Question

Fundamental frequency of an open organ pipe is $f$. Match the following two columns for a closed pipe of double the length.

Answer 1

Let the speed of sound be $v$ and the length of open organ pipe be $L.$

Fundamental frequency of an open organ pipe is given as $f$.

$⟹f=\frac{v}{2L}$

The length of closed pipe $l=2L$

Frequency of different modes of vibration in closed pipe ${\nu }_n^{\prime }=\frac{(2n-1)v}{4l}$ where $n\ge 1$

Thus ${\nu }_n^{\prime }=\frac{(2n-1)v}{8L}$

Now fundamental frequency of a closed organ pipe i.e $n=1$ $⟹{\nu }_1^{\prime }=\frac{v}{8L}=\frac{f}{4}$

For second overtone frequency, $n=3⟹{\nu }_3^{\prime }=\frac{5v}{8L}=1.25f$

For first overtone OR third harmonic frequency, $n=2⟹{\nu }_2^{\prime }=\frac{3v}{8L}=0.75f$