How's the superposed waves are moving?


by KFC
Tags: moving, superposed, waves
KFC
KFC is offline
#1
May8-12, 01:37 PM
P: 369
Hi there,
Suppose there are two plane waves with different wavevector and frequency, the superposition of these waves give
[tex]\phi(x, t) = 2\cos(k'x + w't)\cos(k''x + w''t)[/tex]
with
[tex]k'=(k_1+k_2)/2, w'=(w_1+w_2)/2[/tex]

[tex]k''=(k_1-k_2)/2, w''=(w_1-w_2)/2[/tex]

here [tex]\cos(k''x + w''t)[/tex] gives the oscillation and [tex]\cos(k'x + w't)[/tex] is the envelope. My question is if I look at the very first crest when x=0, t=0 and I attach a "point" to that. How can I trace the movement of that point? Can we just look at [tex]\cos(k''x + w''t)[/tex] and say that the every point is moving at the phase velocity w''/k''? I am not sure the physics behind that but seems it is not correct. But with several trials, I find that it seems the point (crest of the second cosine for example) is moving at the speed [tex](w'+w'')/(k'+k'')[/tex], is that correct? why?

I want to trace the crest point and I know that the magnitude of the crest is changing on the envelope and it is correct at different time and space. So I initially fix the initial position xi = 0; yi = 2; for the crest. Then by enumerating the time, we can find the new x and new y for the crest as

x = (w'+w'')/(k'+k'')*t;
y = 2*cos(k'x + w't);

but when I plot this point at different t, it doesn't really move as I expect. Any idea how to trace a point? I want to plot something like the red point shown here https://en.wikipedia.org/wiki/File:Wave_group.gif

Thanks
Phys.Org News Partner Physics news on Phys.org
Physicists consider implications of recent revelations about the universe's first light
Vacuum ultraviolet lamp of the future created in Japan
Grasp of SQUIDs dynamics facilitates eavesdropping

Register to reply

Related Discussions
SR, electromagnetic waves in moving reference frames. Advanced Physics Homework 1
waves moving in shallow water General Physics 5
Where does "extra" energy come from in superposed waves? Introductory Physics Homework 2
Superposition, amplitudes and superposed waves. Introductory Physics Homework 4
Electric field becomes electromagnetic waves if observer is moving Classical Physics 16