- #1
Quelsita
- 49
- 0
OK, I think I understand the problem, I'm just a little confused on some pieces in the middle.
Problem:
Consider a wave packet formed by the superposition of two waves
psi1=cos(1.00x-2.00t) <--1.00=k, 2.00=w
psi2=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 (psi1 + psi2) 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.
Problem:
Consider a wave packet formed by the superposition of two waves
psi1=cos(1.00x-2.00t) <--1.00=k, 2.00=w
psi2=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 (psi1 + psi2) 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.