Node Placement in Stationary Waves on Pool Surfaces

[jaumzaum]

Do stationary waves in a pool need to necessarily have nodes at the initial/final points where the wave hits the wall?

I'm really asking this because the walls does not seem to be a physical blocker, like a fixed end of a rope that is tied. Considering friction I would say that some energy could be lost in the walls if there were not nodes there, but air resistance would do the same, and that's why tere is no such thing as a completely stationary wave. So, during the majority of the "life" of the wave, will it tend to have nodes (or almost nodes) at the walls?

 

[Halc]

Quite the opposite it seems. A standing wave of water traverses maximum horizontal distance at the nodes, and moves only vertically at the antinodes, which will thus be at the edges of the pool.

Yes, there is always energy drain: Friction with the walls and air. The wave will not sustain itself without some kind of energy input at some regular frequency that is a harmonic of the body of water. Thus round buckets are ideal for standing waves, and irregular ones less so.

 

[sophiecentaur]

the walls does not seem to be a physical blocker,

If the walls are vertical then there will be a displacement antinode (i.e. the wave amplitude will be a maximum) but energy is reflected there. There will be a maximum of stored energy there, too and that's the same sort of situation as at the open end of an organ pipe and most of the energy arriving at the barrier will be reflected.

The energy carried by a wave that's launched towards the wall will be reflected and the reflected wave will add to it to produce a standing wave with up to twice amplitude (much less in practice, due to losses). Multiple reflections from the sides, when the dimensions are suitable, can cause a larger amplitude but surface wave resonances on water have a low Q factor compared with resonances on strings, pipes and plates.

A wide source of waves in a rectangular tank can build up very high peaks but most experimental examples that I could find (Google Ripple Tank) do not involve multiple reflections.

 

[jaumzaum]

@Halc @sophiecentaur thank you very much!

Your responses helped me a lot, but they were in fact the opposite of what I expected. You said that on the walls we would have antinodes (maximum amplitude), as the walls are compared to open ends of a pipe. I was comparing walls to "almost" closed ends of a pipe. Can you explain to me why is the opposite?

Also, Halc said at the antinodes we would have only vertical displacement, where at the nodes we would have maximum horizontal displacement. Could you please explain that to me? For me, in a transverse standing wave, we would have only vertical displacement, no matter where.

 

[berkeman]

You said that on the walls we would have antinodes (maximum amplitude), as the walls are compared to open ends of a pipe. I was comparing walls to "almost" closed ends of a pipe. Can you explain to me why is the opposite?

You are mixing two different kinds of wave motion. The water waves in a pool are transverse, so the water is free to form antinodes at the walls. The sound waves in a pipe are longitudinal, so the air molecules are not free to move at the closed end of the pipe.

 

[jaumzaum]

You are mixing two different kinds of wave motion. The water waves in a pool are transverse, so the water is free to form antinodes at the walls. The sound waves in a pipe are longitudinal, so the air molecules are not free to move at the closed end of the pipe.

THanks @berkeman, but saying that they are free to move, does it mean that they would really move? Why would it bbe?

 

[berkeman]

Which they? Water molecules or air molecules?

 

[sophiecentaur]

Waves on the surface are actually a combination of transverse and longitudinal. The water molecules actually move in circles. Back and forth and up and down. The wall forbids longitudinal motion so, in that respect, it’s a node. Gravity (not gravitational!) waves are a step more complicated than waves inside a medium or on a string. But there’s still the variation of potential and kinetic energy with time and position.