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View Full Version : Does light have timbre? aka Are photons sinusoidal?



clop
2006-Aug-25, 10:50 AM
If a certain colour of light is manifested by photons with a certain frequency, is the wave of the photon sinusoidal?

With sound, you can have a note with a pitch of "Middle C" which is around 256Hz, depending on the definition of the scale. If you play middle C on a piano you hear the same tone as if you play middle C on an oboe. or if you whistle middle C, or go "laaa" at middle C, or pluck a string at middle C, yet you can identify the source of the sound because of timbre - the waveforms may have the same periodic frequency but their structure is different. A square wave middle C has the same pitch as a sinusoidal middle C but it sounds different.

Anyway, I was wondering if EM radiation is sinusoidal, or whether it is something else, or maybe it can have timbre. Colour would then be a trivial property of the light, and the timbre would perhaps show us where it came from?

clop

Roy Batty
2006-Aug-25, 12:43 PM
Maybe it's polarisation (http://www.uwgb.edu/DutchS/petrolgy/genlight.htm) could be considered as such?:think:

clop
2006-Aug-25, 12:45 PM
Maybe it's polarisation could be considered as such?:think:

Polarisation is surely independent of waveform?

clop

pghnative
2006-Aug-25, 12:47 PM
I recall being taught that it was sinusoidal, but I don't feel like looking for links...

Ken G
2006-Aug-25, 01:20 PM
Light does have timbre, but we don't call it that, we call it the "spectrum". It's why there are more colors than what you can see in a rainbow (which separates the sinusoidal components, just as you can do with sound or any waveform). Also, we can use instruments to focus on a narrow range of frequencies, and the the study of the detailed "timbre" we see there is called spectroscopy. It is the very core of astronomy, because that's where most of the information is.

Kaptain K
2006-Aug-25, 02:59 PM
The problem is that although we can hear about 10 octaves of sound - 20Hz-20kHz, we can only see a little less than one octave of light - 400-700nm. Timbre is a result of harmonics. The first harmonic is the octave - double the frequency, half the wavelength. I'm sure that, if we could see several octaves of light, we would see timbre in light.

pghnative
2006-Aug-25, 03:41 PM
Light does have timbre, but we don't call it that, we call it the "spectrum". It's why there are more colors than what you can see in a rainbow (which separates the sinusoidal components, just as you can do with sound or any waveform). Also, we can use instruments to focus on a narrow range of frequencies, and the the study of the detailed "timbre" we see there is called spectroscopy. It is the very core of astronomy, because that's where most of the information is.Ken, I don't think you've answered the OP.

The point of the question is that you can have a 440 Hz tone from a piano and a 440 Hz tone from a guitar, and they sound different because the waveforms are different.

So can 700 nm red be somehow different from another 700 nm red by having a different waveform, or all all waveforms sinusoidal. I thought it was the latter, but do not have a basis for saying so.

Tensor
2006-Aug-25, 03:58 PM
I'm sure that, if we could see several octaves of light, we would see timbre in light.

Hmmmmmmmm, I'm guessing we would also be able to see chords of light, in that situation.

korjik
2006-Aug-25, 04:00 PM
if it had a different waveform it would be a different color.

The 440hz tones from any instrument are made up of the primary 440hz signal and many harmonics that are different frequency. You could split the signal from each into 440, 880, 1320,.... hz signals of different strengths.

The analogy with light would be when you have a color made up of several different spectral lines. You might have some 700nm some 550nm and some 440nm light that could be mixed with different intensities to give you almost any color from red to violet.

Kaptain K
2006-Aug-25, 04:02 PM
A single photon is absolutely monochromatic. It is a quantum of energy.

Kaptain K
2006-Aug-25, 04:06 PM
Hmmmmmmmm, I'm guessing we would also be able to see chords of light, in that situation.
Agreed! :dance:

Ken G
2006-Aug-25, 04:52 PM
The point of the question is that you can have a 440 Hz tone from a piano and a 440 Hz tone from a guitar, and they sound different because the waveforms are different.
All you are saying is that we can't have a 440 Hz tone from either a piano or a guitar-- other tones are mixed in as well. So it is with light, it's just the same. Each unique frequency is identical, but that's as true for sound as for light.

Nereid
2006-Aug-25, 05:46 PM
If we had the right sort of eyes, we would see that some light sources do have resonances (http://xmm.vilspa.esa.es/external/xmm_science/gallery/public/level2a.php?p=0&cat=10&subcat=4) (hence, timbre?). Or, how about the good 'ol Lyman, Balmer, etc series (http://iapetus.phy.umist.ac.uk/Teaching/IntroAstro/Hydrogen.html) - the timbre of hydrogen?

clop
2006-Aug-25, 09:43 PM
All you are saying is that we can't have a 440 Hz tone from either a piano or a guitar-- other tones are mixed in as well. So it is with light, it's just the same. Each unique frequency is identical, but that's as true for sound as for light.

Thank you Ken G. I see this now.

No matter how complex the timbre of a sound wave you can always break it down into a Fourier series with weighted terms representing the relative amplitudes of the different frequencies involved.

So I suppose my question simplifies to whether or not a single monochromatic photon is sinusoidal. I suppose it would have to be, or else it would just be a candidate for more Fourier analysis until it were.

clop

Jeff Root
2006-Aug-26, 09:32 AM
But a sound really can be a pure frequency with a
non-sinusoidal waveform. The fact that the waveform can
be mathematically analyzed into the superposition of a large
number of sine waves is interesting and very useful, but
it isn't necessarily relevant. A triangular sound wave can
be generated synthetically, and it does sound different
from a sine wave of the same frequency.

Light can have other than a sinusoidal waveform, too,
but not on the level of individual photons -- only in bulk.

The interesting question is: At the photon level, what
is the waveform? Is it sinusoidal? Is it something else?
Is it indeterminate? Is the question meaningless?
And why is it whatever it is?

-- Jeff, in Minneapolis

neilzero
2006-Aug-26, 12:16 PM
I think Kaptian k is correct: A single photon is monochromatic = sinusodal for both light and radio waves. If your radio transmitter is malfunctioning it can produce considerable 2nd and third harmonic photons, but even the harmonic photons are sinusoidal. Neil

Ken G
2006-Aug-26, 01:38 PM
But a sound really can be a pure frequency with a
non-sinusoidal waveform.
No, that is not the meaning of frequency as applied to waveforms, which is applied via the Fourier transform (i.e., definitively sinusoidal). Or, if you insist on applying a generalized definition of frequency, then you can also do the exact same thing with light. Ever listen to a radio?


Light can have other than a sinusoidal waveform, too,
but not on the level of individual photons -- only in bulk.
That is not saying anything different about light than sound. Both are quantized, and what the "eigenfunctions" are depends on how you measure them. Sinusoidal eigenfunctions are generally energy eigenfunctions, so if you measure the energy, this is what you are doing. That does not tell you anything about light, it tells you something about your measurement apparatus. On the emitting end, sinusoidal waveforms can be achieved with a resonance, as Nereid pointed out, but again... as true for sound as light!

umop ap!sdn
2006-Aug-29, 05:31 AM
So can 700 nm red be somehow different from another 700 nm red by having a different waveform
In theory, yes, because it is possible to have 700nm light plus 1/4 intensity 350nm plus 1/9 intensity 233nm plus 1/16 intensity 175nm etc. But they would all look the same to a normal human eye as even 350nm is quite outside the visible region.