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I am having a problem with assigning conservation of energy with sinusoidal wave.

For suppose, if I hit a water surface with a stone, then wave is gonna propagate through the whole surface as a sinusoidal wave. But by hitting a portion of the surface I only give a part of the surface to oscillate. But after some time the surrounding molecules will oscillate with the same energy; forming a sinusoidal wave. But where do these molecules energy from?

I am sure I have a misconception somewhere.

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    $\begingroup$ The amplitude of the wave changes getting smaller the further it is from the original disturbance. $\endgroup$
    – Farcher
    Aug 26, 2016 at 4:59

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But after some time the surrounding molecules will oscillate with the same energy; forming a sinusoidal wave. But where do these molecules energy from?

Conservation of energy means that if you sum up all the oscillation energies of the molecules at time t' they should sum up to the energy of the impact at time t. The energy is spread to a bigger volume, the amplitude of the wave falls, and that is why waves dissipate completely. ( there will be radiative etc losses too, but smaller than the geometrical dissipation, unless the medium has great viscossity).

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  • $\begingroup$ Is there any equation that measures the change in amplitude and energy of molecules ahead of the point of disturbance(as the the wave forwards) $\endgroup$ Aug 26, 2016 at 7:19
  • $\begingroup$ it will depend on the type of wave and the medium. see this link which discusses sound waves ccrma.stanford.edu/~jos/pasp/Spherical_Waves_Point_Source.html $\endgroup$
    – anna v
    Aug 26, 2016 at 8:37

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