wave phase velocity vs. group velocity?

  • Imagine you are sipping tea or coffee while discussing various issues with a broad and diverse network of students, colleagues, and friends brought together by the common bond of physics, graduate school, and the physics GRE.

Posts: 1
Joined: Sun Jan 01, 2012 1:49 am

wave phase velocity vs. group velocity?

Postby hadimotamedi » Sun Jan 01, 2012 1:54 am

Dear All
Can you please let me have a clear understanding of the wave phase velocity/group velocity and if phase velocity can exceeds group velocity or vice versa?
Thank you

King Vitamin
Posts: 42
Joined: Sat Nov 12, 2011 5:01 pm

Re: wave phase velocity vs. group velocity?

Postby King Vitamin » Mon Jan 02, 2012 5:17 am

v_p = \frac{\omega}{k}
v_g = \frac{d\omega}{dk}

These are the definitions of phase and group velocity respectively. So given different expressions \omega(k), we can come up with examples of where one exceeds the other.

\omega(k) = c \ k (c is constant)

Here, v_g = v_p.

\omega(k) = k^2

Here, v_g > v_p

\omega(k) = \sqrt{k}

Here, v_g < v_p.

It's helpful to know the graphical interpretations of these if you're studying for the GRE, so I'd recommend looking at the graphs of these functions and understanding when either is larger, smaller, or the same.

Return to “Physics Lounge”

Who is online

Users browsing this forum: No registered users and 1 guest