Project Science Of Electric Guitar: we did wave interference on paper, just estimating dots, then fired up an old school oscilloscope with two signal generators and nailed the same pattern by fluke picking two musical notes. Then we did some soldering, cos we're going to build a proof-of-concept amp. Best first-go soldering I've seen.
I'm learning so much from this. Classic "you don't understand it until you can explain it" stuff.
Today was a review of the work of John Deacon (electrical engineering and the legendary "Deacy Amp"), and Brian May's work on spectroscopy, and the similarities between sound waves, electrical waveforms, and light waves.
Then we started our amp: jack connection wires and input capacitor soldered into place. Next week is the transistor...
I'm surprised to hear beats, given that I don't think I've seen destructive interference of nearby peaks in spectrum ever. Where does this difference come from?
@robryk It's all in (ugly, hacked together) javaScript if you want to play with it :)
Unless I get distracted, I will probably try to make loudnesses of different frequencies to scale.
Now that I think of it: do stars produce coherent light from our POV?
@robryk The spectral lines are all single wavelengths when emitted, but a certain amount of smearing goes on due to doppler shifts from the star's rotation, e.g. the light from the side rotating towards us is bluer, the other side redder.
Further complicated by interstellar hydrogen clouds absorbing different wavelengths depending on their relative velocity, causing the "Lyman-alpha forest", which is a great name for a prog-rock band.
> The spectral lines are all single wavelengths when emitted
That's certainly wrong: the excited states would be stable if they were energy eigenstates. Are you saying that rotational Doppler smear is much larger than this?
> Further complicated by interstellar hydrogen clouds absorbing different wavelengths depending on their relative velocity, causing the "Lyman-alpha forest", which is a great name for a prog-rock band.
TIL. Thank you very much. Do I UC that this basically applies a filter (so can shift peaks only insofar they are not ideal Dirac deltas)?
Sorry for not being clearer: I was thinking more of the spatial coherence than spectral.
> Sorry for not being clearer: I was thinking more of the spatial coherence than spectral.
Or, actually, to be more precise, I was wondering how similar the situation is to a multitude of emitters emitting at different frequencies, esp. as far as phase coherence between them would manifest. (For non-spatially coherent sources the obvious answer is that you have all the possible phases coming from different directions.)
@robryk In phase it's not coherent at the star, but at a distance where the star becomes a point source the light can be considered coherent for interferometry. Exactly *why* I'm not actually sure, it's still two random photons reaching two detectors, even if from a "point" source. Off to read up on it.
Yeah, I'm labouring under the same confusion. (It started from wondering what it would take to get visible beats: that would require absurdly narrow peaks (~single Hz wide) at a distance of less than ~40Hz. But then, if we somehow had that, what would determine the time offset of beats, assuming the star is large and emitting noncoherently across its surface?)
Perhaps thinking of a classical planar wave (and what can be observed about it in finite time) will be helpful here.
@robryk Photons don't (well...very rarely) interact with each other, so it'd have to be an effect at the detector. Do double-slit style patterns count?
@_thegeoff If you want to think in terms of photons, then I guess uncertainty principle on transverse directions might be relevant (as it's the source of diffraction limits).
@robryk going back to my synth, the beats are roughly on the order of seconds, so translating back that's a few nm. So maybe 1% of the human range of vision. It'd be tricky to see directly. What we need is 2x HeNe lasers, one stationary and the other doing about a million mph ;)😉
I don't think this is what matters for visibility of beats. I would rather expect that what matters is relationship between 1/deltafrequency and time period you are integrating over. I'm not sure what's the effective time period eyes-as-EM-receiving-apparatus are integrating over, but it can't be more than ~1/60s. (If we had more resolving power in wavelength I could also estimate based on that, but alas.)
If I'm right and my naive estimate is roughly correct, sadly seeing beats with one's own eyes would require narrower spectra than any laser I know of (IIUC tens of kHz is already extremely narrow).
BTW an easier way of adjusting the frequency (if we had something with a narrow enough emission spectrum to start with) would be to put it in a magnetic field to split the excited state (see Quantum Light Dimmer in https://www.iypt.org/problems/problems-iypt-2024/).
Ah, this surely also relies on the size of the receiver, because it seems to be a consequence of the diffraction limit.
@robryk Huh, TI also L!
The broadening from stellar rotation is ~1000x the broadening from transitions: https://web.njit.edu/~gary/321/Lecture6.html
You also get effects like Doppler shits at the atomic level etc. But in practice the lines are quoted as exact wavelengths, and deviations from that analysed to work out what the star is made of / doing / interstellar environment etc.
@_thegeoff wait, but didn't this map frequencies to (some multiple) of their inverses?
@_thegeoff wait, but didn't this map frequencies to (some multiple) of their inverses?
@robryk Light wavelengths in nm to sound freq in Hz, simply because the numbers are both nicely within the respective human ranges.
So yeah, going backwards, freq to 1/freq with a few orders of magnitude translation between the speed of light and sound.
@robryk The first 10 elements, as I picked, cover roughly the first 5 octaves in the human hearing range. I need to double check Lithium, they're all really borderline low end, which is interesting in itself, because it's possible we can't hear that, but *can* hear the beat freqs.
Sadly, this transformation changes everything far enough that IMO beats do not map to much of anything interesting in the original configuration.
To see that this mapping changes things very significantly, notice that a base frequency and a few harmonics map to something that has no base frequency, but is rather a mixture of a few unrelated frequencies and their common harmonic. This IMO means that interesting relationships between frequencies are not preserved.
If we talk about beats specifically, then the frequency difference "on the audio side" here is a nonlinear function of the frequency difference "on the light side", so even if we were to consider some hypothetical creatures that have very short averaging timescales in vision (so that they can perceive beats at differences e.g. as small as a few MHz[1]), this map to something weird on the audio side (the minimal frequency difference will not be constant over the range we're considering).
[1] This does not necessitate them having awareness of such short time intervals btw.: a human, with help of an FM radio receiver, can do something equivalent to detecting beats with frequency differences of small hundreds of kHz. A creature could have sense organs that can do something similar without their conscious processing having to run at higher speeds.
(BTW. This sounds like a potential worldbuilding idea for a short story.)
@robryk It's nanometer wavelengths converted to Hz sine waves, so not strictly comparable, I just liked the way the numbers matched up. But yeah, the beat frequencies were a lovely surprise, mostly down to the main ~100s nm optical range being tight compared to the 20-20k range of human hearing.