Question

An organ pipe P${}_1$ closed at one end vibrating in its first overtone and another pipe P${}_2$ open at both ends vibrating in third overtone are in
resonance with a given tuning fork. The ratio of the length P${}_1$ to that of P ${}_2$ is

• A. $\frac{8}{3}$
• B. $\frac{3}{8}$
• C. $\frac{1}{2}$
• D. $\frac{1}{3}$

Answer 1

The correct option is B $\frac{3}{8}$

First overtone of pipe closed at one end is $\frac{3v}{4l_1}$

Third overtone of open pipe is $\frac{4v}{2l_2}$

$\therefore f_1=f_2\Rightarrow \frac{3}{4P_1}=\frac{2}{P_2}$

$\frac{P_1}{P_2}=\frac{3}{8}$