I it possible to calculate the resulting frequency when you play two tones with a frequency of X and Y at the same time?
This question has simple answers only when one is talking about sinoidal signals of equal amplitude. Since the respective phase changes all of the time, one can answer this question by starting with both signals at phase 0, and then we have
So basically you get a function with the mean frequency of the two, and it is beating with an envelope with a frequency of the difference of the two functions (formally, it is half the difference but since you cannot hear the difference between an envelope of cos(x) and |cos(x)| and the second has double the frequency of the first, the envelope frequency ends up as the difference itself).
The formula works for any value, but its interpretation as a tone with a beating envelope makes only sense when frequencies a and b are reasonably close.
This is the basic technique with which accordion "tremolo" registers work, and also organ "tremulant" registers.