\magnification=\magstep2


$$
y(x, t) = 
            A \cos(k x - \omega t)
$$

$$
{{\partial^2 y} \over {\partial x^2} } =  \quad
      - k^2 \quad A \cos(k x - \omega t)
$$

$$
{{\partial^2 y} \over {\partial t^2} } =  \quad
      - \omega^2 \quad A \cos(k x - \omega t)
$$

$$
 k^2 \quad A \cos(k x - \omega t)  =  
      \quad ( {{k^2}\over{\omega^2}} ) \quad  \omega^2 \quad A \cos(k x - \omega t)
$$

$$
{{k} \over {\omega}} = {{ 2 \pi / \lambda } \over { 2 \pi f }}  = 
          { {1} \over { f \lambda }}
$$

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

$$
{{\partial^2 E} \over {\partial x^2} } \quad = \quad
           {{1}\over{c^2}} 
        \quad {{\partial^2 E} \over {\partial t^2} }
$$

$$
{  {\nabla^2 E}  } \quad = \quad
           {{1}\over{c^2}} 
        \quad {{\partial^2 E} \over {\partial t^2} }
$$


$$
\eqalign{
y_1(x, t) \quad &= \quad A_1 \cos(k_1 x - {\omega}_1 t + {\phi}_1)  \cr
y_2(x, t) \quad &= \quad A_2 \cos(k_2 x - {\omega}_2 t + {\phi}_2)  \cr
}
$$


$$
\eqalign{
y_1(x, t) \quad &= \quad A \sin(k x - {\omega} t )  \cr
y_2(x, t) \quad &= \quad A \sin(k x - {\omega} t + {\phi})  \cr
}
$$


$$
\sin(\alpha) + \sin(\beta) \quad = \quad 2 \cos( {{\alpha - \beta}\over{2}} )
                                     \thinspace 
                                           \sin( {{\alpha + \beta}\over{2}} )
$$


$$
y1 + y2 \quad = \quad 2 A \cos( {{\phi}\over{2}} )
                           \thinspace
                        \sin(k x - \omega t + {{\phi}\over{2}}) 
$$


$$
\eqalign{
y_1(x, t) \quad &= \quad A \sin(k x - {\omega} t )  \cr
y_2(x, t) \quad &= \quad A \sin(k x + {\omega} t )  \cr
}
$$


\bye

