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 its third overtone are in resonance with a given tuning fork. The ratio of lengths of $P_1$ and P2 is

[EAMCET 1997; MH CET 1999; AFMC 2001]

• A. 1 : 2
• B. 1 : 3
• C. 3 : 8
• D. 3 : 4

Answer 1

The correct option is C

3 : 8

First overtone of closed organ pipe $n_1=\frac{3v}{4l_1}$

Third overtone of open organ pipe $n_2=\frac{4v}{2l_2}$

$n_1=n_2\left(Given\right)\Rightarrow \frac{3v}{4l_1}=\frac{4v}{2l_2}\Rightarrow \frac{l_1}{l_2}=\frac{3}{8}$