Wave Equation

  • #1

Homework Statement



The displacement of particles in a string stretched in the x direction is represented by y. Which of the following expressions for y describe wave motion:

1: cos kx sin wt
2:[tex]k^2x^2-w^2t^2[/tex]
3:[tex]cos^2(kx+wt)[/tex]


Homework Equations



Equation of a progressive wave is of the form [tex]y=f(t-\frac{x}{v})[/tex]


The Attempt at a Solution



The first equation represents a standing wave. The second obviously cant be it (its not of the form f(t-x/v) ). But I thought the third one would represent the equation of a progressive wave. It doesnt though. Why?
 

Answers and Replies

  • #2
529
1
x'=-x
wt+kx=w(t-k/w x')=w(t-x'/v)
(using v=w/k)
 
  • #3
Yeah. I got that. But it isnt the answer. The third equation doesnt represent a wave. Why?
 
  • #4
529
1
Why not?

cos^2 (wt-kx')=1/2+1/2cos(2[wt-kx'])
w'=2w
k'=2k

so the fn=A+Bcos(w't-k'x')

Looks like a sinusoidal wave to me.

What's wrong with using a standing wave? Isn't that what you'd get in a stretched string?
 
  • #5
Yeah, you get a standing wave cause of superpoosition in a string. The thing is, that only one answer is correct. Maybe the language points to a standing wave?
 
  • #6
529
1
You get a standing wave, because the string is stretched- so it must be held at both ends.
 
  • #7
If a string is stretched, it doesnt necessairily mean that you would have to get a standing wave.
 

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