Are EM waves additive like sound waves? Or do they remain distinct?

Factual Questions
1

Background:

When two sonic sine waves of close frequency occur at the same time, we hear them as the average of the two frequencies, with the amplitude pulsing at the rate of the difference between the two frequencies (beats). When they get far enough apart we perceive them as two distinct pitches, depending on their relationship. (We might not, for example perceive two sine waves as separate if one is exactly twice the frequency of the other because of the overlapping harmonic series.)

If two light waves of different frequencies, such as red and green, we perceive them as yellow. All three colors are single-frequency colors. But are red and green somehow averaging into yellow before they reach our eye? Or this is strictly an artifact of our color vision? We can generate a million colors on a computer monitor with just three primary (additive) colors. If red and green both reach our eye at the same time, they excite the sensitivity ranges of the red and green cones that are also stimulated by pure yellow light. So we perceive it as yellow.

Question:

But then again, did the two colors actually combine to average out to yellow by the time they reach our eye? Or is yellow on a computer monitor just an illusion that takes advantage of how our eyes work?

Is there anything in EM waves comparable to beats in sonic waves?

Misread thread titles
2

Light waves can do all of the same wavey stuff as sound waves, but they’re more complicated, since light has polarizations but sound doesn’t.

But red and green aren’t close enough in frequency to meaningfully beat, anyway.

3

And everything about color perception is vastly complicated by how weirdly our eyes work. The ears are a lot closer to a simple FFT of the incoming time-varying pressure wave. Eyes are not like that at all.

4

The way human eyes detect light is with particle interactions. Each cell in the retina reacts to the number of photons it receives. It’s purely magnitude, as phase information is lost, so effects like the beat frequency aren’t generally possible.

One exception is with laser light illuminating a surface. It’s possible to see “speckles”, which are small spots of brighter and darker illumination. This is caused by constructive and destructive interference, which is a special case of beat frequencies. But note that this is outside the eye, with the eye merely observing the effect.

5

Beat frequency is never something that just happens in the detector. The only reason that we never see light beats is that light is so high-frequency, it would be exceedingly difficult to get two sources so close that the human vision system could even detect the beats.

6

No. If you passed the through a prism you would get the original two colors back. Red photons and green photons. Nothing changes the energy (color) of the photons.

Yes.

7

Is there an optical effect where two EM waves will exhibit a beat frequency? Yes.

Could you see this effect with your eyes? Theoretically, yes.

Does that explain the way monitors work, or any other part of color vision? No, not at all.

8

You could also have an animal, or a detector, that had better capability to break up light into frequencies. You could even have one that could fully distinguish between different spectra, though that usually comes at the cost of some of your spatial resolution. Or you could have full spectral and spacial resolution, but at the cost of having to fit what you see to your mental model of the world (we already do something like this with many aspects of our vision). Of course, relying on a mental model like this means that you can be fooled by situations that don’t match the mental model, what we call optical illusions. A creature that had full-spectral eyes would presumably be subject to entirely different categories of optical illusions that we’re not subject to. Though they would also categorize our seeing of a mixture of red and green as yellow as an optical illusion.

9

On a related note, why don’t two light waves seem to interact?

Say I have a green and red laser. I orient them so that the red laser passes through the beam of the green laser. You would think the changing E fields of the red laser would mess up the M fields of the green laser, and vice-versa. But the two laser beams seem to pass through each other “perfectly,” each unaffected by the other.

10

Because both E and B fields from different sources add together linearly. In the region where the two beams overlap, you have a complicated mess of E and B fields, but the only way for that mess to evolve is as two beams leaving the mess.

That said, it’s not quite perfect, and there is is actually a little bit of interaction between the two. But until you get up to around a million electron volts (the mass of an electron-positron pair), it’s negligible.

11

Sure they do. Breit–Wheeler process, for example. They do not “seem” to because we are talking about non-trivial, high-energy experiments.

