Why light is a sinusoidal wave?

[chingel]

If I generate two sound waves with my computer with a few hz difference, the output volume meter definitely goes up and down.

I made a picture of what adding 100 and 152 hz sine waves together looks like:

http://www.freeimagehosting.net/newuploads/ab870.jpg

There is definitely the pattern of the amplitude going up and down 4 hz. Not as dramatic as adding sine waves 100 and 104, where the beat amplitude would go all the way, but it seems that just the addition of the sine waves creates the beating pattern.

Do I understand correctly that basically our ears do a Fourier transform on the sound? Then why don't they just break the sound down into two sine waves and hear them with a constant tone? Is it because the ears don't know they are supposed to do the transform on a 0,25 second chunk, but instead they do it in real time, and they don't know the waves are out of phase and it would look just like the waves have lower amplitudes, or is this a wrong idea?

 

[sophiecentaur]

Our ears detect the power spectrum, which loses the phase information. Part of our processing adds up the powers - hence we can tell the difference in loudness between one singer and a whole choir, which is obvious. But this power measurement involves a non linearity. I may be being picky (heaven forefend) but the fact is that there is NO low frequency component in the linear sum of two sine waves. There is NO low frequency component in an amplitude modulated signal either. (AM signals are all band pass filtered at many stages in the broadcasting process yet they still survive without any low frequency em waves getting to your house) The only way you can 'demodulate' any of these high frequency waveforms is with a non linear process. This may be hidden or 'implied' but it still has to be there.
Of course you can plot the voltage variations of a signal in time and show an overall variation in amplitude. When you look at the graph, you are performing all sorts of data manipulation of the information with your brain. That is all full of non-linear processes (decisions and pattern spotting), which are being ignored in your argument.
Either the LF signal is there or it isn't - and it isn't - so, if we hear it (or can see it on a graph) there must have been some non linear process going on. We can't always believe the evidence of our eyes or our ears.

 

[olivermsun]

Look up "amplitude modulation". You will see that the spectrum consists of a carrier and Two sidebands. Also, the waveform is very different in that there is no phase change of the carrier nor a zero crossing of the envelope.

The traditional amplitude modulation leaves some constant (useful for some practical reasons), so the signal has the form
[ A + f(t) ] \cos(\omega_c t).
If the content signal to be encoded is
f(t) = \sin(\omega t) , then the modulated signal works out to be
A \cos(\omega_c t) + \sin(\omega t) \cos(\omega_c t)
where the first term is the carrier, one recognizes the second term as the quantity we have been discussing through this thread: the sum of two closely spaced frequencies which are the "sidebands". You may choose A = 0 as well and "suppress" the carrier (since it contains no information (other than, "there is a signal centered here") thereby saving a considerable amount of energy in transmission.

A quick lookup of "amplitude modulation" returns lots of pictures which show different types of modulated signals for various values of A.

You need a non linearity (diode detector etc.) to get the envelope signal from it.
...
Also, how would this machine measure the Power without using a non linear process? Power would be V², which looks pretty non-linear to me!

Your electronic detector would need nonlinearity to do a Fourier transform (or its equivalent) and decompose the signals into two linear waves in the first place, so I don't understand your point.

 

[olivermsun]

Do I understand correctly that basically our ears do a Fourier transform on the sound? Then why don't they just break the sound down into two sine waves and hear them with a constant tone?

There is a limit to our ears' resolution. If two tones are quite far apart, e.g., your 100 and 152 Hz example, then usually people do hear them as separate tones but sometimes also perceive one or more "interaction tones" or beats. If the tones are very close, however, most people can only perceive the slow beats.

 

[sophiecentaur]

My point was one of those 'what's really there' things. Some views seemed to be that the beat was really there because you can hear it. My view is that the whole of the signal (i.e. the two tones or whatever) is just those two tones and that any beat that you can 'see' or hear will only be there after some non-linear process. No piece of linear electronic gear could be 'aware' of or detect a beat, so I conclude that our senses must be non-linear. And, of course, with our basically logarithmic sensitivity to most inputs, they clearly are.
Perhaps I just find the Maths of this sort of thing so compelling that I just don't feel any need for the subjective approach. I may just have been involved in it for so long. . . .

As for the perception of beats vs tones, I think that we essentially hear an intermod tone as a tone if we would have heard a tone at that frequency. Beats are at sub-sonic frequencies which we are usually aware of as 'vibrations' via our touch senses, rather than our ears. In pre-history, we wouldn't have been exposed to many such beats (there are not many natural sources of cw tones) and the evolution of our hearing system could well have meant that beats confuse us.

 

[lovetruth]

Can anyone conclusively prove that light coming out of prism is sine wave and not any non-harmonic wave.

 

[sophiecentaur]

If there are no higher energy components, how can it be other than a sinusoid? I don't see where you are coming from about this.