Wave going into positive direction has the equation:

$$p(x)=\sin(x+\omega t)$$

Into the negative direction:

$$n(x)=\sin(x-\omega t)$$

Their sum:

\begin{align}
p(x)+n(x)&=\sin(x+\omega t)+\sin(x-\omega t) \\ 
&=\sin(x)\cos(\omega t) + \cos(x)\sin(\omega t) + \sin(x)\cos(\omega t) - \cos(x)\sin(\omega t)\\
&=2 sin(x)cos(\omega t)
\end{align}

As you can see, the wave on the bottom is a *standing* sine wave, whose amplitude is multiplied by the original frequency of the moving waves.