Two traveling waves with equal and opposite wave-vectors form a standing wave, which is easy to prove.
But what about combining two standing waves?
Can we derive the velocity of the wave/disturbance created by combining two standing waves?
For example take two standing waves:
$$ y_1(x,t)=A_1sin(k_1x)cos(\omega_1t) $$ $$ y_2(x,t)=A_2sin(k_2x)cos(\omega_2t) $$
And combine them:
Does this result in a traveling wave? If so, what is its wave-vector and velocity?