### ASA 127th Meeting M.I.T. 1994 June 6-10

## 3pMU2. A study on radiation pattern and radiation efficiency of an upright
piano soundboard.

**Philippe Derogis
**

**
Rene Causse
**

**
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*I.R.C.A.M., 1 place Igor Stravinsky, 75004-Paris, France
*

*
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In this study, a modal analysis of the soundboard of an upright piano with
strings mounted was performed. The measurements of the frequency response
functions and the use of modal testing software have allowed us to find the
eigenfrequencies and the mode shapes. The results agree for the most part with
earlier measurements [I. Nakamura, ``The vibrational character of the piano
soundboard,'' Proc. 11th ICA Paris, 385--388 (1983)]. Indeed, below 300 Hz the
mode shapes are almost the same for an isotropic rectangular plate. However
above 300 Hz, they become more complicated. These results were used to compute
the acoustic field resulting from the vibrations of the soundboard by
calculating numerically the Helmholtz Huygens integral. Then the radiation
pattern curves obtained were compared with measurements and with two simple
models (isotropic baffle plate and isotropic plate radiating on one side). The
integration of the calculated acoustic field was performed in order to
determine the radiation efficiency of the soundboard. Finally, the radiation
efficiency as a function of the plate characteristics (size, stiffness) was
computed using the models above.