Jump to content
Sign in to follow this  
gokul.er137

phase velocity question.

Recommended Posts

i was intrigued by how to solve this.

 

the phase velocity of ocean waves is sqrt(g*lambda/2*pi) where g - acceleration due to gravity, lambda is the wavelength of the wave. The question is find the group velocity.

 

I tried many things but was not able to get to a proper answer. Any help?

Share this post


Link to post
Share on other sites

Can you write down the equation for the phase velocity and the equation for the group velocity?

Share this post


Link to post
Share on other sites

vp -> phase velocity

vg -> group velocity

 

generally vp ->c^2(speed of light squared)/vg

 

Doing that and substituting does not give me a satisfactory answer.

 

On a more conceptual note -> group velocity is the rate of change of angular velocity('delta'omega) with the change in wave number('delta'k). Phase velocity is omega/k , that is at any particular instant. So to get the group velocity I could also differentiate omega with respect to k, but I do not know anything about them either.

Share this post


Link to post
Share on other sites

Your second part is correct. The first is a special case.

 

[math] v_g = \frac {d \omega} {dk}[/math]

 

 

[math] v_p = \frac { \omega} {k} = \frac {\lambda} {T} [/math]

 

[math] v_p = \sqrt{g*\lambda/2*pi} [/math]

 

From that you can make some substitutions and find vg

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
Sign in to follow this  

×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.