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?
What other information do you have?
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?
Start with the wave equation:
where is the speed of propagation.
We assume the at and , the displacement .
The solution to the equation is separable, which means
Solving the wave equation with this general solution, be the method of separation of variables, we find that
and
where is an integer corresponding to the frequencies of vibrations (modes)
Thus the displacement is
The most general solution is an superposition of the solutions for all values of