Work out organ pipe frequency instantly with clear inputs, formula shown and shareable results.
An open pipe holds a half wavelength and sounds v/2L; a stopped pipe holds only a quarter wavelength and sounds v/4L, an octave lower for the same length. A closed end forces a displacement node, which suppresses the even harmonics entirely - the reason a stopped organ rank has its distinctive hollow tone.
Open pipe
f(n) = n v / 2L, all n
Stopped pipe
f(n) = n v / 4L, odd n only
It fits only a quarter of a wavelength instead of a half, so the wavelength is twice as long for the same tube - which halves the frequency.
Real open ends radiate slightly beyond the tube, adding roughly 0.6 times the radius per open end. This calculator uses the ideal length.