\magnification=\magstep1

$$
y(x, t)
$$

$$
{{\partial^2 y}\over{\partial x^2}} \quad = \quad
   {{\mu}\over{T}} \ {{\partial^2 y}\over{\partial t^2}}
$$

$$
{{\partial^2 y}\over{\partial x^2}} \quad = \quad
   {{1}\over{v^2}} \ {{\partial^2 y}\over{\partial t^2}}
$$

$$
v \quad = \quad \sqrt{ {{T}\over{\mu}} }
$$

$$
z(x, y, t)
$$


$$
{{\partial^2 z}\over{\partial x^2}} 
  \ + \  
  {{\partial^2 z}\over{\partial y^2}} 
          \quad = \quad
   {{\sigma}\over{S}} \ {{\partial^2 z}\over{\partial t^2}}
$$

$$
v \quad = \quad \sqrt{ {{S}\over{\sigma}} }
$$

$$
\omega_{n_x n_y} \quad = \quad \pi \ \sqrt{ {{S}\over{\sigma}} } \   
              {\biggl[ {{n^2_x}\over{L^2_x}} + {{n^2_y}\over{L^2_y}} \biggr]}^{{1}\over{2}}
$$



\bye
