Physics - Sound Wave Question with Solution | TestHub

For pipe $P_1$ (closed at one end), the frequency of the first overtone corresponds to the third harmonic. Its frequency is given by:

$f_1=\frac{3v}{4L_1}$

For pipe $P_2$ (open at both ends), the frequency of the third overtone corresponds to the fourth harmonic. Its frequency is given by:

$f_2=\frac{4v}{2L_2}$

Since both pipes are in resonance with the same tuning fork, their frequencies must be equal:

$f_1=f_2$

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

$\frac{3}{4L_1}=\frac{2}{L_2}$

$\frac{L_1}{L_2}=\frac{3}{8}$

The ratio of the length of pipe $P_1$ to that of $P_2$ is $3:8$.

Answer: $3:8$