Resulting amplitude due to two equidistant sound sources

Question

If sound sources have same amplitude say $A$ and nearly same angular frequency like say $\omega_1$ and $\omega_2$ then at a point equidistant from them is it correct to assume that the resulting amplitude after superposition will be nearly $2A\cos((\omega_1 -\omega_2)/(2 t))$ ?

If yes,why?

If the waves are $A\sin(\omega_1 t - k_1 x)$ and $A\sin(\omega_2 t - k_2 x)$ then won't the terms $k_1$ and $k_2$ also affect the resulting amplitude?

Asking this because my physics teacher made that assumption in a certain problem but I did'nt receive a satisfactory answer when I asked a reason for it.

Answer 1

Since this is clearly homework and excercises question, I will provide just hints.

• This kind of treatment is the same how beats are descripted. Study this article, it will help you get that.
• Since $k=\frac{\omega}{c}$ where $c$ is constant and the distance is the same for both the signals, it will not cause any more uncertain phase shifts.