\[f_n=\frac{nv}{2L}\]
Variables
fnstanding wave frequency (Hz)
nharmonic number
vwave speed (m/s)
Lstring length (m)
Description
What is this formula?
The Standing Wave Frequency formula calculates the resonant frequencies that can exist on a stretched string or similar system with fixed ends. Each allowed frequency corresponds to a harmonic mode.
When to use it
Use this formula when analyzing vibrating strings, resonant mechanical systems, musical instruments, and laboratory wave experiments.
Example
Given:
n = 3
v = 120 m/s
L = 1.5 m
Formula:
fn = nv/(2L)
Substitution:
fn = (3 × 120)/(2 × 1.5)
fn = 360/3
fn = 120 Hz
Result:
fn = 120 Hz
Applications
Stringed musical instruments.
Mechanical resonance analysis.
Wave mechanics.
Laboratory standing-wave experiments.
Acoustical engineering.