Can We Calculate the Momentum of a Mechanical Wave?

[davidbenari]

I haven't seen differential equations yet so please do not answer at that level.

Suppose I'm on the beach, in the water, and some wave crashes against me. Can we talk about the momentum of that wave as being just the mass of the bump times the velocity of the wave? Can we speak of conservation of momentum for a mechanical wave? And if yes, why?

I saw some explanations of whip cracking in terms of conservation of momentum and KE and I thought it was interesting. How do you calculate the momentum of a mechanical wave? I've seen some threads on forums that say that momentum in this case is meaningless.

What do you think?

Thanks

 

[olivermsun]

Suppose I'm on the beach, in the water, and some wave crashes against me. Can we talk about the momentum of that wave as being just the mass of the bump times the velocity of the wave?

No, for the simple reason that the wave moves through the water much faster than actual mass (water) is moving.*

Although arguably if you are on the beach and the wave is actually breaking over you, then some of the water is moving at the speed of the wave or even slightly faster (which is why it's breaking). But then it's not really behaving like a "wave" anymore—it's just a bunch of water flowing forward.

*) It's actually kind of strange, but waves are associated with a momentum flux (they can be thought to transport momentum between points) but the momentum is not exactly contained in the wave itself!