12

One very arm-wavy way to think about it is that sound waves need a medium. A solid, liquid, or a gas. Which constituent particles have mass, momentum, density, coupling constants, etc.

Conversely, EM doesn’t need an aether. It runs off a much more fundamental set of properties of our universe.

So some wavy aspects work similarly between the two and others do not. Which is which gets beyond my pay grade very quickly. But the idea that there should be both similarities and differences is readily graspable to a layperson.

13

The presence of a medium for sound waves mostly just means that in extreme cases, they don’t act quite as wave-like as they should, because a medium has things like attenuation and a minimum pressure.

14

I need to have my eyes checked. Or maybe my brain. I read this is as

Which is which gets beyond my gay pride very quickly.

15

To be fair, there is the auditory illusion of “binaural beats”.

16

Hah! That’s a good one.

I’m sure there are some terrible jokes to be made about AC-DC and E, B, and M fields.

17

Sound waves are almost additive like EM waves, but actually you get distortion if the sound is very large. Normally, this is unwanted noise, but you can use this to generate audible tones from additive distortion of ultra-sound.

EM waves just add together. The don’t form anything different when added: 2+3 just equals 2+3, not 2-and-half or 5.

18

Yeah, sound behaves weirdly.

In principle any sound wave interferes with itself. The change in pressure changes the speed of sound, and this results in the pressure peaks travelling faster than the troughs. So a sine wave becomes more sawtooth. This can be perceivable over longer distances as an increase in harmonic content. However, countering this is a frequency related adsorption of higher frequencies. That is dependent upon other of factors, humidity being important in an unhelpfully non-linear manner. So there is a lot of “it depends” involved.

19

The additive nature of EM waves is actually the reason why AM radio works. In the time domain, the amplitude of the signal is the sound that it is carrying. In the frequency domain, sidebands are the spectrum of the sound offset by the carrier frequency. The amplitude of the signal varies as the carrier and sidebands, at slightly different frequencies add and subtract.

20

For photons, energy would be an applicable metric, but not for EM waves, where we’d need to talk about energy density or field strength.

The Schwinger limit gives a sense of the field strengths above which non-linearity comes strongly into play – about 1018 V/m for electric fields.

To add more words to the “EM is linear” explanation: if you leave quantum effects aside, the behavior of electric fields all stems from Coulomb’s law, and Coulomb’s law is a statement about forces on charges due to other charges, and having one charge here and another charge there doesn’t change the charges and thus doesn’t change the components of the forces as you make the situation more complicated. And electric fields are another way of describing the forces on charges independent of what causes those electrical forces. And so, electric fields can be added together just like forces can. When you then allow moving charges, you just take the electric fields and run them through special relativity to see how the forces change, and out pops the concept of a magnetic field, but the additive properties are preserved. Then you jump to time-varying fields – which leads to EM waves – but the additive properties continue.

For fun, we could calculate how much of your crossed beams is “lost” due to non-linear effects. Here I’ll model it with a quantum treatment as it will be easier to consider it as a collection of photons trying – and generally failing – to interact.

Let’s assume two 5 mW green handheld lasers with 1 mm beam widths at the crossing point. For simplicity let’s model the beam profiles as perfect squares rather than bell curves.

The number of photons from one of the beams in the cubic interaction region at any given time is (power)*(1 mm)/c/(energy per photon) = about 50,000.

The cross section for photon-photon scattering at energies well below the electron mass scales dramatically as the sixth power of the energy. At the energies here, it evaluates to 10-61 mm2. (Details available.) So, every photon has a probability of scattering with one of the other beam’s photons of

P = (10-61 mm2) * (50,000 target photons / mm3) * (1 mm) = 5x10-57

Each laser is pumping out 1016 photons per second, so the rate of photon-photon scattering in this beam crossing experiment is around 5x10-41 Hz. Or once in every 1022 current ages of the universe. So, not too often.