A metal bar when clamped at its centre resonantes in the fundamental frequency with longitudinal waves of frequency 4kHz. If the clamps is moved to one end.What will be its fundamental resonanace frequency ?

Explanation

When a metal bar of length l is clamped in the middle , it has one node in the middle and two antinodes at its free ends. In the fundamental mode `l = ( lambda)/(2) implies lambda = 2l`

In the fundamental mode of frequency of bar = frequency of wave `= 4kHz`
`:. v = ( v)/(lambda) = ( v)/(2l) = 4kHz` ....(1)
When clamp is moved to one end.
`l =( lambda')/(4) implies lambda =4l`
`:. v^(1) = ( v)/( lambda) = ( v)/(4l) = ( 4kHz)/(2) =2kHz` [ `:'` from (1) ]