1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Why does f(x-vt) represent a wave along +x?

  1. Jan 31, 2012 #1
    I just can't understand how this makes sense. Why does f(x-vt) represent a transverse wave along +x? Where v is the velocity, t is time, and x is position along the x axis. It seems to be exactly the opposite to what I would think makes sense, with f(x+vt) representing a wave along +x and f(x-vt) representing a wave along -x. But this isn't the case! I've been trying to wrap my head around it, not matter how I look at it.
    Can anyone explain this concept in a way that makes sense?

    Thanks! :smile:
     
  2. jcsd
  3. Jan 31, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Let's for simplicity set our coordinates so that x= 0 when t= 0. If the object is moving at speed v, then at any future time, t, x= vt. So x-vt= 0. That is, f(0) "moves" along the x-axis at speed v.
     
  4. Jan 31, 2012 #3

    Ken G

    User Avatar
    Gold Member

    Think of the function f(x-vt) as being a pattern of some kind. The pattern will propagate in the +x direction at speed v, because at x=0 and t=0, the pattern is f(0) (think of this as the center of the feature that is propagating), but at any other time t and x=vt, the pattern will still be f(0). So the center of the feature is always found at some x=vt, so is moving at speed v in the +x direction, because that's just what x=vt means.
     
  5. Jan 31, 2012 #4
    Oh! Okay, so you just have to look at the equation for the position x first as x=vt. Thanks much! :biggrin:
     
  6. Feb 1, 2012 #5
    Just remember that this statement does not apply to every f(x-vt) only suitable ones, although there are a great many such.
     
  7. Feb 1, 2012 #6
    Which would be those restrictions? continuity?
     
  8. Feb 1, 2012 #7
    The simplest example would be

    f(x-vt) = k
     
  9. Feb 1, 2012 #8

    sophiecentaur

    User Avatar
    Science Advisor
    Gold Member

    I had this problem too and eventually came to this conclusion (a nice arm waving one).
    f(x-vt) tells you what the function will be at x in terms of what it was, at the origin, t seconds ago (i.e. t is the time it took to propagate to x from the origin) - hence the negative t sign.
    Confused more? - Sorry if you are but it helped me, once.
     
  10. Feb 1, 2012 #9

    Ken G

    User Avatar
    Gold Member

    I believe the issue was the idea that the wave is "transverse", which is not a requirement of the f(x-vt) form. Anything that propagates at v has the form f(x-vt), including longitudinal and water waves.
     
  11. Feb 1, 2012 #10
    Actually, this helps allot! Thanks! :)
     
  12. Feb 1, 2012 #11

    Pengwuino

    User Avatar
    Gold Member

    If you have mathematica or a scientific calculator, you can plot the functions f(x) = cos(x - vt), let v equal some random number, and plot it as you vary t between different graphs. You'll actually SEE the graph moving to the right as you increase t.

    I think it's a fantastically convincing argument for seeing how this works.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Why does f(x-vt) represent a wave along +x?
  1. Why x^2 for PE? (Replies: 4)

Loading...