# 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:

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

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

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:

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.