Standing-wave frequencies

f_n=n\dfrac{v}{2L}

Result unit: Hz (hertz)

What it describes

The natural vibration frequencies of a string or air column fixed at both ends.

f_n

frequency of the n-th harmonic

[Hz]

n

harmonic number

v

wave speed

[m/s]

L

length

[m]

A string fixed at both ends vibrates only at certain frequencies (harmonics) —

n=1

is the fundamental tone, higher

n

are the higher components.

String and wind instruments, acoustic resonance.

A string with

L=0.5

m, wave speed

v=100

m/s. Calculate the fundamental frequency (

n=1

Substitution

n=1

v=100

L=0.5

Result

f_1=\dfrac{1\cdot100}{2\cdot0.5}=100

Hz.

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