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My guess is that, in an ideal case and considering a single particle, it must be the case. With my current (lack of) knowledge, I imagine the opposite would imply some kind of delay between the reception of the original wave and the oscillation generating the new wave, which would imply the scattering is not fully elastic, right? Is this reasoning valid for dense matter too?

In the other hand, I'm not sure what would happen in a less ideal case. Would the partial energy dissipation cause a delay in the wave "repetition", or would this merely cause a wave with the same phase as in the ideal case, but with a weaker amplitude?

I would appreciate if you could confirm or reject my reasonings, with accompanying explanations. Thank you very much in advance.

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Not actually. And your question is a little messy so I am answering in a general way, hope this helps.

In case of Rayleigh Scattering, it constitutes a phase shift of the initial free-space wave. And scattering is, ideally a non-elastic interaction, but considering lesser mass-distribution for scattering, and also with smaller dimension of particles, one achieves near-elastic interaction. And in general cases, this is considered to be elastic. And Partial energy dissipation will constitute some 'delay' (it is the phase shift actually) and the dissipated energy is observed by the decrement of amplitude.

And with higher frequency, the rate of decrement of amplitude or the rate of Energy Dissipation is larger, and vice versa.

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