Question

An organ pipe A with both ends open, has a fundamental frequency of 300 Hz. The third harmonic of an organ pipe B, with one end open, has the same frequency as the second harmonic of pipe A. How long are pipes A and B? Speed of sound in air is $330m{s}^{–1}$ and the end correction is to be neglected.

Answer 1

Pipe A is open at both ends, hence its fundamental frequency $v_A\text{equals}\frac{v}{2l_A}$

$\therefore v_A=300=\frac{330}{2l_A}$

$\Rightarrow l_A=\frac{330}{2\times 300}=0.55m=55cm$

The frequency of the second harmonic of A i.e., $v_A$, is twice its fundamental frequency.
It, therefore, equals 600 Hz.
The frequency $v_B$, of the third harmonic of pipe B is therefore equal to 600 Hz. Since $v_B$, is the frequency of third harmonic of pipe B which is closed at one end, we have
$v_B=\frac{3v}{4l_B}$
or $600=\frac{3\times 330}{4l_B}$
or $l_B=\frac{3\times 330}{4\times 600}=0.41m$
$=41cm$