JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Waves & Sound

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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.

Answer: 80

Solution

For an open organ pipe, the first overtone (second harmonic) has frequency

f_{1} = \frac{2 v}{2 l _{1}} = \frac{v}{l _{1}}

, where

l_{1}

is the length of the open pipe.

For a closed organ pipe, the fundamental frequency is

f_{2} = \frac{v}{4 l _{2}}

, where

l_{2}

is the length of the closed pipe.

Given that

f_{1} = f_{2}

\frac{v}{l _{1}} = \frac{v}{4 l _{2}}

Solving:

l_{1} = 4 l_{2} = 4 \times 20 = 80

cm.

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Integer answer

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