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An organ pipe of length L open at both e...

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 ?

Text Solution

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Initially, first harmonic of open pipe is equal to 480 Hz.
Hence `(v)/(2L) =480 " "…(1)`
(Where v = volocity of sound in air)
Finally, first harmonic of closed pipe is equal to 480 Hz.
Hence, `(v)/(4L)=480" "…(2)`
From `(v)/(2L) = (v)/(2L) implies L. = (L)/(2)`
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