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Waves: The ampltitude of two waves

  1. Dec 7, 2008 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    I have two loudspeakers placed on the x-axis at -L and L respectively. Now I have found the resulting wave at a point z0 on the z-axis. I've used the superposition-principle, and I've arrived at the following expression:

    \widetilde f(\overrightarrow r ,t) = 2A\exp \left[ {i\left( {\frac{{\alpha \left( {\left( {x + y} \right) + \left( {x - y} \right)} \right)}}{2} - \omega t} \right)} \right]\cos \left( {\alpha \frac{{\left( {\left( {x + y} \right) - \left( {x - y} \right)} \right)}}{2}} \right)

    where the tilde over f indicates that it is complex.

    Question: What part of the expression for f is the ampltitude? Is it only 2A, or is it the expontential term and 2A the ampltitude?

    Thanks in advance.

  2. jcsd
  3. Dec 8, 2008 #2


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    It depends on what you mean. AFAIK, there is no standard definition of "amplitude", even in physics. You have obviously encountered the term regarding the constant multiplier in front of a sinusoid. And, perhaps you have also encountered it in QM, since you think you might want to include a complext phase? Anyway, it just depends on why you need to know. I would suggest that, since the time-dependence is entirely contained in the exponential, then "the amplitude" may be most suitably identified as everything else besides the complex exponential.
  4. Dec 8, 2008 #3
    Hmm, I would think it is everything besides the cosine, especially because cosine determines the magnitude of the amplitude then.
  5. Dec 8, 2008 #4


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  6. Dec 9, 2008 #5
    Ok, bad way of expressing it. The cosine-term determines when the wave is at it highest positition (i.e. the amplitude).
  7. Dec 9, 2008 #6


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    No. The cosine factor partly determines WHERE (not when; where) the wave will be maximum. The cosine factor doesn't contain any time-dependence. But, anyway, it doesn't matter. You are quite free to call everything besides the cosine factor as the amplitude. That was my main point.
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