Perception of sound: Beatings

When we have two sounds whose frequencies differ little from each other, we perceive an extra sound. This sound is similar to the other two but we can also perceive a beat whose pace is dictated by the two sounds' frequencies. If these two frequencies are too far apart, our brain no longer perceives this beating sound. This is because in order to perceive the two as a beating they both have to stimulate the hair-cells that reside in the same critical band. The beatings' frequency is equal to the number of times the two sinusoids are in phase and out of phase per second. Let's see a practical example.

Consider two pure sinusoids with frequencies 400 Hz and 405 Hz respectively:

Pure sinusoidal wave (f=400 Hz)  [Track 11]

Pure sinusoidal wave (f=405Hz)  [Track 12]

The sum of these two sounds can be heard in the following sound:

Sum of two sinusoids with frequencies 400Hz and 405Hz  [Track 13]

As we can hear, a new oscillation takes place. If the two frequencies had been further apart this phenomenon wouldn't have taken place [Combination of pure sinusoids ] .

Finally let's see the new waveform's rate resulting from the combination of the two:

Sum of two sinusoids with frequencies 400 Hz and 405 Hz