Open Pipe Harmonics

Open Cylindrical Pipe

A pipe open at both ends (flute, organ open pipe) has pressure antinodes at each end. The resonant frequencies follow the same formula as a string:

f_n = rac{nv}{2L}, quad n = 1, 2, 3, ldots

• n — harmonic number
• $v = 343$ m/s (speed of sound in air)
• L — pipe length (m)

All Harmonics Present

An open pipe supports all integer harmonics — the same as a string. This gives it a bright, rich timbre (flute, recorder, human vowels).

Changing Pitch

Halving the pipe length doubles the frequency — one octave up. This is why flutes are shorter than tubas.

Your Task

Implement openPipeMode(n, L) returning the nth resonant frequency ($v = 343$ m/s).

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