Difference between particle velocity and phase velocity

[iVenky]

According to wiki-

For surface gravity waves, the water particle velocities are much smaller than the phase velocity, in most cases. Then have shown this diagram

http://en.wikipedia.org/wiki/File:Wave_group.gif


How is particle velocity of a wave related with the phase velocity of the wave generally?

Thanks a lot

 

[Simon Bridge]

In general - the particle velocity is not related to the waves phase velocity.
I'll explain what I mean:

Water particles typically move in a circle and so don't go very far.
A transverse wave particles may just go up and down. A fast wave will have the particles bobbing up and down faster, but only if the wavelength is unchanged.
If you differentiate the wave equation to get the transverse particles velocity, you'll find that the particle velocity can vary with time even if the wave velocity is a constant.

Aside: the term "gravity wave" conjures images of neutron stars and general relativity.

 

[Philip Wood]

Another pointer: particle velocity is proportional to wave amplitude; wave velocity is usually independent of wave amplitude (as long as that amplitude is not too large).

 

[Simon Bridge]

The Wave Power Group at Edinburgh University went through a lot of trouble to simulate ocean waves... eg.

... but what I'm looking for is a side-on of a wave tank which has stuff floating in it, untethered, so the motion is clear.

I found
this animation showing circular particle motion with traveling waves - but I'd rather have a real-life example.

This vodeo is close; but it has tethered objects floating at different depths - you can see a bit of how the actual water moves by watching the objects.

I remember, as an undergraduate, experimenting with a wave-tang full of murkey water and how impressive and clear the particle motion was. Surely someone has done this with video?

 

[olivermsun]

In general - the particle velocity is not related to the waves phase velocity.

Of course they are related, because the phase velocity and the particle velocity are consequences of the same equations of motion.

A fast wave will have the particles bobbing up and down faster, but only if the wavelength is unchanged.

Sort of. The dispersion relation actually tells us that the phase speed of the wave is a function of the wavelength, but as pointed out in the next post:

...particle velocity is proportional to wave amplitude; wave velocity is usually independent of wave amplitude (as long as that amplitude is not too large).

This is the key point. The particle velocity has to depend on the wave amplitude, while the phase speed-wavelength relationship is for linear waves (independent of amplitude).

Aside: the term "gravity wave" conjures images of neutron stars and general relativity.

"Gravity wave" follows the traditional naming convention, which names waves after the associatedrestoring force. You are probably thinking of "gravitational waves."