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Combining multiple arbitrarily chosen frequencies of sound makes a complicated wave, not a new sine wave. Doesn't light also do this? If I add a 650nm (reddish) wave and a 550nm (greenish) wave, I get a complicated wave. If I shine this light on a prism, presumably it would resolve into red and green, I guess because the two wavelengths have different refractive indexes. But neither of those wavelengths is going into the prism. Or are they? Does nature do some kind of Fourier transform to white (or multiple-mixed-frequency) light? Or does white/mixed light somehow retain the component frequencies?

There are a lot of questions out here that are closely related to mine, but none of them seem to ask this particular question, and none of the answers shed any...light...on the problem, perhaps only because I lack the needed physics and mathematics background.

A very closely related question, maybe even a duplicate, but asked very differently.

  • How is your problem any different from, say, why connecting two AA batteries in series gives 2.4V? How do the electrons know that 1.2+1.2=2.4? – hyportnex Sep 28 '21 at 01:05
  • @hyportnex I've never heard that voltage exhibits wavelike properties – SaganRitual Sep 28 '21 at 01:08
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    It never forgot to begin with. The 550 nm components continue to act like 550 nm components and the 650 nm components continue to act like 650 nm components, etc. They only became "white" when your eye detected all the different components at once and your brain interpreted that as "white". – The Photon Sep 28 '21 at 01:08
  • @ThePhoton I'm not talking about eyes. I'm talking about combining electromagnetic waves, which (I thought) should combine in a wavelike fashion – SaganRitual Sep 28 '21 at 01:10
  • If you want an analogy...Think about how when they record several musical instruments playing at once onto a record album or magnetic tape and then when they play it back you can hear all the different instruments. – The Photon Sep 28 '21 at 01:10
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    They "combine" by never actually combining. The different components don't interact so long as they are propagating in a linear medium. That "complicated waveform" is just what you get when two signals of different frequency are present in the same place without interacting. – The Photon Sep 28 '21 at 01:11
  • @ThePhoton Gravitational wave detectors depend on interference. If light waves don't combine, then how can interference happen? – SaganRitual Sep 28 '21 at 01:15
  • connect the battery (batteries) to a series of L and R and watch what happens to the voltage across the R or L when periodically switch the circuit on/off, 1 battery vs. 2 batteries; see, linear superposition. – hyportnex Sep 28 '21 at 01:16
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    The detector is a nonlinear device. Photons can interact in a detector. – The Photon Sep 28 '21 at 01:17
  • @ThePhoton Are you suggesting that without the detector, the beam wouldn't interfere with itself? – SaganRitual Sep 28 '21 at 01:18
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    It wouldn't interact with itself. Interaction and interference are different concepts. You can pass two beams through each other and you would see interference if you put a screen where they overlap, but if you remove the screen the two beams pass through each other without either one changing the behavior of the other one. – The Photon Sep 28 '21 at 01:19
  • @ThePhoton Then I'm confused about your sound analogy. Sound (pressure waves) does indeed combine to truly make complicated waves, I know that much. My understanding about hearing the different instruments has to do with our hearing mechanisms. Others on this site have suggested that our inner ear actually performs a Fourier transform on sound. What am I missing? – SaganRitual Sep 28 '21 at 01:27
  • OK, here's another thing to think about: A time domain signal and its Fourier transform are not two different things. They're just two different ways of mathematically describing the same thing. – The Photon Sep 28 '21 at 02:19
  • @ThePhoton I derailed us by talking about the Fourier transform. I should have asked, how/why does light not combine like sound does? I understand that it's not really a compression wave in the em field, but I keep thinking of the two-slit experiment--is that interference pattern a result of each photon interfering with itself, even when we blast the slits with non-coherent (is that the right word for noisy/complicated?) light? – SaganRitual Sep 28 '21 at 02:25
  • @SaganRitual How do you know that the waveform of superposed EM waves with various frequencies are not as complicated as these of sound waves? Have you seen any such waveforms for white light? – nasu Sep 28 '21 at 02:49
  • Sorry to chime in so late, I think that @SaganRitual is at the right path, but still can't wrap his head around the concept. Yes, the waveform of the E-field is "complex", literally and mathematically, but like an orchestra, you can still easily distinguish the different instruments and notes, because in the end, its nothing but a bunch of sine-waves with an amplitude and phase and we can easily decouple all of them. – José Andrade Oct 28 '21 at 21:47

4 Answers4

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If I add a 650nm (reddish) wave and a 550nm (greenish) wave, I get a complicated wave. If I shine this light on a prism, presumably it would resolve into red and green, I guess because the two wavelengths have different refractive indexes. But neither of those wavelengths is going into the prism. Or are they?

They are. Your "complicated wave" is still made up of red components and green components. No indigo or yellow or blue components are created when you spatially overlap a beam of red light with a beam of green light.

