Beat Frequencies

When two sounds are played which are very close in frequency, they create a beat frequency. This is a sound which consecutively produces constructive, then destructive interference. It is heard as a warbling of the volume of the note.

This makes sense if you consider additive super positioning. The two frequencies will mix together. At times, they will mix constructively, making a loud sound, while at other times, they will combine destructively, nullifying the sound. The number of constructive and destructive "beats" per second depends on the difference of the two frequencies.

The frequency of the beats indicates the frequency difference between the two tones being generated. For example, if we had a piano playing the note of A at 440 Hz and a violin playing 442 Hz, we would hear the waves become constructive and destructive twice per second as the two tones came in and out of phase.

Mathematically, you can see the effect in the following graphs. Notice how the two waveforms consecutively add constructively, then destructively, creating the beat frequencies in the lower graph.

Beat Frequencies

Musicians use this property when tuning their instruments. One instrument or calibrated electronic device will create a note, say, A at 440 Hz. The musician then plays the note of A and listens for a beat frequency of consecutive constructive and destructive interference patterns. By tuning their instrument, they can eliminate the beat frequencies and know that they are "in-tune" with the other instrument.