Question

An open organ pipe filled with air has a fundamental frequency 500Hz. The first harmonic of another organ pipe closed at one end and filled with carbon dioxide has the same frequency as that of the first harmonic of the open organ pipe. Calculate the length of each pipe. Assume that the velocity of sound in air and in carbondioxide to be 330 and 264 m/s respectively.

Answer 1

Fundamental frequency of open organ pipe with air=$\frac{v_{air}}{2l_1}=500Hz$

$⟹l_1=\frac{330}{2\times 500}=0.33m=33cm$

Frequency of first harmonic pipe closed at one end=$\frac{v_{C{O}_2}}{4l_2}=\frac{v_{air}}{2l_1}=500Hz$

$⟹l_2=13.2cm$