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Homework Help: Phase difference

  1. Jul 7, 2008 #1
    1. The problem statement, all variables and given/known data
    Two sinusoidal waves in a string are defined by functions
    y1= (2.00cm)sin(20x-32t)
    y2=(2.00cm)sin(25x-40t)
    where y and x are cm and t is sec
    (a) What is the phase difference between these two waves at the point x = 5 cm and t = 2 s?
    (b) What is the position x value closes to the orgin for which the two phases differ by +/- pi at t = 2 s? (This location is where the two waves add to zero)



    2. Relevant equations
    I use the equation given to me as y1 and y2
    not sure if there is an equation for phase difference

    3. The attempt at a solution

    (a) I plugged in 5 cm and 2 s for y1 and y2
    y1 = -1.9835 and y2 = 1.7018
    but Im not sure what these answers mean and if they are relevant
    b) (2sin(20x-32*2) + 2sin(25x-40*2) = 0 and solve for x? Is this correct?Do I do inverse sin and then move the (32*2 and 40*2) to the other side?

    Thanks for any help!!!!
     
  2. jcsd
  3. Jul 7, 2008 #2

    kreil

    User Avatar
    Gold Member

    A few words on phase difference:

    Phase is a way of telling "where" the graph of a function is.

    For example, the graph of sin(x) is 0 at x=0 and 1 at x=pi/2. If I were to change the function to sin(x-pi/2), then the function would be -1 at x=0 and 0 at x=pi/2.

    Effectively, I dragged the entire graph of the function to the right by pi/2, so we would say that this second function has a phase of pi/2 relative to the first (phase is typically only important when comparing two functions).
     
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