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Math Help - Develop Model Emulating Given Wave Pattern

  1. #1
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    Develop Model Emulating Given Wave Pattern

    Question:
    Develop a model for producing a repeating pattern of 8 waves, with 6 smaller waves of approx. the same size and the second and sixth waves much larger. The sketch below gives a general indication of the eight wave pattern.





    (Sorry for large image)

    I would like to know how to "take a shot" at it, the solution must be a sine function. Can be generic, by that I mean no definite amplitude, only that the model clearly resemble the one given.

    I have tried to emulate it by trial and error, combining functions such as in the form [y=sin x + 0.3sin3x] with no luck.

    Thanks in advance,
    -Ausmate
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Develop Model Emulating Given Wave Pattern

    Quote Originally Posted by ausmate View Post
    Question:
    Develop a model for producing a repeating pattern of 8 waves, with 6 smaller waves of approx. the same size and the second and sixth waves much larger. The sketch below gives a general indication of the eight wave pattern.





    (Sorry for large image)

    I would like to know how to "take a shot" at it, the solution must be a sine function. Can be generic, by that I mean no definite amplitude, only that the model clearly resemble the one given.

    I have tried to emulate it by trial and error, combining functions such as in the form [y=sin x + 0.3sin3x] with no luck.

    Thanks in advance,
    -Ausmate
    I don't have a complete answer for you, but I think that adding the functions is going to be harder to do than multiplying. For example:
    Develop Model Emulating Given Wave Pattern-wave.jpg

    I can't manage three "humps" between the large ones, though. You can, of course, do this using Fourier analysis, but it would involve a large number of terms.

    -Dan
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  3. #3
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    Re: Develop Model Emulating Given Wave Pattern

    Thanks for the answer Dan, but I think I am required to add sine functions to get the desired pattern, any ideas on how to start?

    -ausmate
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  4. #4
    Super Member Matt Westwood's Avatar
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    Re: Develop Model Emulating Given Wave Pattern

    My general approach would be as follows.

    For the small humps, I'd take a simple sine function of frequency \nu.

    For the large humps, I'd start with a more complicated function which is of frequency \frac \nu 4 which will basically consist of just the top half of a single sine wave, being zero everywhere else.

    Then I would do a Fourier analysis on the latter, which ought to be more-or-less tractable, in a similar way to how it works for the half-wave rectified sine.

    Then you add this to the raw sine function of frequency \nu.

    I haven't tried it out, but it's an approach that may work for you.
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