Shock spectra of piano hammers

Abstract

It has been suggested [I. Bork, Appl. Acoust. 30 (in press)] that an effective way to characterize the frequency dependence of energy transfer efficiency from a piano hammer to a string is by means of the shock spectrum, which describes the vibration amplitudes of a simple oscillating system with a resonance frequency f, either during (initial shock spectrum) or after (residual shock spectrum) an impact. Shock spectra of piano hammers striking a string segment have been recorded by means of a force transducer and an FFT analyzer. Initial results indicate that as the hammer speed increases, the shock spectrum broadens and its maximum shifts systematically upward in frequency (fmax is nearly proportional to the square root of speed for most hammers). In a carefully voiced piano, fmax increases from bass to treble but does not double each octave. Experimental results are compared to various hammer models that include a nonlinear spring characteristic.