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An organ pipe of length L open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz. What should be the length of a pipe closed at one end, so that it also vibrates in its first harmonic with the same tuning fork ?

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$\frac{L}{2}$

$\frac{L}{4}$

$\frac{2 L}{3}$

$\frac{3 L}{4}$

answer is A.

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Detailed Solution

$\frac{V}{2 L} = \frac{V}{4 L'}$ ( $∵$ speed remains constant)

$\Rightarrow L' = \frac{L}{2}$

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