\[f_n=\frac{nv}{2(L+2e)}\]
Variables
fnresonant frequency (Hz)
nharmonic number
vspeed of sound (m/s)
Lphysical pipe length (m)
eend correction per open end (m)
Description
What is this formula?
The Resonant Frequency of an Open Pipe formula calculates the natural frequencies of a pipe open at both ends using an effective acoustic length. Because the air column extends slightly beyond each open end, the effective length is L + 2e instead of only the physical pipe length.
When to use it
Use this formula when analyzing real open pipes, organ pipes, flutes, acoustic tubes, and resonators where end correction improves frequency accuracy.
Example
Given:
n = 1
v = 343 m/s
L = 0.50 m
e = 0.010 m
Formula:
fn = nv/(2(L + 2e))
Substitution:
fn = (1 × 343)/(2(0.50 + 2 × 0.010))
fn = 343/(2 × 0.52)
fn = 329.8 Hz
Result:
fn ≈ 329.8 Hz
Applications
Organ pipe design.
Flute acoustics.
Acoustic resonator tuning.
Laboratory tube resonance.
Musical acoustics.