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Waves
Waves

Standing Wave (Closed Pipe)

fn=nv4Lf_n = \frac{nv}{4L}

Resonant frequencies for pipe closed at one end.

Variables

f_n
Resonant frequency
Odd harmonics only
Hz
n
Harmonic number
Odd integers 1, 3, 5...
unitless
v
Sound speed
In the pipe
m/s
L
Pipe length
Closed at one end
m

Derivation

Node at closed end, antinode at open: λ_n = 4L/n (odd n).

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Common questions

What is the Standing Wave (Closed Pipe) formula?

Standing Wave (Closed Pipe) is written fₙ = nv/4L. Resonant frequencies for pipe closed at one end. It belongs to Waves, under Superposition.

What are the units in fₙ = nv/4L?

In SI units, f_n is resonant frequency, measured in 1/s; n is harmonic number (dimensionless); v is sound speed, measured in m/s; L is pipe length, measured in m.

How is the Standing Wave (Closed Pipe) formula derived?

Node at closed end, antinode at open: λ_n = 4L/n (odd n). The result is fₙ = nv/4L.