Sinusoidal Wave Problem

  1. 1. The problem statement, all variables and given/known data

    Consider the sinusoidal wave in the figure, with the wave function below.

    At a certain instant, let point A be at the origin and point B be the first point along the x axis where the wave is 60.0° out of phase with point A. What is the coordinate of point B?

    y = (15.0 cm) cos(0.157x - 50.3t)

    and I am not allowed to post the image but heres some helpful information:
    its a cosine graph, and [tex]\lambda[/tex] = 40 cm, T = 0.125 s, f = 8.00 hz, k = 0.157 rads/cm

    2. Relevant equations

    Some equations that I have are:

    3. The attempt at a solution
    What I have tried so far is:
    y=15*sin((.157)x-(50.3)t + [tex]\pi[/tex]/3)
    The example says " The vertical position of an element of the medium at t = 0 and x = 0 is also 15.0 cm "
    The only problem is that I am really stuck and I cannot seem what to set the 60.0[tex]\circ[/tex] equal to. Help would be much appreciated! Thank you!
  2. jcsd
  3. cepheid

    cepheid 5,189
    Staff Emeritus
    Science Advisor
    Gold Member

    Everything in the argument of the cosine is the phase of the wave. So the phase is a function of both x and t. However, we're looking at this wave at a particular "instant", which means that t is constant. So, the only thing that would cause a phase change is x. So how far from the origin would the x coordinate of point B have to be in order for 0.157x - 50.3t to differ from 0.157*(0) - 50.3t by 60 degrees, given that t is constant?
  4. Would x = 6.37 * [tex]\pi[/tex] because that would make it ([tex]\pi[/tex]/3 -50.3t)
  5. cepheid

    cepheid 5,189
    Staff Emeritus
    Science Advisor
    Gold Member

    I think you might be off by a factor of 3. Check your work again.
Know someone interested in this topic? Share this thead via email, Google+, Twitter, or Facebook

Have something to add?