Do All EM Waves Have a Sinusoidal Shape?

[rmberwin]

I understand that sinusoidal EM waves result from charged particles in harmonic motion, e.g., up and down an antenna. But what if the charge is undergoing some more complicated periodic motion? Wouldn't the EM waves be non-sinusoidal? I saw in a textbook a hypothetical EM wave with infinite wave length, i.e., the E and B fields were constant.

Also, why don't accelerating positive charges produce EM waves?

 

[blue_leaf77]

To the best of my knowledge, sinusoid is closely related to monochromaticity. EM wave whose temporal profile is perfectly sinusoidal is said to be monochromatic, i.e. contain only a single frequency,. If not sinusoidal, relying on the Fourier transformation, such temporal profile may be expanded into continuous linear combination of infinitely many sinusoidal waves of varying frequencies, in that case we say the wave to be polychromatic.

Also, why don't accelerating positive charges produce EM waves?

Why not?

 

[mfb]

To the best of my knowledge, sinusoid is closely related to monochromaticity. EM wave whose temporal profile is perfectly sinusoidal is said to be monochromatic, i.e. contain only a single frequency,. If not sinusoidal, relying on the Fourier transformation, such temporal profile may be expanded into continuous linear combination of infinitely many sinusoidal waves of varying frequencies, in that case we say the wave to be polychromatic.

Right. Every shape is possible, but sinusoidal waves are the easiest case so you frequently see them discussed in textbooks.

 

[jtbell]

Also, you can construct any other shape of wave by adding sinusoids together (Fourier analysis).

 

[rmberwin]

So accelerating positive charges produce EM waves? Textbooks I've read mention only electrons.

 

[Frabjous]

Yes. They only mention electrons because they are available in metals.

 

[Vanadium 50]

Note that if only pure sinosoids were allowed, radio would not work.

 

[tech99]

I understand that sinusoidal EM waves result from charged particles in harmonic motion, e.g., up and down an antenna. But what if the charge is undergoing some more complicated periodic motion? Wouldn't the EM waves be non-sinusoidal? I saw in a textbook a hypothetical EM wave with infinite wave length, i.e., the E and B fields were constant.

Also, why don't accelerating positive charges produce EM waves?

Any charged particle which is given an acceleration can radiate, but they are mostly heavy so it does not work very well. (Electromagnetic Vibrations and Waves by Bekerfi and Barrett, page 265 discusses proton radiation). If the wave is non sinusoidal, the various harmonics of which it is composed could, in principle, be radiated, preserving the wave shape. It is usually said that a zero frequency signal cannot radiate, so I am interested that you have seen a reference. Usually we say that if a wave shape has a DC component then this cannot be radiated. It is like placing a capacitor in the circuit. (As a boy, when FM broadcasting started, I remember being bothered that a frequency modulated signal was non sinusoidal and could not therefore be radiated!)

 

[vanhees71]

Note that if only pure sinosoids were allowed, radio would not work.

Not only that! There are no purely sinusoidal (monochromatic) waves in nature, because you'd need an infinite amount of energy to produce them. They are formal solutions of the Maxwell equations used to build up the physical waves of finite energy content ("wave packets") by Fourier series and Fourier integrals. I'd rather call them "field modes" then "electromagnetic waves" to make this very clear. The notion "electromagnetic wave" I'd reserve for electromagnetic wave fields that really exist in nature.

 

[Andy Resnick]

I understand that sinusoidal EM waves result from charged particles in harmonic motion, e.g., up and down an antenna. But what if the charge is undergoing some more complicated periodic motion? Wouldn't the EM waves be non-sinusoidal? I saw in a textbook a hypothetical EM wave with infinite wave length, i.e., the E and B fields were constant.

Also, why don't accelerating positive charges produce EM waves?

There are two independent interpretations of "sinusoidal EM waves": one is spatial [for example, sin(kz)], and the other temporal [for example, sin(ωt)]. AFAIK, the temporal part is always sinusoid (standard disclaimer of monochromatic applies), but the spatial part does not have to be sinusoidal and can be a wide variety of other functions: Bessel functions, Gaussian functions, decaying exponential, etc. etc.

 

[Khashishi]

Temporal part has no more need to be sinusoidal than the spatial part.