The question is as follows, there is a cylinder with length L and radius R, there is a sound wave with a phase velocity v, they ask for the normal modes and the 5 lowest frequencies when L=R
Wave equation for 3D, (d^2/dt^2)ψ=v^2*(∇^2)ψ
The Attempt at a Solution
I have used the wave equation and derived an expression for ψ as function of t,ϑ,z,ρ using bessel formula.
the expression I derived is: Ψ=e^(-iωt)e^(inϑ)e^(ikz)*J(κρ)
I wouldnt like to post all the derivation here (it will take hours to type everything), but the idea was clear, assume that ψ is a function of R,Θ,Z,T which are all independent of one another, and insert into the wave equation.
I`m not sure how to continue, what initial conditions should I use?
Hopefully that was clear enough, that`s my first post, so I hope i did it well :)