Physics Behind Music An Introduction

The harmonic vibrational frequencies of an ideal string under tension, fixed at the ends, are developed, starting with the results from the harmonic oscillator. The corresponding resonances result in sinusoidal standing waves. The end conditions restrict the possible solutions to be those with an integer number of half wavelengths between the ends of the string. A general vibration of the string, such as from a pluck, can be described as the sum of sinusoidal solutions. More general end conditions include a free end, in which case there is an odd number of quarter wavelengths between the ends.