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I had read that for the formation of beats, two waves must interfere such that they have similar frequencies but not identical, and their amplitudes should be identical. I don't understand why should their amplitudes be identical for the formation of beats. What would happen if their amplitudes were not identical? Can someone help me out in this?

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Beat frequency is as you say when the difference in frequency is low enough for us to make out a beat. When the beats occur the signal is ideally interfered into $0\%$ amplitude. If the amplitudes of the two signals however are very different we'd have a reduction in intensity but not an attenuation to $0\%$ but maybe instead to $90\%$ if one of them is $10$X the other one. This would not be as easy for us to detect.

In other words, the amplitude does not need to be identical, but it helps us to show the phenomenon.

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    $\begingroup$ I can realise that now very well, can you just tell me should i proceed in the same way for finding the beats in the case of different amplitudes as we do for identical ones? $\endgroup$ – Abhinav Tahlani Jan 27 at 7:09
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    $\begingroup$ @AbhinavTahlani: Even if the amplitude is not the same, the beat frequency is still given by the magnitude of difference between the frequencies of the two waves. $\endgroup$ – Guru Vishnu Jan 27 at 7:10
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    $\begingroup$ Wow i just forgot that amplitude should have no effect on the frequency, so the resulting intensity would only be affected in this case,right?Correct me if i'm wrong,i'm just a beginner in physics! $\endgroup$ – Abhinav Tahlani Jan 27 at 7:13
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    $\begingroup$ Yes, the frequency is not affected by the relative amplitudes, only our ability to notice it. $\endgroup$ – DakkVader Jan 27 at 7:49
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As an illustration to the other answers, here are two waves that we'll later superimpose (their frequencies ratio $\nu_1/\nu_2=15/16$):

two waves

Their superposition with identical amplitudes of 1 will look like this (red is the envelope, green – the sum):

beats from identical-amplitude waves

And here's what happens when one of the waves has amplitude 1, while the other 0.7:

beats from different-amplitude waves

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  • $\begingroup$ Nice graphics, do you have a link to them? Here is a similar one that I created which generates diminishing frequencies with consistent amplitudes. I have a simulator for single edge, single slit, double slit and other multiple slit interference calculations. singleedgecertainty.files.wordpress.com/2016/07/… You can find them at billalsept.com $\endgroup$ – Bill Alsept Jan 27 at 22:06
  • $\begingroup$ @BillAlsept I've made these myself in Wolfram Mathematica. $\endgroup$ – Ruslan Jan 27 at 22:07
  • $\begingroup$ they look great. Can you simulate any set up? If you get a chance could you download and take a look at my simulators and see if you have any advice. Thanks Bill $\endgroup$ – Bill Alsept Jan 27 at 22:11
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    $\begingroup$ It's amazing how you can see the envelope pattern inside the first graph if you blur your vision! $\endgroup$ – alseether Jan 28 at 8:12
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    $\begingroup$ @alseether that's known as moire. $\endgroup$ – Ruslan Jan 28 at 8:21
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It's not necessary for the interfering waves to have the same amplitudes. When the interfering waves have slightly different frequencies and different amplitudes, the resultant wave also shows the phenomenon of beats. But unlike the case when both waves have the same amplitude, there will be no time when the amplitude of the resultant wave is zero. Or in other words, there will be no moment of silence which you'd normally observe when amplitudes of interfering waves are same.

If you're interested in this topic, I'd highly recommend you to do the experiment yourselves using an "Online Tone Generator". I used this one for the experiment.

Open the above website in two different tabs. The default frequency will be at $440$ hertz and the default volume will be at $75$%. Leave the first tab aside, and in the second tab, change the frequency slightly, say to $444$ hertz. Now, press the play button in both the tabs separately. Now you'd observe the phenomenon of beats with a beat frequency of $|444-440|=4$ hertz. This is the ordinary case when both the interfering waves have the same amplitude but slightly different frequency.

Now in order to experiment the case in the question i.e., amplitudes of the interfering waves are different, you must change the volume in either one of the tabs to a lower (maybe a higher!) value say $15$%. Now press the play button in both the tabs. Again you'll here the phenomenon of beats, but this time there will be no moment of silence. The minimum amount of sound you'd here will be some non zero value.

I also experimented it (using the values mentioned above) before I posted this answer. It's really interesting to experiment something you learn from your textbooks.


Note: If you find any difficulties in using the tone generator to observe the phenomenon of beats, watch this video from Bozeman science. Although he does this experiment for component waves with same amplitude (or less specifically, volume)

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