We've started doing waves in our physics class, but we're doing things very quickly and the teacher doesn't explain anything. And I don't understand why waves work.

I was thinking that when I fill a bowl with water, and wait until it's still, and then I put a finger in it, then my finger needs some space where the water is, so the water has to move away, like Archimedes said. So some of that water goes up because it's the only place where there's no finger or the rest of the water, and it's easier for the water to push away the air than the finger or the rest of the water. I think it's only the displacement thing that's working here because I tried putting the finger in the water faster, and the effect was pretty much the same except I spilled a lot of water trying different things.

But I don't get it why after the water has formed this something like a wall around my finger (not that I can see this moment; it's too quick), the wall starts to move towards the rim. Why doesn't the water just flow down the wall, like dry sand flows down a sand wall? Then I think the excess water should spread itself over the surface, but it doesn't do that. So how does this work?

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    $\begingroup$ A finger is not the best instrument to study the behavior of waves in water. see here youtube.com/watch?v=AfKF07n2pwA waves from a pebble thrown in the water. $\endgroup$ – anna v Aug 8 '12 at 18:45
  • $\begingroup$ @annav Thanks, this is a very cool video. With the finger, there was only one moving bumb on the water that I could see. Here there are many. Some strange things are happening at the beginning and then it looks pretty regular. So that can't be just displacement. A little pebble couldn't have displaced that much water, right? And the wider the ring is, the more water is in the bump, right? Or does the bump get smaller when it gets wider? It doesn't look like it does. $\endgroup$ – przemo Aug 8 '12 at 18:52

When you first put your finger into the water, the situation is pretty much as you describe; the water is not solid and so the molecules can move, unlike those of your finger or the bowl, so they must move (no two atoms can be in exactly the same place at exactly the same time). Liquids are classically defined as incompressible (technically most liquids including water can be compressed, but the ratio of force to volume is much greater than with a gas), so not only must the water molecules move, they must push all the other water molecules out of the way instead of simply getting closer to them. However, air, a gas, can move and can compress, so initially it is easier for the water to move up against the air than out against more water to get out of the way of your finger.

That's what happens in the first fractions of a second after your finger enters. What happens next involves some very complex math, but the concept is still simple; while water is incompressible, it is still a fluid, and so as gravity pulls on all the water molecules, those molecules move around each other trying to reach a new equilibrium between the force of gravity and the forces exerted by all the other molecules of water. In short, the surface of the water wants to settle down to a new "level". The water that moved up when you inserted your finger now tries to move back down, pulled by gravity. That pushes other water molecules aside, just as your finger did, and with a similar result; some of them find it easier to go up than out. This process repeats itself over time, with the result that a wave of water is generated as water molecules get out of the way of other molecules and then settle. When this wave hits the edges of the bowl, well, that's a solid surface that won't move, so the water can't move out, so it moves up again, and then when it settles there's only one way the water can push and that's back in the opposite direction.

Now, the second law of thermodynamics states that "you can't get the same energy out of a system that you put in"; even at the molecular level, there is "friction", where molecules will simply absorb the energy as heat instead of moving. In addition, as waves bounce around the edges of the bowl, they meet, and when the crest of the wave meets a trough, the two cancel out (the sum of the energies of the peak and trough of a waveform of given amplitude is zero). Eventually, the waves cancel out enough that the water molecules themselves simply absorb the energy and do not move (perceptibly) at all, and the system has then reached its new resting state.

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  • $\begingroup$ Thanks, this is exactly the kind of answer I wanted. So the water that went up after I put my finger in has enough energy to push the farther water molecules up again instead of just sliding down and staying on top of the farther molecules? And why does the pebble on anna v's video produce more bumps than one? Is it because the pebble keeps going down, and my finger stops immediately after entering the water? $\endgroup$ – przemo Aug 8 '12 at 19:19
  • $\begingroup$ Not exactly. By putting your finger in the water, the water is forced aside; at first it's easier for water molecules to go up than out because it takes less force to compress the air above it and to work against gravity than to push the incompressible water to its sides or underneath it. But remember gravity; it's not just a good idea, it's the law. Gravity will pull the water back down, and in the process force more water to be displaced to make room for the incoming water. Again at first, that water can move up more easily than out, but gravity keeps winning forcing the wave to move out. $\endgroup$ – KeithS Aug 8 '12 at 21:10
  • $\begingroup$ A pebble makes more than one wave because as it enters the water, it shoves it aside like your finger does, but unlike your finger, as it moves completely underneath the surface, water can then move back in to fill the space above it. This creates more oscillations; the initial impact pushes a column of water aside, then once that force has been applied and generates the initial wave, the water rushes back in above the pebble from all sides. That results in too much water moving in to take the place of the pebble, so in finding somewhere to go it moves up, then gravity pulls it down, etc. $\endgroup$ – KeithS Aug 8 '12 at 21:14
  • $\begingroup$ It is a natural explanation. However, it can not explain why the waves produced by a finger are always concentric circles even if I use triangle or square "fingers" to produce them. $\endgroup$ – Shaktyai Aug 8 '12 at 21:20
  • $\begingroup$ @KeithS Super! I think I see it now. Thanks a lot! $\endgroup$ – przemo Aug 8 '12 at 21:23

I think you are really asking why waves move - i.e. why the waves move away from your finger, as opposed to just staying in one place, or disappearing, or maybe going away and them coming back.

One way to think about it is, imagine holding one end of a long rope. If you suddenly shake the rope to one side, you start a wave that moves away from you down the rope.

An even more fun example is in a crowd at a sports stadium doing "the wave". If a bunch of people suddenly stand up, raise their hands, and then sit down, this prompts the people next to them to do the same - standing up, waving their hands, and sitting down. However, they cannot do it at exactly the same time as the first people. They're not that quick. They do it a little bit later, so the peak of the raised hands moves in one direction, from the first people to the second, and so on, and so on, in that direction.

So why doesn't the second group of people feed back and affect the first? They do. The first group of people are in the process of sitting down while the second are standing up. The first group sees the second group standing up, so the first group slows down its downward motion and settles to a stop in its seat.

(A little far-fetched, I know, but I think it's the right basic idea.)

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