1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Develop Model Emulating Given Wave Pattern

  1. Jul 19, 2014 #1
    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.

    8QPnLAZ.jpg

    (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
     
    Last edited: Jul 19, 2014
  2. jcsd
  3. Jul 20, 2014 #2

    Mentallic

    User Avatar
    Homework Helper

    All I could come up with was a relatively complicated solution which is of the form

    [tex]y=sin(x)+k(x)s(x)[/tex]

    where k(x) is equal to 1 everywhere that you want the amplitude of sin(x) to be higher, and 0 everywhere else. s(x) is a function that uses [itex]sin(x)^2[/itex] because it has a derivative of 0 where it touches the x-axis.

    [tex]k(x)=\frac{1}{2}\left(\frac{|r|}{r}+1\right)[/tex]

    where

    [tex]r=\sin{\left(\frac{x+3\pi/2}{4}\right)}-\frac{1}{\sqrt{2}}[/tex]

    and I'll leave s(x) to you if you're interested in pursuing this further.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Develop Model Emulating Given Wave Pattern
  1. Function Patterns (Replies: 3)

Loading...