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. `500 Hz`
B. `2500 Hz`
C. `3500 Hz`
D. `1500 HZ`

Answer

C

Explanation

Since the full length of the rod is set into a single mode of vibration in which four antinodes are seen .
Hence if `lambda` be the wavelength for this mode of vibration
We have `( 3 lambda)/(2) + (lambda)/(4) = 2.5`
`lambda = ( 4 xx 2.5)/(7) = (10)/(7) m`
Hence frequency of vibration
`= (5000)/(10//7) = 3500 Hz`