We know that light is an electromagnetic wave which follows the wave equation. We write the wave as $$f(x, t) = A\sin(kx - \omega t + \phi ),$$ which is sinusoidal. So my question is why can't it be a square wave or any other wave form which follows the wave equation?
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Emilio Pisanty
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Dark Vader
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2Actually, any function of the form $f(x\pm ct)$ is a solution to the wave equation. – Rumplestillskin Jul 06 '17 at 12:57
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Well - It can be a square wave, as a square wave can be considered to be an infinite sum of sin waves - see Fourier series for more information. We just use the sin representation as its a nice basis to work in, solutions fall out.
A good answer to the question 'why sin waves' might be 'because electromagnetism obeys the wave equation'. Why this is the case, is more complicated.
Tom
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Second paragraph. No, that would be a poor answer. The form of the wave is not demanded by the wave equation. – ProfRob Jul 06 '17 at 15:01
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Who says that it can't? Monochromatic light is sinusoidal in time (but it can be non-sinusoidal in space, like e.g. Bessel waves in a cylindrical waveguide, or inverse-square decays for spherical waves), simply because that's how we define monochromaticity, but not all light is monochromatic. Add monochromatic beams together, each with a different colour, and you'll get non-sinusoidal waveforms; add enough of them and you'll be able to reproduce any arbitrary temporal waveform.
Light waveforms come in all shapes and sizes. In introductory texts we focus on sinusoidal solutions because they are easy to analyze, and because they are useful tools to study more complicated situations, but that is all that's going on.
Emilio Pisanty
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