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Math Help - Product of two sinusoids

  1. #1
    Member wiseguy's Avatar
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    Product of two sinusoids

    del
    Last edited by wiseguy; August 6th 2010 at 10:29 AM.
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  2. #2
    A Plied Mathematician
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    I think you're right on top of the answer. You've got the correct amplitude out front. I would pay close attention to the period of the outside envelope function (carrier), and the inside modulating function. How many times does each of those sinusoids vary in 60 degrees? Use the info from that to inform the multipliers of theta inside the trig functions.
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  3. #3
    Member wiseguy's Avatar
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    Okay,

    I double checked the period of the envelope equation... it looks correct - sin(6x)

    So how can I get the second equation from flipping under the x axis?
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  4. #4
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    The smaller sinusoid appears to vary 5.5 times over the 60 degree period of the envelope function. What does that tell you?

    [EDIT]: See post below by Unknown008 for a correction to this post.
    Last edited by Ackbeet; July 26th 2010 at 09:41 AM. Reason: Correction.
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  5. #5
    Member wiseguy's Avatar
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    So 4sin6xsin55x would work?
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  6. #6
    MHF Contributor Unknown008's Avatar
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    Remember that a sine curve has two parts, one upper and one lower. So, one complete sine curve in your drawing takes two 'upper envelopes' that is, one complete sine curve ends at 120 degrees.
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  7. #7
    Member wiseguy's Avatar
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    Right, I got the sin6x ending at 120. I just cant get the second sinusoid to stay on top of the x axis at every 60 degree interval.
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  8. #8
    A Plied Mathematician
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    Keep in mind that if Unknown008 is right, the envelope (outer) sinusoid will be negative immediately after 60 degrees. Does that help?
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  9. #9
    MHF Contributor Unknown008's Avatar
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    Anyway, I did not get it completely right. I didn't look closely at the axes earlier, but this is what I've got:

    4sin(x)sin(11x - Wolfram|Alpha

    The problem is that it's in 360 degrees instead of 120 degrees. =S
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  10. #10
    MHF Contributor Unknown008's Avatar
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    Ok, I got it now. For any sine curve, the coefficient of x gives the number of cycles of the curve in 360 degrees right?

    Ok, since the envelope sine curve completes a cycle in 120 degrees, in 360 degrees, there are three cycles.
    So, equation of the envelope is y = 4sin(3x)

    For the modulated curve now. There are 11 cycles in 120 degrees, in 360, there are 33.
    So, equation becomes y = sin(33x)

    Combine those two to get your answer: y = 4sin(3x)sin(33x)

    y = 4sin(3x)sin(33x - Wolfram|Alpha
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