Does Waves have Inertia and Momentum?

william chan

Consider a disturbance, lets say a stone is dropped in the middle of the pond.
That disturbance will cause circular waves to be propagated equally in all directions away from the disturbance.

Next, consider a wave that is traveling towards one end of a pond.
If we take a snapshot of the wave with a camera, we can visualize the crest and the trough of that wave.
At the point of time when the snapshot was taken, the crest and trough can be considered a vertical disturbance to the equilibrium of the water.
Theoretically, after the snapshot, new circularly outward waves should have been created from that momentary disturbance seen from the snapshot.

In practice however, we notice no such thing and the wave continues to propagate in the same direction after the snapshot, as if it has horizontal inertia and momentum.

Any explanations?

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Phil Pilgrim (PhiPi)

If you freeze a ripple pattern and treat every point in it as a new point disturbance of the given amplitude, as if starting from scratch, the ripple pattern will continue to propagate as before. This is due entirely to addition and cancellation of the multiple new circular wave patterns and has nothing to do with any sort of horizontal momentum. Moreover, except in the case of breaking waves near shore, an object floating on the surface of a wave-filled body of water will experience no net horizontal movement because of the waves.

-Phil

Mike Green

Your description shows the error in making judgements (calculations) with inadequate (static) information. A snapshot shows position in two dimensions at an instant of time. It shows nothing about the 3rd dimension (depth) and nothing of velocity or acceleration. You would gain much more information by photographing a neutral buoyancy marker (like a weighted pingpong ball as a proxy for a small volume of water) using a video camera for several frames where the frames are marked with a time code. Better still would be the use of two cameras with orthogonal views. If the ball were of a known size, that could be used for a distance standard. The frames could be analyzed to determine the velocity of a point in the pond and that would clearly show why the wave propagates.

localroger

Waves do indeed have momentum; there are these guys who exploit this every day, called "surfers," who use the momentum for transportation.

It's complicated a the seashore by the fact that the waves are reflected from the shore, often with great distortion due to the shallow slope, so it might not seem like the water is "going anywhere." But as we see with tsunamis, waves are capable of transporting large amounts of energy for very large distances. If the sea were infinitely large the wave would travel forever, taking a certain amount of water permanently away from the place where you dropped the stone. But in practice all waves end up getting reflected back to their point of origin, so it's not as obvious that they transport energy.

william chan

What phil has mentioned is very interesting.

At the point of the snapshot, new circular wavelets are generated from every disturbance point, especially the whole length of the wave front.
The sum interference of all the circular wavelets will add to become a new wavefront which seems to propagate in one direction.

The question is,
Why did the sum of all circular wavelets add up in such a way to create a major wave that continue in the same direction of propagation?
Is due to the shape and manner of the disturbances at the point of snapshot? Is it due to an inherent "wave inertia"?
As far as we know, only mass has inertia.

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SRLM

localroger said...
If the sea were infinitely large the wave would travel forever, taking a certain amount of water permanently away from the place where you dropped the stone. But in practice all waves end up getting reflected back to their point of origin, so it's not as obvious that they transport energy.

Not quite accurate. If the wave were linear, then sure. But, in the case of a dropped stone (or perhaps soyuz spacecraft) the waves would be radial. In that case the waves would get progressively smaller the further you are from the origin, until you get to infinity (via a limit), in which case the wave is gone (negligible).

Also a point to note is that waves (as defined in physics) are a form of transmitting energy through a medium. Waves are not matter, therefore they cannot have momentum or inertia. The medium that the waves act upon (the water, a rope, air, etc.) can have momentum and inertia, since there's mass. But the wave itself, no.

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Phil Pilgrim (PhiPi)

There's no horizontal inertia to consider. If you propagate a circular wavefront from each point displacement in the snapshot, you automatically continue the same advancing wavefronts you observed from the original disturbance, due to constructive and destructive interference. It's just the way the math works out. 'No special physical considerations required!

-Phil

FlyingFishFinger

I am constantly amazed at the amount of even unrelated knowledge that is here. Way to go!

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CannibalRobotics

A wave in water is a pressure front. It's the distribution of the displacement of the water where the stone 'is' then rushing back in to where it 'was'. Waves have no momentum. The water is not moving but the pressure fronts are. Water is mostly incompressible so the pressure front distorts the surface and we see the wave.
In the case of a breaking wave, the undersea surface is even more incompressible than the water and coming up so the pressure front has to go up higher. At some point it gets pushed so high it's unstable and falls. The falling action does create horizontal displacement.
I love physics!

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