GREPhysics.NET: GR9277 #79

GR9277 #79

Problem

GREPhysics.NET Official Solution

\prob{79}

The dispersion curve shown above relates the angular frequency $\omega$ to the wave number k. For waves with wave numbers lying in the range $k_1

They are in opposite directions.
They are in the same direction and the phase velocity is larger
They are in the same direction and the group velocity is larger
The phase velocity is infinite and the group velocity is finite.
They are the same in direction and magnitude

Wave Phenomena $\Rightarrow$ }Group Velocity

Recall that the group velocity is given by $v_g = \frac{d\omega}{dk}$ and the phase velocity is given by $v_p = \omega/k$ .

In the region between $k_1$ and $k_2$ , the derivative is a constant negative quantity (approximately just the derivative of a line with negative slope). However, $\omega/k$ is positive in this region. Thus, the phase and group velocity are traveling in opposite directions. Thus, choose choice (A).

Alternate Solutions

There are no Alternate Solutions for this problem. Be the first to post one!

Comments

hoyas08
2007-12-30 12:08:56

The second sentence of the question doesn't display right for me. It should read:

For waves with wave numbers lying in the range k₁ < k < k₂ , which of the following is true of the phase velocity and the group velocity?

Reply to this comment

jcain6
2005-11-23 06:46:20

Choice (c) states that they are in the same direction and the group velocity is larger. This isn't true and just looks to be a typo on your part. Your description is consistent with choice (A) which is the correct answer.

yosun
2005-11-23 14:59:43

jcain6: thanks for the typo-alert; it has been corrected.

Reply to this comment

Post A Comment!

You are replying to:

The second sentence of the question doesn't display right for me. It should read: For waves with wave numbers lying in the range k₁ < k < k₂ , which of the following is true of the phase velocity and the group velocity?

Bare Basic LaTeX Rosetta Stone
LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces $\alpha^2_0$ .
type this...	to get...
$\int_0^\infty$	$\int_0^\infty$
$\partial$	$\partial$
$\Rightarrow$	$\Rightarrow$
$\ddot{x},\dot{x}$	$\ddot{x},\dot{x}$
$\sqrt{z}$	$\sqrt{z}$
$\langle my \rangle$	$\langle my \rangle$
$\left( abacadabra \right)_{me}$	$\left( abacadabra \right)_{me}$
$\vec{E}$	$\vec{E}$
$\frac{a}{b}$	$\frac{a}{b}$

The Sidebar Chatbox...
Scroll to see it, or resize your browser to ignore it...

<a href="http://www6.shoutmix.com/?grephysics">View shoutbox</a>
ShoutMix chat widget

Free 3D Virtual World. Largest User-Created Fantasy World. Don't Play, Experience. Join Now!

Bored, got time to kill, and want to earn micro-cash by mindlessly clicking on links? Join CrownGPT. Click Offers. Click the Paid to Click button... then click to your heart's delight.

FREE 3D Virtual World Chat - Join Second Life Today!

All-Solutions List | Latest Comments | Unanswered Questions (Cries for Help!) |::| About

This site is not affiliated with ETS, nor is it officially endorsed (yet) by ETS. This site is the work of an individual named Yosun Chang. The solutions, sans user comments and ETS questions, are © 2005 by Yosun Chang except where noted. All rights reserved. / The comments appending particular solutions are due to the respective users. / Educational Testing Service, ETS, the ETS logo, Graduate Record Examinations, and GRE are registered trademarks of Educational Testing Service. The examination questions are © 1997 and © 2001 by ETS.

Bare Basic LaTeX Rosetta Stone