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Phases in SHM

  1. Jan 29, 2008 #1
    My teacher told me that in SHM and wave motion phase refers to the argument in the corresponding function. then she said that if there is a difference of 2pi in the arguments then the phases are equal (sin ,cos function)

    but isn't it wrong , i know that their effect in terms of velocity , acc. ,displacement will be same but I cant get how they are equal if their is a difference of 2 pi between them??
     
  2. jcsd
  3. Jan 29, 2008 #2

    Doc Al

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    What's the difference between [itex]\sin (\theta)[/itex] and [itex]\sin (\theta + 2 \pi)[/itex]?
     
  4. Jan 29, 2008 #3
    they are same , but they are not the phases the phase is the term inside which is not same
     
  5. Jan 29, 2008 #4

    Doc Al

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    Not sure what you mean. If two sinusoids are "out of phase" by [itex]2 \pi[/itex], then they are actually in phase. A phase difference of [itex]2 \pi[/itex] is the same as no phase difference at all.
     
  6. Jan 30, 2008 #5
    I still think that it is counter intuitive, how can two quantities have a difference between them and then be equal , how can it be possible mathematically .
     
  7. Jan 30, 2008 #6

    jtbell

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    I think the problem here is simply subtle differences in terminology. People use the word "phase" to mean two different (although related) things. Sometimes it means "which point in a single complete cycle of the sine or cosine" and in that case [itex]0, 2\pi, 4\pi, ...[/itex] are all the same phase because they are all at the beginning of a cycle.

    Sometimes it means "the argument of the sine or cosine" and in that case [itex]0, 2\pi, 4\pi, ...[/itex] are different phases. This difference can be significant when you consider oscillations over more than one cycle: phase = 0 is the beginning of the first cycle, phase = [itex]2\pi[/itex] is the beginning of the second cycle, etc.

    I personally think the second meaning is more precise. I prefer to say that two waves with phases of 0 and [itex]2\pi[/itex] are "in phase," not that they have the "same phase."
     
  8. Jan 30, 2008 #7

    Doc Al

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    Good clarification, jtbell. I like it!
     
  9. Jan 30, 2008 #8
    Thanks for your clarification!
     
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