Alexander Fufaev
My name is Alexander FufaeV and here I write about:

Acoustic Beat: What Happens When Two Similar Sounds Interfere

Acoustic beat is a periodic increase and decrease in amplitude in the resulting wave caused by the overlapping of two oscillations that differ only slightly in frequency.

The resulting oscillation \( s_r(t) \) is described by the following function:

0
Oscillation beat amplitude
s_{r}(t) ~=~ 2s \, \cos\left( 2\pi \, \frac{f_1 ~-~ f_2}{2} \, t \right) \, \sin\left( 2\pi \, \frac{f_1 ~+~ f_2}{2} \, t \right)
0

The frequency of the resulting oscillation is given by the following equation:

1
Resulting frequency of the oscillation
f_{r} ~=~ \frac{f_1 ~+~ f_2}{2}
0

Let's take a look at the amplitude of the resulting oscillation:

0
Amplitude of the resulting oscillation
2s \, \cos\left( 2\pi \, \frac{f_1 ~-~ f_2}{2} \, t \right)
0

The amplitude fluctuates due to the time-dependent cosine term. The beat frequency \( f_{\mathrm S} \) is embedded in the cosine argument. With this frequency, the amplitude of the resulting oscillation fluctuates:

1
Oscillation frequency of the resulting amplitude
f_{\mathrm S} ~=~ \frac{f_1 ~-~ f_2}{2}
0

Since the two output frequencies \( f_1 \) and \( f_2 \) differ only slightly (e.g. \( f_1 ~=~ 120 \, \text{Hz} \) and \( f_2 ~=~ 100 \, \text{Hz} \)), your ear is not able to perceive the individual frequencies separately - instead you hear a periodic loud-quiet sound.