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Beat Frequencies

  Beat frequencies are a side effect of wave interference.  Sounds are composed of waves; sound waves can interfere with each other.  The amplitudes of any two sound waves that meet at a given point always add; if one amplitude is negative and the other is positive, this "addition" causes one to cancel the other out, either partially or, if the waves' amplitudes' magnitudes are identical, completely.  If the waves have different frequencies, they will interfere "constructively" and "destructively" in an alternating pattern, creating "beat frequencies".  There's really no good way to explain this; the best way is to take two guitars that are in tune with each other, and slightly (very slightly) off-set the tuning of one string on one of the guitars.  Then, play both strings at once, and enjoy the sound.  In any case, here's a set of graphs demonstrates what beat frequencies "look" like, with the adding of two sine waves whose frequencies are offset by a factor of 1.05.