The interference of two sound waves of slightly different frequencies produces

The interference produces 'beats' ... two new sounds
in addition to the original ones.

The frequencies of the beats are

   -- the sum of the two original frequencies
and
   -- the difference of the two original frequencies .

Technically, there are actually even more new sounds than that.
There are: 
-- beats between the beats, and
-- beats between each beat and each of the original two sounds.
But their amplitudes are so low that they can be detected only with
sensitive equipment, and they can't be heard in the presence of
the two original sounds and the two 'first order' beats.