String Harmonics

Standing Waves on a String

A stretched string fixed at both ends supports standing waves. Only wavelengths that fit a whole number of half-wavelengths between the endpoints are allowed:

f_n = rac{nv}{2L}

• n — harmonic number (1, 2, 3 …)
• v — wave speed along the string (m/s)
• L — string length (m)
• $f_n$ — frequency of the nth harmonic (Hz)

Harmonic Series

$n = 1$ is the fundamental (lowest pitch). Higher harmonics are integer multiples — the tone colour (timbre) of an instrument depends on how much energy each harmonic carries.

Your Task

Implement stringHarmonic(n, v, L) returning the frequency of the nth harmonic.

Run the code to hear the fundamental and the second harmonic of a 1-metre string.