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Standing Wave Equation

  1. Apr 19, 2010 #1
    My lecturer said that a standing wave is formed when two waves that travel in the opposite have the same frequency.

    He said that if the waves are y1 and y2, then the resulting wave y can be given as the sum:

    y = y1 + y2.

    y = Asin([tex]\omega[/tex]t - kx) + Asin([tex]\omega[/tex]t + kx). (1)

    Where the plus and minus kx denotes their direction.

    However, when (with a bit of trigonometric identity work) equation (1) is simplified it gives:

    y = 2Asin([tex]\omega[/tex]t)cos(kx).

    But how can this be? I mean, if x = 0, then the equation tells us that there is an antinode, which (for a string) isn't true.

    I've seen the equation y = 2Acos([tex]\omega[/tex]t)sin(kx), which makes more sense when I consider a string for example.

    To get to it you need the equation

    y = Asin(kx - [tex]\omega[/tex]t) + Asin(kx + [tex]\omega[/tex]t) (2)

    My question is, why would you use equation (2) and not equation (1)?

    Thank you in advance for your help!
  2. jcsd
  3. Apr 19, 2010 #2
    It's OK, I've solved it now.
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