Alexander Fufaev
My name is Alexander FufaeV and here I will explain the following topic:

Acoustic Beat: What Happens When Two Similar Sounds Interfere

Explanation

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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:

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

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

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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:

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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.