I have two ultrasonic transducers, an emitter and a receiver, and I'd like to know how the energy of the spherical wave is conserved. I guess the energy is proportional to its amplitude and it decreases as $1/r^2$, but I'm not sure if what is seen by the microphone is that amplitude or something else. Thank you very much
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$\begingroup$ couldn't you measure that? $\endgroup$– anon01Commented Apr 19, 2016 at 3:23
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$\begingroup$ Yes I did measure it, and it fits more or less well to the curve $1/r^2$ , but I want to be sure of the theoretical expected behaviour $\endgroup$– MBolinCommented Apr 19, 2016 at 9:09
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1 Answer
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Energy is proportional to amplitude squared. The energy in the wave is spread out over the surface of a sphere. The area of this surface increases as the wave propagates outwards from the source and is proportional to $r^2$. So the intensity of the wave (power/area) decreases in proportion to $1/r^2$.
answered May 16, 2016 at 22:21