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Is “reflecting back” an intrinsic property of water waves?

Physics Asked by Roberto Valente on December 15, 2020

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?

2 Answers

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.

Correct answer by Pieter on December 15, 2020

EDIT 2: This answer doesn't answer the question asked, sorry :(

I think gifs help explain it pretty well. Here's how waves traveling in opposite directions (green and red) combine to form a standing wave (blue): standing wave

Then, you can imagine the green wave as being the red wave bounced off a wall, creating something like this:

https://imgur.com/gallery/otPYS (Sorry, can't embed it)

EDIT: To actually give you an answer to your question. It is definitely possible, but uncommon because you'd need pretty ideal geometry and wave conditions for it to work out like this.

Answered by Leo Adberg on December 15, 2020

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