Question

The first overtone of an open organ pipe beats with the first overtone of a closed organ pipe with a beat frequency of $2.2$ Hz. The fundamental frequency of the closed organ pipe is $110$ Hz. Find the lengths of the pipes.

Answer 1

Given,

$v=330m/s$

$\frac{2v}{2L_1}-\frac{3v}{4L_2}=2.2$

$\frac{3v}{4L_2}=110$

$L_2=\frac{9}{4}=2.25m$

$\frac{v}{L_1}=\frac{3v}{9}+2.2=112.2$

$L_1=\frac{330}{112.2}=2.94m$