Node Placement in Stationary Waves on Pool Surfaces

In summary: Water molecules move because they have a lot of energy. They can’t just sit there. Even sound waves are made up of tiny air molecules. When they move, they create pressure waves.
  • #1
jaumzaum
434
33
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 hav nodes (or almost nodes) at the walls?
 
Last edited:
Physics news on Phys.org
  • #2
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.
 
  • #3
jaumzaum said:
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.
 
  • #4
@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.
 
  • #5
jaumzaum said:
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.
 
  • #6
berkeman said:
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?
 
  • #7
Which they? Water molecules or air molecules?
 
  • #8
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.
 
  • Like
Likes berkeman

FAQ: Node Placement in Stationary Waves on Pool Surfaces

1. What are stationary waves in a pool?

Stationary waves in a pool are a phenomenon that occurs when two or more waves of the same frequency and amplitude travel in opposite directions and interfere with each other, creating a pattern of nodes (points of no displacement) and antinodes (points of maximum displacement) that do not move. This creates the appearance of a wave that appears to be standing still, hence the name "stationary" waves.

2. How are stationary waves formed in a pool?

Stationary waves are formed by the interference of two or more waves with the same frequency and amplitude that are traveling in opposite directions. When these waves meet, they create areas of constructive and destructive interference, resulting in the formation of nodes and antinodes. The distance between these nodes and antinodes depends on the wavelength of the waves and the size of the pool.

3. What factors affect the formation of stationary waves in a pool?

The formation of stationary waves in a pool is affected by several factors, including the frequency and amplitude of the waves, the depth and width of the pool, and the speed of the waves. The wavelength of the waves also plays a crucial role, as it determines the distance between nodes and antinodes. Additionally, the presence of any obstacles or boundaries in the pool can also impact the formation of stationary waves.

4. What is the significance of stationary waves in a pool?

Stationary waves in a pool have several practical applications, including in musical instruments such as stringed instruments and wind instruments. They also play a crucial role in the study of fluid dynamics and can help scientists understand the behavior of waves in different environments. Additionally, they are also used in various industries, such as wastewater treatment, to control and manipulate the movement of fluids.

5. How are stationary waves different from traveling waves?

The main difference between stationary waves and traveling waves is that stationary waves do not move, while traveling waves propagate through a medium. Stationary waves are formed by the interference of two or more waves traveling in opposite directions, while traveling waves are created by a disturbance that travels through a medium. Additionally, stationary waves have fixed nodes and antinodes, while traveling waves continuously change in amplitude and wavelength as they move.

Similar threads

Replies
4
Views
2K
Replies
1
Views
1K
Replies
15
Views
2K
Replies
0
Views
4K
Replies
3
Views
4K
Replies
1
Views
3K
Replies
5
Views
4K
Back
Top