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Wave function question

  1. Jan 25, 2012 #1
    1. The problem statement, all variables and given/known data
    Not a homework problem, just a general question that I find confusing.

    2. Relevant equations

    3. The attempt at a solution

    So, back in Trigonometry and Classical Mechanics I learned that the equation that best represents a wave. Now, Solving the differential equation that is the wave function gives this:
    [tex]f(x,t)=Y_{m}cos(kx-ωt)[/tex]

    What has me confused is the new "phase", specifically that it's not ωt+[itex]\phi[/itex].

    I gather that k is the wave number, well, the number of wavelengths per unit distance, x is the distance down the wave of course. ω is now the Angular Frequency (not velocity!), which is simply the number of rotations per unit time more or less. So if ω is 2π over the period, what exactly is that other t representing? Seems like it's unit would cancel with ω which is clearly desired, but I just don't see how this whole thing is working exactly.

    I can do any of the rote number-plugging homework problems assigned to me, but I simply don't see the relationship between this newer (for me) wave funtion and the one with [itex]\phi[/itex] that I am more familiar with. I can't even find a resource outside my text pertaining to this equation, all searches yield the equation with phi.
     
  2. jcsd
  3. Jan 25, 2012 #2
    Phi just shifts time or position a bit, if you set your clocks right you can make phi go away.

    Your old function which just involved time might describe the position of a vibrating mass connected to a spring.

    The new function might describe a wave on a vibrating string, the height of the string now depends on both time and where you are along the string.
     
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