1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sine Wave Addition

  1. Mar 7, 2010 #1
    If two sine waves have the same frequency and amplitude but have different phase shift do they still produce a standing wave?
    Thanks for the help.
  2. jcsd
  3. Mar 7, 2010 #2
  4. Mar 7, 2010 #3
    As far as i can see it doesn't say anything about phase shift so does that mean it doesn't affect anything?
  5. Mar 7, 2010 #4
    wt is the phase shift

    see http://en.wikipedia.org/wiki/Phase_(waves [Broken])
    Last edited by a moderator: May 4, 2017
  6. Mar 7, 2010 #5
    I'm sorry but I'm still confused. If y1 = Asin(kx-wt+phi) and y2 = Asin(kx+wt)
    the addition is y= 2Acos(wt-phi/2)sin(kx+phi/2) where phi is the phase shift between 0 and 2pi. Does this still fit the standing wave equation y=(2Asin(kx))cos(wt) meaning its a standing wave or does the difference in phase shift mean they do not create a standing wave?
  7. Mar 7, 2010 #6
    You have one forward-traveling wave (wt-kx) and one backward wave (wt+kx) of the same amplitude, which is a standing wave. My CRC Math Tables (10th Ed, 1954) on page 345 shows the sum

    sin(x) + sin(y) = 2·sin[(x+y)/2]·cos[(x-y)/2]

    Bob S
  8. Mar 9, 2010 #7

    Your equations will be easier to read if you typeset them in LaTeX.

    Yes, the equation you give is a standing wave. If you start with

    [itex] \Psi(x,t) = A\cos(\omega \left[t-t_0\right]) \sin (k\left[x-x_0\right]) [/itex]

    you can just define a new time coordinate and new space coordinate by

    [itex] t' = t - t_0 [/itex]
    [itex] x' = x - x_0 [/itex].

    Then your original equation is just

    [itex] \Psi(x',t') = A \cos(\omega t')\sin(k x')[/itex],

    showing that the waveform is exactly the same as the standing wave you're used to.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook