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Waves
Waves

Standing Wave on String

fn=n2LTμf_n = \frac{n}{2L}\sqrt{\frac{T}{\mu}}

Resonant frequencies for string fixed at both ends.

Variables

f_n
Resonant frequency
nth harmonic
Hz
n
Harmonic number
Integer 1, 2, 3...
unitless
L
String length
Fixed at both ends
m
T
Tension
String tension
N
μ
Linear density
Mass per length
kg/m

Derivation

λ_n = 2L/n, f_n = v/λ_n = (n/2L)√(T/μ).

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Common questions

What is the Standing Wave on String formula?

Standing Wave on String is written fₙ = n/2L√(T/μ). Resonant frequencies for string fixed at both ends. It belongs to Waves, under Superposition.

What are the units in fₙ = n/2L√(T/μ)?

In SI units, f_n is resonant frequency, measured in 1/s; n is harmonic number (dimensionless); L is string length, measured in m; T is tension, measured in kg·m/s²; μ is linear density, measured in kg/m.

How is the Standing Wave on String formula derived?

λ_n = 2L/n, f_n = v/λ_n = (n/2L)√(T/μ). The result is fₙ = n/2L√(T/μ).