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Waveledngth vs frequency

  1. Mar 29, 2010 #1
    If the frequency of a water wave is doubled in a ripple tank, is the wavelength halved? The depth of water is kept constant.
     
  2. jcsd
  3. Mar 29, 2010 #2
    Yes. In shallow water, the speed of the water waves is dependent only on the depth (and the gravitational acceleration g).

    The general expression for the speed of a water wave is given by:
    [tex]v = \sqrt{\frac{g\lambda}{2\pi}\,tanh(2\pi\frac{d}{\lambda}})[/tex]

    which simplifies in the shallow depth limit into
    [tex]v = \sqrt{gd}[/tex]
     
  4. Mar 30, 2010 #3
    so,
    v=freq x wavelength

    Thus double the frequency the wavelength is halved in shallow water.
     
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