First slide

Experiments to find speed of sound

Question

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L metre long. The length of the open pipe will be

Easy

A

L
B

2L
C

$\frac{L}{2}$
D

4L

Solution

Second overtone of an open organ pipe
$= Third harmonic = 3 \times v_{0}^{'} = 3 \times \frac{v}{2 L^{'}}$
First overtone of a closed organ pipe
$= Third harmonic = 3 \times v_{0} = 3 \times \frac{v}{4 L}$
According to question
$3 v_{0}^{'} = 3 v_{0} \Rightarrow 3 \times \frac{v}{2 L^{'}} = 3 \times \frac{v}{4 L} \Rightarrow L^{'} = 2 L$

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