Question

A cylindrical metal tube, has a length of $50cm$ and is open at both ends. Find the frequencies between $1000Hz$ and $2000Hz$ at which the air column in the tube can resonate. Speed of sound in air is $340m{s}^{-1}$.

Answer 1

The resonant frequencies in an open organ pipe is given as $\nu =\frac{nV}{2L}$. Where n = 1, 2, 3, ...

Given $V=340m/s$ and $L=50cm=0.50m$.

Hence, $\nu =n\left(\frac{340}{2\times 0.50}\right)=340n$.

The resonant frequencies between $1000Hzto2000Hz$ can be found by putting $n=3,4and5$ in it.

For $n=3,{\nu }_3=340\times 3=1020Hz$

For $n=4,{\nu }_4=340\times 4=1360Hz$,

For $n=5,{\nu }_5=340\times 5=1700Hz$.