Or does white/mixed light somehow retain the component frequencies?

Yes. White light is just a mix of light of different colors that happen to fall on the same spot. That might be because they came from the same source, but it might just be because three or more monochromatic beams were shone on the same spot (this situation wouldn't actually be "white" as physicists define it, but it could be arranged to appear white to your eye).

The Photon
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  • Ok, but is it made up of red components and green components in the sense that there is a combined wave that would look like the two frequencies added together, or is it simply that photons don't interfere with each other as they propagate through the em field? – SaganRitual Sep 28 '21 at 02:47
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    Signals added together (of two frequencies or just one) is exactly what we mean when we say interference in physics. What they don't do is interact. They don't create other frequencies, the presence of a second signal doesn't cause the first signal to propagate differently, etc. – The Photon Sep 28 '21 at 02:52
  • I don't have the necessary intuitions in this area to understand your answer. I thought you had ruled out interference earlier because of the linear medium. It seems like I could reword my original question as, "do photons interfere with each other as they propagate through the em field?" Could you give me a yes/ no on that, or is it a bad question? – SaganRitual Sep 28 '21 at 02:55
  • I posted before I saw your edit. I get what you're saying now. So basically, every photon propagates through the em field as a pure sine wave, it sounds like. Could you confirm? Also, the two-slit experiment: is the interference pattern also due to there being a screen? Or is it because the wave in the two-slit experiment is actually a probability wave rather than an em wave? – SaganRitual Sep 28 '21 at 02:59
  • In a linear medium, they interfere but they do not interact. If you look at what I said earlier I said, "The different components don't interact so long as they are propagating in a linear medium." Interference is just two signals being in the same place so that their fields add up. Interaction is one signal affecting the behavior of the other. – The Photon Sep 28 '21 at 03:00
  • The two slit experiment demonstrates interference between two signals of the same frequency. The interference occurs wherever the two signals overlap. We can observe it because the detection process is nonlinear --- the intensity of light we (or a camera or a photodetector) see is proportional to the square of the field strength. – The Photon Sep 28 '21 at 03:02
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Your assumed difference between behaviour of EM waves and sound waves is not real. Sound waves experience refraction at the interface of two media and if at least one of the two media is dispersive for the acoustic waves you will have a separation of frequencies. However, whereas common media like glass and water are dispersive enough in the visible range to make the effect visible, most comon media for sound propagation, including air, water, solid metals, show very small dispersion for audible acoustic waves. But the dispersion (so, sepration of the frequencies) can be found and measured in some media, including bones.

Also, to actually see the waveform of a complex sound is enough to use your computer or phone, with a simple microphone and a free app. To see the same for visible light of mixed frqencies you need a very rapid and wide band detector and an oscilloscope working in the hundreds of terahertz range.

nasu
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  • Right! Acoustic prisms, I was just looking them up the other day. So something about the medium picks up pure(ish?) frequencies from the complicated waveform entering it. But then, I don't know whether em works the same way. It seems like not – SaganRitual Sep 28 '21 at 03:11
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    No, there is no picking. Dispersion result in refraction at different angles, same as for light. The result depends on the input, again as for light. You may get a continuous spectrum or a line spectrum after dispersion. – nasu Sep 28 '21 at 03:24
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Sine waves are eigenfunctions of the basic wave equation. When we do "Fourier analysis" of a wavefunction, what we're really doing is diagonalizing the wave equation operator. The set of sine and cosine waves is just a basis for wavefunctions. The math of applying an operator is simpler if the wavefunction is given in terms of a basis that consists of the eigenfunctions of the operator, but the final result is the same regardless of how the calculation is performed. Fourier analysis is just a method for doing the calculation; nature just finds the right answer, it doesn't have a specific computational algorithm. The wavefunction is the sum of the two frequencies, so in that sense it does "retain" those components.

  • The previous answers prompted me to investigate waves per se rather than specifically light waves or sound waves. I think what I've found is that all you have to do to decompose any waveform into its components is to pass it through a function that "refracts" -- changes the speed of -- the wave. Is that similar to "diagonalizing the wave equation operator"? – SaganRitual Sep 28 '21 at 04:10
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Photons don't ever mix. They maintain their own frequencies. The mixing is when your brain interprets a simultaneous combination of frequencies. This video https://www.youtube.com/watch?v=Y3HXR2OYEqo shows how separate colors appear to mix and make white but the photons of different frequencies travel independently and only become a perceived mixture when they hit your eyes.

Bill Alsept
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  • I think I'm starting to understand it, but one thing still confuses me. If em radiation doesn't mix, then what causes the interference pattern in the two-slit experiment? – SaganRitual Sep 28 '21 at 17:55
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    @SaganRitual see my explanation at billalsept.com “Single Edge Certainty” the interference or mixture is at the screen. – Bill Alsept Sep 28 '21 at 18:12