Why does eg a falling stone crate many ripples on a water surface?

[Antti]

So I've studied physics at the university quite a bit and was a bit surprised when I couldn't answer this simple question a friend asked me. When something lands in water why are several ripples created? Like why is the resulting water wave made up of several peaks and valleys and not just one peak, valley or peak/valley pair?

The only possible explanation I could come up with at the time was that an object does not cross the water surface instantaneously. It transfers energy to the water over some period of time and thus the water wave would have some spatial extension because of that. However I suspect that it's not the whole story.

 

[Jeremy87]

Make a sudden movement at the end of a long rope, and you will see a wave propagate even though no part of the rope follows the wave. The rope won't oscillate because it loses its energy hitting the ground, but water will keep moving until friction stops it.

So the waves aren't water moving outwards, they are water oscillating back and forth, giving the illusion of something moving in one direction.

 

[haruspex]

When the stone hits the water it creates a well. Displaced water flows back into the well, but the energy it has gained from the stone means it 'overshoots' and creates a peak, which then collapses, forming a well.. Each of these motions generates a ripple and saps some of the energy from the centre.

 

[Antti]

When the stone hits the water it creates a well. Displaced water flows back into the well, but the energy it has gained from the stone means it 'overshoots' and creates a peak, which then collapses, forming a well.. Each of these motions generates a ripple and saps some of the energy from the centre.

Thanks, that sort of makes sense. But he might say "well why doesn't the center return to its original state just once and only create one ripple?". Somehow I suspect energy conservation has something to do with it.

 

[A.T.]

But he might say "well why doesn't the center return to its original state just once and only create one ripple?

Because of inertia and the fact that the restoring forces (which try to bring it into the original state) depend on the displacement from the original state. When the water is moving back upwards it has some velocity, and cannot suddenly stop in the original state, especially since the restoring forces at the original state are zero.

Also note that the disturbance propagates in all directions, from every position that is disturbed. Not just from the the original position, where the disturbance was caused externally by the stone. So you cannot have a single circular ripple propagating just outwards, with calm water inside. Because every point on that ripple is a source of a circular wave front. See:
http://en.wikipedia.org/wiki/Huygens–Fresnel_principle

 

[tiny-tim]

"well why doesn't the center return to its original state just once and only create one ripple?". Somehow I suspect energy conservation has something to do with it.

tell him, "same as why a cork bobs up and down when you push it down"

(and yes, it's energy conservation … the restoring force is always in the same direction (on the way up), so that's lots of energy when it reaches the start position!)