y(x, t)

\frac{∂^{2}y}{∂x^{2}} = \frac{μ}{T} \frac{∂^{2}y}{∂t^{2}}

\frac{∂^{2}y}{∂x^{2}} = \frac{1}{v^{2}} \frac{∂^{2}y}{∂t^{2}}

v = \sqrt{\frac{T}{μ}}

z(x, y, t)

\frac{∂^{2}z}{∂x^{2}} + \frac{∂^{2}z}{∂y^{2}} = \frac{σ}{S} \frac{∂^{2}z}{∂t^{2}}

v = \sqrt{\frac{S}{σ}}

ω_{n_{x}n_{y}} = π \sqrt{\frac{S}{σ}} [\frac{n_{x}^{2}}{L_{x}^{2}} + \frac{n_{y}^{2}}{L_{y}^{2}} ]^{\frac{1}{2}}