Question

A pipe open at both the ends has a fundamental frequency of 600 Hz. The first overtone of a pipe closed at one end has the same frequency as the first overtone of the open pipe. How long are the two pipes?

Answer 1

Given : Open pipe, n_o = 600 Hz, n_c 1 = n_o 1 (first overtones)

For an open pipe, the fundamental frequency,

n_O = v/2Lo

 The length of the open pipe is

Lo = v /2n_O = \(\frac{330}{2×600}\) = 0.275 m

For the open pipe, the frequency of the first overtone is

2n_O = 2 x 600 = 1200 Hz

For the pipe closed at one end, the frequency of the first overtone is 3v/Lo

By the data 3v/4L = 1200

∴ Lc = \(\frac{3×330}{4×1200}\)  = 0.206 m

The length of the pipe open at both ends is 27.5 cm and the length of the pipe closed at one end is 20.6 cm.