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:

$$ \begin{align} s_{r}(t) ~=~ 2s \, \cos\left( 2\pi \, \frac{f_1 ~-~ f_2}{2} \, t \right) \, \sin\left( 2\pi \, \frac{f_1 ~+~ f_2}{2} \, t \right) \end{align} $$

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

$$ \begin{align} f_{r} ~=~ \frac{f_1 ~+~ f_2}{2} \end{align} $$

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

$$ \begin{align} 2s \, \cos\left( 2\pi \, \frac{f_1 ~-~ f_2}{2} \, t \right) \end{align} $$

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:

$$ \begin{align} f_{\mathrm S} ~=~ \frac{f_1 ~-~ f_2}{2} \end{align} $$

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.