An experimental study of the mechanical impedance of a piano soundboard in the frequency range is reported. The results differ significantly from the behavior reported by Wogram above a few kHz, but are consistent with the measurements of Conklin. The data presented here are also in good agreement with the predictions of our recent numerical calculations. Those calculations found that the soundboard ribs have an important effect on the frequency dependence of above a few kHz, and our measurements confirm that prediction.
REFERENCES
1.
For a very complete review see
H. A.
Conklin
, Jr., “Design and tone in the mechanoacoustic piano. Part I. Piano hammers and tonal effects
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Conklin
, Jr., “Design and tone in the mechanoacoustic piano. Part II. Piano structure
,” J. Acoust. Soc. Am.
100
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(1996
);H. A.
Conklin
, Jr., “Design and tone in the mechanoacoustic piano. Part III. Piano strings and scale design
,” J. Acoust. Soc. Am.
100
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(1996
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A.
Chaigne
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A.
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A.
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and A.
Askenfelt
, “Numerical simulations of piano strings. II. Comparisons with measurements and systematic exploration of some hammer-string parameters
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D. E.
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I. Nakamura, “The vibrational character of the piano soundboard,” Proc. 11th ICA, Paris (1983), Vol. 4, p. 385.
8.
H.
Suzuki
, “Vibration and sound radiation of a piano soundboard
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J. Kindel and I-C. Wang, “Modal analysis and finite element analysis of a piano soundboard,” in Proceedings of the 5th International Modal Analysis Conference (Union College, Schenectady, New York, 1987), p. 1545.
10.
J. Kindel, “Modal analysis and finite element analysis of a piano soundboard,” Masters thesis, University of Cincinnati, 1989.
11.
N.
Giordano
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K. Wogram, “Acoustical research on pianos. Part I: Vibrational characteristics of the soundboard,” Das Musikinstrument 24, 694 (1980);
24, 776 (1980);
24, 872 (1980).
13.
K. Wogram, in The Acoustics of the Piano, edited by A. Askenfelt, Royal Swedish Academy of Music Publication No. 64 (Stockholm, 1990), p. 83.
14.
We should also note that Suzuki (Ref. 8) has reported some results concerning the mechanical response up to a few kHz. While his measurements do not yield values for the mechanical impedance, they imply that this impedance is approximately constant up to his highest frequencies. Suzuki’s results are thus consistent with the findings of Conklin (Ref. 1).
15.
N. H. Fletcher and T. D. Rossing, The Physics of Musical Instruments (Springer-Verlag, New York, 1991).
16.
The piano was an upright made by the Charles Fredrich Stein Company, and was approximately 60 years old. It appeared to have relatively new dampers, but the hammers and strings were probably original. For all of our measurements the dampers were always in contact with the strings.
17.
The shaker was a model V102 from Ling Dynamical Systems.
18.
The force sensor was a model 209C01 from PCB Piezotronics.
19.
Two different accelerometers, both obtained from PCB Piezotronics, were used. One (model 352B68) had a mass of 2.0 g and had a base which was designed to be screwed into the object to be studied, while the other (model 352A10) had a mass of 0.7 g and was attached with a small amount of wax.
20.
The Art of Electronics, edited by P. Horowitz and W. Hill (Cambridge U.P., Cambridge, England, 1989), 2nd ed.
21.
Details of this concern, and a very instructive discussion of the difficulties that can be encountered in such measurements, were communicated to the author by H. A. Conklin, Jr. Similar ideas were also conveyed to us by G. Weinreich.
22.
L. Cremer and M. Heckl, Structure-Borne Sound (Springer-Verlag, New York, 1973).
23.
The model calculation in Ref. 11 considered a soundboard with ribs, but for simplicity ignored the effect of the bridges. However, the presence of bridges does not change any of our qualitative arguments.
24.
Two comments need to be made concerning the phase results in Ref. 11. First, in that paper we plotted the phase of which is in the notation of the present paper. Second, the results for the phase reported in Ref. 11 have a minor error. In the notation of the present paper, negative values of were in Ref. 11 erroneously given a positive sign. Correcting this error yields results in good agreement with the measurements in Fig. 7, especially for the average value of at high frequencies (above ).
25.
Our measurements also indicate that Wogram’s results for the the sound intensity normalized by the soundboard velocity, underestimate the sound production at high frequencies. We will present our results for the sound production elsewhere.
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