OK, I think I understand the problem, I'm just a little confused on some pieces in the middle.(adsbygoogle = window.adsbygoogle || []).push({});

Problem:

Consider a wave packet formed by the superposition of two waves

psi_{1}=cos(1.00x-2.00t) <--1.00=k, 2.00=w

psi_{2}=cos(1.01x-2.03t) <--1.01=k, 2.03=w

where x and t are measured in meters and seconds respectively. What is the Phase velocity?

What is the group velocity?

We know:

Vp= w/k

Vg=dw/dk

-To find the Vp, can we simply say that Vp=2.00/1.00=2.00m/s?

Now, to find the Group Velocity, we can use the suerposition principle and find the net wave by the sum of the two individual waves (psi_{1}+ psi_{2}) which gives us

psi=2cos(1.00*1.01)x*cos(-2.00*-2.03)t = 2cos(1.01)x*cos(4.06)t

thus Vg=dw/dk= -(2/1.01)sin(1.01)x*cos(4.06)t - (2/4.06)doc(1.01)x*sin(.06)t?

Is this correct? Is the partial derivative correct?

Thanks.

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# Homework Help: Group and Phase velocity of wave packet

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