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A travelling wave has the frequency v an...

A travelling wave has the frequency `v` and the particle displacement amplitude `A`. For the wave the particle velocity amplitude is ………………… and the particle acceleration amplitude is ……………………..

Text Solution

Verified by Experts

The correct Answer is:
A, B
Since `y = A sin (omegat - kx)`
`Displacement amplitude = A` (Max displacement)
Particle velocity, `v = (dy)/(dt) = A omega cos (omegat - kx)`
:. Velocity amplitude `= Aomega = 2pivA`
Particle acceleration
Acc = (dv)/(dt) = -Aomega^(2) sin (omegat - kx)`
:. Acceleration (Max acc) amplitude = Aomega^(2) = 4pi^(2)v^(2)A`
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Knowledge Check

  • In (Q. 10.) the ratio of particle velocity amplitude and wavelength is

    A
    `pi`
    B
    `2pi`
    C
    `3pi`
    D
    `4pi`

  • For a particle in S.H.M. if the amplitude of displacement is a and the amplitude of velocity is v the amplitude of acceleration is

    A
    `va`
    B
    `(v^(2))/(a)`
    C
    `(v^(2))/(2a)`
    D
    `(v)/(a)`

  • The frequency of oscillation of a particle executing SHM with amplitude A and having velocity 'v' at the mean position is

    A
    `(v)/(2piA)`
    B
    `(v)/(A)`
    C
    `(A)/(v)`
    D
    `(2piA)/(v)`

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