Physics - Sound Wave Question with Solution | TestHub

For an open pipe of length $L$, the frequency of the $n$-th harmonic is $f_n=\frac{nv}{2L}$.

The second overtone corresponds to the third harmonic ($n=3$).

$f_o=\frac{3v}{2L}$

For a closed pipe of length $L$, the frequency of the $m$-th harmonic is $f_m=\frac{mv}{4L}$, where $m$ is an odd integer.

The second overtone corresponds to the fifth harmonic ($m=5$).

$f_c=\frac{5v}{4L}$

The ratio of their frequencies is:

$\frac{f_o}{f_c}=\frac{\frac{3v}{2L}}{\frac{5v}{4L}}=\frac{3}{2}\times \frac{4}{5}=\frac{6}{5}$

Answer: $6:5$