Difference between particle velocity and phase velocity

AI Thread Summary
Particle velocity in waves is generally not directly related to phase velocity, as particle motion often involves circular or vertical movements that do not correlate with the wave's speed. For surface gravity waves, particle velocities are typically much smaller than phase velocities. The particle velocity is influenced by wave amplitude, while phase velocity remains largely independent of amplitude, especially in linear waves. The dispersion relation indicates that phase speed is a function of wavelength, but particle velocity varies with time and amplitude. Overall, both velocities arise from the same equations of motion, highlighting their interconnectedness despite their differences.
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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
 
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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.
 
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).
 
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?
 
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Simon Bridge said:
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.

Simon Bridge said:
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:

Philip Wood said:
...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).

Simon Bridge said:
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."
 
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