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The displacement of a progressive wave i...

The displacement of a progressive wave is represented by `y = A sin (omegat - kx),` where x is distance and t is time. Write the dimensional formula of (i) `omega and (ii) k.

Text Solution

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Here, `y = A sin (omegat- kx)`
An angle is dimensionless, therefore `omegat = (1)/(t) rarr [T^(-1)] , kx =1, k =(1)/(x) rarr [L^(-1)].`
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Knowledge Check

  • The displacement of a progressive wave is represented by y=Asin(omegat-kx) where x is distance and t is time. The dimensions of (omega)/(k) are same as those of

    A
    velocity
    B
    wave number
    C
    wavelength
    D
    frequency

  • In equation varepsilon =A sin (omegat-kx) where t is in second and x is in meter, the dimensional formula for

    A
    `omega "is" [M^0L^0T^(-1)]`
    B
    k is `[M^0L^(-1)T_0]`
    C
    `(omega)/k "is" [M^0LT^(-1)]`
    D
    a is `[M^0LT^(-1)]`

  • If x=k sin (k l t) , where x is displacement and t is time then dimensional formula for l will be (k, l="constant")

    A
    `[M^(0)L^(0)T^(0)]`
    B
    `[M^(0)L^(1)T^(0)]`
    C
    `[M^(0)L^(-1)T^(-1)]`
    D
    `[ML^(-1)T^(-1)]`

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