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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.

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To find the dimensional formulas for \( \omega \) and \( k \) from the wave equation \( y = A \sin(\omega t - kx) \), we will follow these steps: ### Step-by-Step Solution: 1. **Understanding the Wave Equation**: The wave equation is given as \( y = A \sin(\omega t - kx) \). Here, \( y \) is the displacement, \( A \) is the amplitude, \( \omega \) is the angular frequency, \( k \) is the wave number, \( t \) is time, and \( x \) is distance. 2. **Identifying the Arguments of the Sine Function**: ...
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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
  • A progressive wave is represented by y = 5 sin(100pit - 2pix) where x and y are in m and t is in s. The maximum particle velocity is

    A
    `100pims^(-1)`
    B
    `200pims^(-1)`
    C
    `300pims^(-1)`
    D
    `500pims^(-1)`
  • The displacement of an elastic wave is given by the function y=3 sin omega t +4 cos omegat . where y is in cm and t is in second. Calculate the resultant amplitude.

    A
    3 cm
    B
    4 cm
    C
    5 cm
    D
    7 cm
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