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Homework Help: Ate of energy transfer by sinusoidal waves on a string q

  1. Nov 18, 2006 #1
    Q: A two-dimensional water wave spreads in circular wave fonts. Show that the aplitude A at a distance r from the initial disturbance is proportional to [tex]\frac{1}{\sqrt{r}}[/tex]. (Hint: Consider the energy carried by one outward moving ripple.)

    Comments:
    Let's consider the energy carried by one outward-moving ripple:
    [tex]E_\lambda = \frac{1}{2} \mu \omega^2 A^2 \lambda[/tex]
    and I suppose there is another wave directly across the origin for some particle. But how do I relate this to r?

    thanks!
     
  2. jcsd
  3. Nov 19, 2006 #2

    Kurdt

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    Consider the energy density of the ripple. That is the energy per unit length. The length of the wave being a circle is [tex]\pi r[/tex] and then consider the equation you have given above for energy as it contains the amplitude.
     
  4. Nov 19, 2006 #3

    OlderDan

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    All you really need to know to do this problem is that the energy is proportional to A². Since the wave is spreading out in a circle, the energy is being spread over the curcumference of the wave front.
     
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