A pipe open at both ends has a fundamental frequency 'f' in air. The pipe is dipped in water, so that 2 3 ^ rd length of pipe is in water, Now the fundamental frequency of the air column is

Step-by-step solution

For a pipe open at both ends, the fundamental frequency is given by f = v 2L , where v is the speed of sound and L is the length of the pipe. When the pipe is dipped in water such that 2 3 of its length is submerged, the length of the air column remaining above the water surface is L' = L - 2L 3 = L 3 . The pipe now behaves as a pipe closed at one end. The fundamental frequency of a closed pipe is given by f' = v 4L' . Substituting L' = L 3 , we get: f' = v 4 ( L 3 ) = 3v 4L Since v 2L = f , we can write: f' = 3 2