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

Consider the situation shown in the diagram

As the organ pipe is open at both ends, hence for first harmonic
`" " l=(lambda)/(2)`
`rArr " " lambda=2lrArr(c)/(v)=2lrArrv=(c)/(2l)`
wherer c is speed of the sound wave in air .
For pipe closed at one end
`" " v'=(c)/(4L')`
c for harmonic

Hence `" " v=v'" "` [ for resonance wit same tuning fork]
`rArrr" " (c)/(2L)=(c)/(4L')" "` [` :.` speed remains constant ]
`rArr" " (L')/(L)=(2)/(4)=(1)/(2)rArrL'=(L)/(2)`