A study on radiation pattern and radiation efficiency of an upright piano soundboard

Abstract

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.