Physics Behind Music An Introduction

Wave solutions of short duration, or transients, are shown to be equivalent to the sum of a large number of sinusoidal solutions over a range of frequencies. The range of frequencies is inversely proportional to the time duration. This result can be expressed mathematically as an uncertainty principle and explains why waves of very short duration do not have an identifiable pitch. A similar phenomenon occurs during a rapid rise or fall of a signal. Spectrographs can be used to represent a changing spectrum as a function of time, where data are collected and analyzed with a moving time window, similar to what appears to happen for human perception. In contrast to periodic signals, for a short transient signal, the phase factors in the Fourier series are most important for perception.