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  4. The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe iscm.

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Q. The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is $20 \,cm$. The length of the open organ pipe is_______$cm$.

JEE MainJEE Main 2022Waves

Solution:

$f _{1}=\frac{2 v }{2 l _{1}}$
$f _{2}=\frac{ v }{4 l _{2}}$
$f _{1}= f _{2}$
$=\frac{2 v }{2 l _{1}}=\frac{ v }{4 l _{2}}$
$l _{1}=4 l _{2}=80\, cm$