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Wize University Physics Textbook (Master) > Sound & Hearing

Beats

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Beat Frequency


What happens when we play two different sounds with slightly different frequency at the same time?

By the principle of superposition, we can just add the waves up together. We will get this new wave that will oscillate in amplitude!

Let's consider two waves shown by blue and red colors below which has slightly different frequencies of f1f_1and f2f_2:






Beat frequency is the difference in the frequencies that are received by the receiver. This is the frequency of the fading in and out of the sound heard; the frequency of the "beats" heard.

fb = ∣f1−f2∣ \boxed{f_b\ =\ \left|f_1-f_2\right|\ }


Wize Concept
This is actually how musicians tune their instruments! They tune the frequency of their note with a given one until they can't hear the beat frequency anymore. That's when they are in tune.


Example: Beat Frequency


Reef is enjoying his classical music mixtape with his surround sound system. He arrives at a point where the note 280 Hz is being played by the violins, and notices a beat with frequency 3 Hz. He spots the malfunctioning speaker and replaces it. Which frequencies could the malfunctioning speaker be playing? (List all possible frequencies)

Solution:

The beat frequency is the difference between two close frequencies. Therefore, the possible frequencies are 277 Hz and 283 Hz.

Practice: Finding the Frequency of a Flute Sound


A flute is sounded alongside a 256256 Hz tuning fork and 1919 beats are heard in one second. Next the flute is sounded alongside a 288288 Hz tuning fork and 1313 beats are heard in one second. Determine the frequency of the flute.