Results 1 to 3 of 3

Thread: Modelling the shape of a vibrating guitar string

  1. #1
    Newbie
    Joined
    Feb 2011
    From
    Argentina
    Posts
    5

    Modelling the shape of a vibrating guitar string

    Hello, I am Marckutt and I teach at an underprivelleged school outside Buenos Aires. We are trying to model the shape of a guitar string as it vibrates. More specifically, I need to be able to determine the displacement of any point along the string from the restpoint as the string oscillates. This requires incorporating two independent variables - the point along the string and time. What type of model could I use to model this scenario?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,237
    Thanks
    33
    Well for a start lets say displacement is a function of two variables the point x horizontally along the sting and t time, the time a note is held?

    $\displaystyle \displaystyle d(x,t) = \dots \sin (\dots) +\dots$

    What other information do you have?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2010
    Posts
    23
    Start with the wave equation:

    $\displaystyle \[\frac{\partial^2 y}{\partial x^2}=\frac{1}{v^2}\frac{\partial^2 y}{\partial t^2}\]
    $

    where $\displaystyle v$ is the speed of propagation.

    We assume the at $\displaystyle x=0$ and $\displaystyle x=L$, the displacement $\displaystyle y=0$.

    The solution to the equation is separable, which means

    $\displaystyle y(x,t)=X(x)T(t)$

    Solving the wave equation with this general solution, be the method of separation of variables, we find that

    $\displaystyle X(x)=sin(\frac{n\pi x}{L}) $

    and

    $\displaystyle T(t)=sin(\frac{n\pi vt}{L}) $

    where $\displaystyle n$ is an integer corresponding to the frequencies of vibrations (modes)

    Thus the displacement is

    $\displaystyle y(x,t)=sin(\frac{n\pi x}{L})sin(\frac{n\pi vt}{L}) $

    The most general solution is an superposition of the solutions for all values of $\displaystyle n$

    $\displaystyle y(x,t)=\sum_{n=1}^{\infty}B_{n}sin(\frac{n\pi x}{L})sin(\frac{n\pi vt}{L})$
    Last edited by dats13; Apr 6th 2011 at 02:32 PM. Reason: Typo
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: Aug 16th 2011, 05:01 AM
  2. amplitude of guitar string
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: Oct 8th 2009, 05:40 AM
  3. String
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Mar 23rd 2009, 05:04 PM
  4. Replies: 5
    Last Post: Mar 3rd 2009, 09:33 AM
  5. Modeling a Guitar Note
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: Jan 11th 2008, 06:11 PM

Search Tags


/mathhelpforum @mathhelpforum