Am. 104, 3608-3615 (1998).
[CrossRef]

J. Bretos Linaza, C. Santamaria, and J. Alonso Moral, “Vibrational patterns and frequency responses of the free plates and box of a violin obtained by finite element analysis,” J. Acoust. Soc. Am. 105, 1942-1950 (1999).
[CrossRef]

N. E. Molin, L.-E. Lindgren, and E. V. Jansson, “Parameters of violin plates and their influence on the plate modes,” J. Acoust. Soc. Am. 83, 281-291 (1988).
[CrossRef]

E. B. Arnold and G. Weinreich, “Acoustical spectroscopy of violins,” J. Acoust. Soc. Am. 72, 1739-1746 (1982).
[CrossRef]

A. Runnemalm, N.-E. Molin, and E. Jansson, “On operating deflection shapes of the violin body including in-plane motions,” J. Acoust. Soc. Am. 107, 3452-3459 (2000).
[CrossRef] [PubMed]

H. O. Saldner, N.-E. Molin, and E. V. Jansson, “Vibration modes of the violin forced via the bridge and action of the soundpost,” J. Acoust. Soc. Am. 100, 1168-1177 (1996).
[CrossRef]

Meas. Sci. Technol.

P. Gren, K. Tatar, J. Grandström, N.-E. Molin, and E.V. Jansson, “Laser vibrometry measurements of vibration and sound fields of a bowed violin,” Meas. Sci. Technol. 17, 635-644 (2006).
[CrossRef]

Phys. Scr.

E. Jansson, N.-E. Molin, and H. Sundin, “Resonances of a violin body studied by hologram interferometry and acoustical methods,” Phys. Scr. 2, 243-256 (1970).
[CrossRef]

Sound Vib. Mag. 30th Anniversary Issue

M. H. Richardson, “Is it a Mode Shape, or an Operating deflection shape,” Sound Vib. Mag. 30th Anniversary Issue (March 1997), pp.1 -11.

Speech Transm. Lab. Q. Prog. Status Rep.

E. V. Jansson and N.-E. Molin, “On deviating results of optical hologram interferometry and modal analysis of a violin,” Speech Transm. Lab. Q. Prog. Status Rep. 30 (4), 45-52 (1989), http://www.speech.kth.se/qpsr.

Other

D. J. Ewins, Modal Testing: Theory, Practice, and Application (Wiley, 1998).

H. G. Natke, Einfuehrung in Theorie und Praxis der Zeitreihen-und Modalalalyse (Vieweg, 1992).

The STAR system version 3.02 D. Theory and application. User's Manual (SMS, 1990).

STAR. The STAR system. Advanced Curve Fitting reference manual (SMS, 1992).

L. E. Drain, The Laser Doppler Technique (Wiley, 1980).

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Figures (4)

Fig. 1
Fig. 1

Thickness of back plates (numbers): Regina violin at left; Joanna violin at right.

Fig. 2
Fig. 2

Areas where the back plate was squeezed when the upper plate was measured.

Fig. 3
Fig. 3

Measurement mesh for modal analysis with the response point indicated by a black dot: (a) the back plate and (b)  the top plate. Response points from mechanical measurements served as excitation points during the optical measurements.

Fig. 4
Fig. 4

Example of the FRF measured on the back plate during the modal experiment.

Tables (2)

Tables Icon

Table 1 Modal Frequency and Modal Damping Determined by the Mechanical Modal Analysis Experiment

Tables Icon

Table 2 Examples of Mode Shapes from Mechanical Modal Analysis (Rows 1 and 3) and Modal Deformation from the LDV Experiment (Rows 2 and 4).

Metrics