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PHI constant

  1. Jan 26, 2013 #1
    Hi,

    In the equation
    y(x,t) = ym * sin(kx - wt - PHI)

    I thought I understand why we have that phase constant atleast mathmetically but after thinking about it I don't think I understand it completely like here in my book it says the phase constant moves the wave forward or backward in space or time. Now lets say
    we have wave at t = 0 and x = 0;

    we would have y(x,t) = ym * sin(-PHI) that wouldn't really move it forward or backward in space or time if we had y(x,t) = ym + PHI then yeh it would have but I don't see how it would moves it backward or forward in that case ?

    I can see how they derived
    y(x,t) = ym * sin(kx - wt) but that PHI keeps confusing me.
     
  2. jcsd
  3. Jan 26, 2013 #2

    Philip Wood

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    Gold Member

    You might try sketching a 'snapshot' of the wave (that is a graph of y against x) at t = 0, first for the case [itex]\phi[/itex] = 0, then for the case [itex]\phi[/itex] = [itex]\pi[/itex]/2. The shift (in the x direction) of the wave profile brought about by [itex]\phi[/itex] should then be clear.

    The purpose of including [itex]\phi[/itex] is so we have an equation which fits the general case: when y doesn't happen to be zero when x = 0 and t = 0. [An alternative, sometimes permissible, sometimes not, is to choose our zero of time (or of x) expressly to ensure that y = 0 and [itex]\frac{\partial y}{\partial x} > 0[/itex] when t = 0 and x = 0. Then we don't have to bother with [itex]\phi[/itex].]
     
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