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Waves on a string

A wave is an oscillation that travels through space. On a string, the wave speed is set by the tension and the mass per unit length. When the string is fixed at both ends, only certain wavelengths can form standing waves, and these give the string's possible tones.

v = f\lambda

relation between wave speed, frequency and wavelength

v = \sqrt{F/\mu}

wave speed on a string

f_n = \dfrac{nv}{2L}

standing waves, fixed at both ends, n = 1, 2, 3, ...

Symbols

$\mu$	mass per unit length	kg/m
$F$	tension	N
$L$	length of the string	m

Example

A string with $L = 0.65$ m, $F = 80$ N and $\mu = 0.5$ g/m gives $v = \sqrt{80/0.0005} = 400$ m/s, so the fundamental is $f_1 = 400/(2\cdot 0.65) \approx 308$ Hz.

The fundamental has only half a wavelength between the endpoints:

L = \lambda/2

, not

L = \lambda

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Part of Physics: Oscillations and waves.