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A steel rod 2.5 m long is rigidly clampe...

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 two antinodes are observed on either side of `C` , the frequency of the node in which the rod is vibrating will be

A

`1000 Hz`

B

`3000 Hz`

C

`7000 Hz`

D

`1500 Hz`

Text Solution

Verified by Experts

The correct Answer is:
B
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`
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Knowledge Check

  • 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

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

  • 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 amplitude of the wave at the antinode , when it is vibrating in its fundamental mode is 2 xx 10^(-6) m , the maximum velocity of a steel particle in its vibration is

    A
    `1.25 xx 10^(-2) m//s`
    B
    `1.25 xx 10^(-3) m//s`
    C
    `1 m//s`
    D
    `0.12 m//s`

  • If the young's modulus of the material of the rod is 2 xx 10^(11) N//m^(2) and its density is 8000 kg//m^(3) then the time taken by a sound wave to traverse 1m of the rod will be

    A
    `10^(-4)s`
    B
    `2 xx 10^(-4)s`
    C
    `10^(-2)s`
    D
    `2 xx 10^(-2)s`

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