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Homework Help: Why can a velocity of a wave be negative?

  1. Jun 30, 2011 #1
    Hi yall,

    Im trying to understand waves and I am wondering why the velocities are negative sometimes and or positive.

    I think that the velocities are negative because of the slope of the wave as it is coming down? I just want to completely understand it and am a little confused.

    Like the equations i use are x(t)-Acos(wt+(phi)) or v(t)=-Awcos(wt+(phi))
  2. jcsd
  3. Jun 30, 2011 #2


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    Strictly speaking, I wouldn't call those waves. They're just sines and cosines (by the way your velocity is not correct, it should not have the negative sign and should be sin(wt + phi) instead. The derivative you calculated is simply the slope.

    When people talk about the velocity of a wave, they're typically talking about something propagating as cos(kx - wt) where k is the http://en.wikipedia.org/wiki/Wave_number" [Broken]. The former being the velocity of the wave you're probably thinking about, the latter being something when you talk about frequencies that are not constant.
    Last edited by a moderator: May 5, 2017
  4. Jun 30, 2011 #3
    the positive and negative velocity means different directions
  5. Jun 30, 2011 #4
    yea that was a mistype.

    But why cant the velocities always be positive? I seem to feel like the wave is always moving in one direction unless it's reflected back at me.
  6. Jun 30, 2011 #5
    the two equations you offer are for simple harmonic motion,not waves.so if the velocity is negative,it means the direction of it is opposite from displacement(or x in your first equation)
  7. Jun 30, 2011 #6


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    You have to specify what you're talking about. Like azureth is saying, what you have could tell you about the velocity of a simple harmonic oscillator such as a spring. The positive/negative tells you about whether or not it's traveling to the left or right.

    When you're talking about say, waves in the air or a vibration you make on a string that actually propagates, your propagation has to be something like cos(kx - wt). If you plotted this function for various times of 't', you'd find a wave that propagates in the positive-x direction.
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