Coupling between transverse and longitudinal waves in piano strings

Abstract

It is known that longitudinal waves in piano strings noticeably contribute to the characteristic sound of the instrument. These waves can be induced by directly exciting the motion with a longitudinal component of the piano hammer, or by the stretching of the string associated with the transverse displacement. Longitudinal waves that are induced by the transverse motion of the string can occur at frequencies other than the longitudinal resonance frequencies, and the amplitude of the waves produced in this way are believed to vary quadratically with the amplitude of the transverse motion. We present the results of an experimental investigation that demonstrates the quadratic relationship between the magnitude of the longitudinal waves and the magnitude of the transverse displacement for steady-state, low-amplitude excitation. However, this relationship is only approximately correct under normal playing conditions.