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March 27, 2017

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A plane progressive wave is represented by the equation: y= 0.1sin(200pi(t)-20pi(x/17) where y is the displacement in millimetres, t is in seconds and x is the distance from a fixed origin O in metres. Find (i) the frequency of the wave, (ii) its wavelength (iii) its speed, (iv) the phase difference in radians between a point 0.25m from O and a point 1.10m from O.

  • physics - ,

    (i) For the frequency f, require that
    200*pi*t = 2*pi*f*t
    and solve for f. Obviously f = 100 Hz
    (ii) For the wavelength L, require that
    20 pi (x/17) = 2 pi (x/L).
    That means in this case
    10/17 = 1/L
    L = 1.7 meters.
    (iii) The wave speed is f*L = 170 m/s
    (iv) The phase difference can differ by added multiples of 2 pi. I assume you want the minimum phase difference.
    The difference between 1.1 and 0.25 is 0.85 m. That is 1/2 of a wavelength, so that would be the phase shift.

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