An organ pipe of length L open at both ends is found to vibrate in its harmonic when sounded with a tuning fork of 480Hz. 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?

Explanation

For open organ pipe, the frequency of first harmonic
`v = (upsilon)/(2l) = 480 Hz" "...(i)`
For closed organ pipe, the frequency of first harmonc
`v' = (upsilon)/(4l') = 480" "...(ii)`
From (i) and (ii), we have
2l = 4l'
or `l' = (l)/(2)`