Is it possible to determine the depth of a lake (for example) according to the waves of a stone thrown in this lake ?
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1$\begingroup$ I doubt it. The water motion associated with waves doesn't penetrate very far downward from the surface of the water. I think that the depth of penetration is comparable to the wavelength of the surface waves. $\endgroup$– user93237Commented Nov 7, 2015 at 21:13
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$\begingroup$ You can find the answer by looking at waves as they break on a shallow beach. Only very near the waterline, where the water is very shallow do the waves get pushed up and fall over themselves. So unless the lake is very shallow water waves provide no information re. the depth of the lake. $\endgroup$– GertCommented Nov 7, 2015 at 21:20
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The amplitude does not depend on lake depth, and the celerity depends on deph only when the depth is less than a few wavelenghts ("shallow water" case). Since the largest triggered wavelenght is the order of magnitude of the size of your stone, you should throw stone having about (e.g. 25-400%) the size of the expecte lake depth.
