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I have come across an interesting answer here on Physics SE which states that you get standing waves when you throw a rock in a lake, because of an “intrinsic property” of even dimensional waves.

“(...) waves in an even number of dimensions, such as on water, reflect back, even if the wave impedance is constant. For example, if you drop a rock in a lake, the wave does not just circle out leaving the center undisturbed (like a light flash would). Instead, the wave also reflects back and forms a standing wave in the center.”

I have not been able to find more evidence of this phenomenon. What is the best way to interpret this information?

anna v
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Standing waves require boundary conditions. Such systems have resonance frequencies. One can create circular standing waves in a cup, with large heights in the center when the excitation is at resonance.

Or in three dimensions, one can even create sonoluminescence at the center.

I would not talk about standing waves in connection with a stone in a lake or those drops of milk that jump back up or the central mountain in a crater. It is something else, not related to boundary conditions or resonant frequencies.