FFT Frequency bin relationship
Yes, simply use a trigonometric addition formula.  The results can vary from complete constructive interference to most destructive interference.  Depending on the relative phases at your microphone.

Here is the math:

$$ W_1 = A_1 \cos( F t + P_1 ) $$
$$ W_2 = A_2 \cos( F t + P_2 ) $$

$$ W_1 = A_1 \cos( F t ) \cos( P_1 ) - A_1 \sin( F t ) \sin( P_1 ) $$
$$ W_2 = A_2 \cos( F t ) \cos( P_2 ) - A_2 \sin( F t ) \sin( P_2 ) $$

$$ W_3 = W_1 + W_2 = [ A_1 \cos( P_1 ) + A_2 \cos( P_2 ) ] \cos( F t ) - [ A_1 \sin( P_1 ) + A_2 \sin( P_2 ) ] \sin( F t ) $$

Now

$$ W_3 = A_3 \cos( F t ) \cos( P_3 ) - A_3 \sin( F t ) \sin( P_3 ) $$

so

$$ A_3 \cos( P_3 ) = A_1 \cos( P_1 ) + A_2 \cos( P_2 ) = C $$
$$ A_3 \sin( P_3 ) = A_1 \sin( P_1 ) + A_2 \sin( P_2 ) = S $$

Calculate $C$ and $S$.

$$ A_3 = \sqrt{ C^2 + S^2 } $$
$$ P_3 = \operatorname{atan2}( S, C ) $$

If they are in phase $(P_1 = P_2)$ then $ A_3 = A_1 + A_2 $.

If they are completely out of phase $( P_3 = P_1 = P_2 + \pi )$ then $ A_3 = A_1 - A_2 $.

Also, the FFT is a linear operator, so the FFT of your sum is the sum of your FFTs.

Hope this helps.

Ced