Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

EM waves are all sinusoidal?

  1. May 30, 2015 #1
    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?
  2. jcsd
  3. May 30, 2015 #2


    User Avatar
    Science Advisor
    Homework Helper

    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.
    Why not?
  4. May 30, 2015 #3


    User Avatar
    2016 Award

    Staff: Mentor

    Right. Every shape is possible, but sinusoidal waves are the easiest case so you frequently see them discussed in text books.
  5. May 30, 2015 #4


    User Avatar

    Staff: Mentor

    Also, you can construct any other shape of wave by adding sinusoids together (Fourier analysis).
  6. May 30, 2015 #5
    So accelerating positive charges produce EM waves? Textbooks I've read mention only electrons.
  7. May 30, 2015 #6


    User Avatar

    Yes. They only mention electrons because they are available in metals.
  8. May 30, 2015 #7

    Vanadium 50

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

    Note that if only pure sinosoids were allowed, radio would not work.
  9. May 31, 2015 #8


    User Avatar
    Gold Member

    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!)
  10. Jun 1, 2015 #9


    User Avatar
    Science Advisor
    2016 Award

    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.
  11. Jun 1, 2015 #10

    Andy Resnick

    User Avatar
    Science Advisor
    Education Advisor
    2016 Award

    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.
  12. Jun 2, 2015 #11
    Temporal part has no more need to be sinusoidal than the spatial part.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: EM waves are all sinusoidal?
  1. EM Waves and EM Pulses (Replies: 4)

  2. Em waves (Replies: 6)

  3. EM waves (Replies: 4)