Question

A pipe open at both ends has the fundamental frequency n. If the pipe is immersed vertically in water up to half its length, what would be the fundamental frequency of the resulting air column?

Answer 1

Let L be the length of the pipe open at both ends whose fundamental frequency is n. Then, ignoring the end correction, n = \(\frac v{2L}\) where v is the speed of sound in air.

When the pipe is immersed vertically in water up to half its length, it becomes a pipe closed at one end with an air column of length L’ = L / 2. Then, its fundamental frequency n’ is

n' = \(\frac v{4L'}\) = \(\frac v{4(L/2)}\) = \(\frac v{2L}\)

which is equal to n, the fundamental frequency of the open pipe.