# Why do we hear beats?

I've learnt quite recently that to hear beats the sources must emit sound in almost near frequencies

Here is a scenario I have a two tunning forks and together the produce a beats of frequency 2hz

But humans can only hear from 20hz How can we hear this beat?

• – lorenzo Baldessarini Feb 20 at 8:43
• Imagine fork A & B vibrates at 998Hz & 1kHz respectively, you will hear something much higher due to constructive interference then it fades away before coming back again... rinse and repeat, this is exactly what you hear the beat frequency of 2Hz ;D – user6760 Feb 20 at 10:03
• Well, the "much higher" user6760 refers to has to do with the amplitude, which will "fluctuate" between the sum and the difference of the two sounds. The average frequency that will be heard will be the mean of the two frequencies. – ZaellixA Feb 22 at 15:37

As very well J Thomas states, beats are not perceived as sound. They are perceived as a periodically repeating amplitude variation. This does not define the beat as sound but does define it as a perceivable variation in (at least) one parameter of a sound (in practice there's some small variation in frequency but it is not easily perceived and for most practical cases it can be omitted and consider the frequency of the modulated sound as constant).

As for the ultrasound beating that can result in audible sound (what Pieter has peresnted), I believe this is true and if I am not mistaken it is one of the ways that ultra-directional (the term is not standardized but I hope you understand the meaning) speakers are built upon. If one manages to create a beat at an audible frequency then this will be perceived as sound. This means that if the two ultrasounds create a beating the amplitude variation frequency will be given by

$$f_{beat} = \frac{\left| f_{1} - f_{2} \right|}{2}$$

which, using the given values should be

$$f_{beat} = \frac{\left| 100 KHz - 102 KHz \right|}{2} \implies f_{beat} = \frac{2 KHz}{2} \implies f_{beat} = 1 KHz$$

which is an audible frequency, while the modulated frequency will be given by

$$f_{sound} = \frac{f_{1} + f_{2}}{2} \implies f_{sound} = 101 KHz$$

which of course is not audible.

20 hertz gives you a sound that you can probably hear as a tone.

2 hertz gives you a series of beats. It doesn't sound like a tone.

If you beat a bass drum twice a second it won't sound like a musical note, but you can hear it.

This is wrong in at least one textbook (here: Hewitt):

To be clear: one does not hear anything (unless the intensity of the ultrasound is at 100 dB or so). Beats are a slowly varying amplitude. You can try here from the loudspeaker of your computer: https://onlinetonegenerator.com/binauralbeats.html

(Or with headphones, you would hear the spooky phenomenon of binaural beats.)