Can beat frequencies occur when the amplitude of the waves are different?

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SUMMARY

Beat frequencies occur when two waves of the same amplitude but differing frequencies are combined, resulting in amplitude modulation at the frequency equal to the difference between the two frequencies. When more than two waves are involved, such as three or more sine waves, the concept of beat frequencies becomes more complex, and while there may be modulation effects, they do not strictly adhere to the same principles as with two waves. The necessity for equal amplitude in generating beat frequencies is clarified; beat frequency is fundamentally a function of frequency differences, not amplitude variations. The mathematical relationship governing this phenomenon is expressed through the formula cos u + cos v = 2 cos(½(u+v)) cos(½(u−v)).

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  • Basic knowledge of frequency and amplitude concepts
  • Mathematical skills to interpret trigonometric identities
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Dekans6
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When two waves of same amplitude but differing frequencies are added together, the frequency of the amplitude modulation of the resulting wave is the difference b/w the frequencies of the two parent waves.

How about beat frequencies from the interference of more than 2 waves, say 3, 4, or 10? How do we calculate that?

Also, it hasn't been clear to me why the two waves need to have the sample amplitude for beat frequency to occur...Isn't beat frequency only a function of the differences in frequencies and not a function of amplitude?

Could someone help me clarify these two questions?

Thanks!
 
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Could someone please help me with this?
 
Dekans6 said:
When two waves of same amplitude but differing frequencies are added together, the frequency of the amplitude modulation of the resulting wave is the difference b/w the frequencies of the two parent waves.

How about beat frequencies from the interference of more than 2 waves, say 3, 4, or 10? How do we calculate that?

2 sine waves add together to create 1 sine wave modulated by "beats".
3 sine waves add together to create 3 sine waves added together.

There may be some equivalent of "beats" in this case, but it wouldn't be exactly the same concept, and it would get a little fuzzy.

Also, it hasn't been clear to me why the two waves need to have the sample amplitude for beat frequency to occur...Isn't beat frequency only a function of the differences in frequencies and not a function of amplitude?

Beats aren't magic, it's just math. cos u + cos v = 2 cos(½(u+v)) cos(½(u−v))

Notice that formula doesn't work if you multiply one of the cosines by something. That's all there is to it. The sum of 2 sine waves with different amplitudes is just 2 sine waves with different amplitudes added together.
 

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