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
NEET 2016, Medium
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Second overtone of an open organ pipe
$\text { (Third harmonic) }=3 \times v_{0}^{\prime}=3 \times \frac{v}{2 L^{\prime}}$
First overtone of a closed organ pipe
$\text { (Third harmonic) }=3 \times v_{0}=3 \times \frac{v}{4 L}$
According to question,
$3 v_{0}^{\prime}=3 v_{0} \Rightarrow 3 \times \frac{v}{2 L^{\prime}}=3 \times \frac{v}{4 L}$
$\therefore \quad L^{\prime}=2 L$
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