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 [2016]

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Solution

Q.
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 [2016]

1 $L$

2 $2 L$

3 $\frac{L}{2}$

4 $4 L$

Ans.
(2)

Second overtone of an open organ pipe

(Third harmonic) $= 3 \times υ_{0}' = 3 \times \frac{v}{2 L'}$

First overtone of a closed organ pipe

  (Third harmonic) $= 3 \times υ_{0} = 3 \times \frac{v}{4 L}$

According to question,

   $3 υ_{0}' = 3 υ_{0} \Rightarrow 3 \times \frac{v}{2 L'} = 3 \times \frac{v}{4 L}$

$∴$    $L' = 2 L$

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