A steel rod `2.5 m` long is rigidly clamped at its centre `C` and longitudinal waves are set up on both sides of `C` by rubbing along the rod . Young's modulus for steel ` = 2 xx 10^(11) N//m^(2)` , density of steel ` = 8000 kg//m^(3)`

If the clamp of the rod be shifted to its end `A` and totally four antinodes are observed in the rod when longitudinal waves are set up in it , the frequency of vibration of the rod in this mode is

Options

A. `1000 Hz`
B. `3000 Hz`
C. `7000 Hz`
D. `1500 Hz`

Answer

B

Explanation

Velocity of the longitudinal waves in the rod
`v = sqrt(Y//d) = sqrt( 2 xx 10^(11)//8000) = 5000 m//s`
The wavelength of the wire for the mode of vibration in which `2` antinodes occur is
`lambda = (1.25)/((3//4)) = (5)/(3) m`
Hence frequency of vibration
`n = (V)/(lambda) = (5000)/( 5//3) Hz = 3000 Hz`