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 of $P_1$ to that of $P_2$ is

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

Answer 1

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

An organ pipe $P_1$ closed at one and vibrating in its first overtone.
$\Rightarrow 3\times \frac{v}{4l_c}$
Another pipe $P_2$ open at both ends vibrating in third overtone,
$\Rightarrow 4\times \frac{v}{2l_0}$
Comparing,
$\Rightarrow 3\times \frac{v}{4l_c}=4\times \frac{v}{2l_0}$
$\Rightarrow \frac{3}{4l_c}=\frac{4}{2l_0}$
$\Rightarrow \frac{l_c}{l_0}=\frac{3}{4}\times \frac{2}{4}$
$\Rightarrow \frac{l_c}{l_0}=\frac{3}{8}$
Final answer :$\left(b\right)$