Wave Equation—Disk

Author

Eric W. Weisstein
April 30, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DifferentialEquations/WaveEquationDisk.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/WaveEquationDisk.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Separation of Variables

ψ=R[r]Θ[θ]T[t]

ExpandAll[(((1/r)D[r D[ψ,r],r]+(1/(r^2))D[ψ,{θ,2}]-(1/(v^2))D[ψ,{t,2}])(1/ψ))]

DSolve[((Θ''[θ])/(Θ[θ]))==-(k^2),Θ[θ],θ]