Question

The first overtone of a closed pipe $P_1$ and third over-tone of an open pipe $p_2$ are in resonance with a tuning fork. The ratio of the length of the pipes $p_1$ and $p_2$ are

• A. 3 : 8
• B. 8 : 3
• C. 1 : 2
• D. 2 : 1

Answer 1

Answer: (A)

3 : 8

frequency of first overtone of a closed pipe $P_1=\frac{3v}{4L_1}$
frequency of third overtone of a open pipe $P_2=\frac{4v}{2L_2}$
since both pipes are in resonance with same tuning fork which means
frequency of first overtone of a closed pipe $P_1$ = frequency of third overtone of a open pipe $P_2$
$\Rightarrow \frac{3v}{4L_1}=\frac{4v}{2L_2}$
$\Rightarrow \frac{L_1}{L_2}=\frac{3}{8}$