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Does non-sinusoidal electric/magnetic fields generate EM waves

  1. Mar 10, 2014 #1
    why all EM waves are sinusoidal ?
    or this is not true at all, i.e., EM waves of other waveforms do exist ?

    the above 2 questions are among the most vague in classical EM theory, of which i studied many topics in collage as an electrical engineering student, and i liked the subject so i kept reading about it in text books and over the internet, but unfortunately i still cannot find clear and convincing answers to them, iam not seeking a PURE mathematical answer, since what iam trying to understand is the logical link between pure mathematical equations and what really happens in the physical world.

    lets take the following example:
    if the excitation voltage applied to an antenna was of square waveform rather than sinusoidal, would this generate EM waves that can be detected by another antenna and then converted back to the original voltage waveform across some load connected to the receiving antenna ?
    and, most importantly; WHY ?
    Last edited: Mar 10, 2014
  2. jcsd
  3. Mar 10, 2014 #2


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    EM waves certainly need not be sinusoidal. In vacuum any superposition of Fourier modes is a valid EM wave e.g. localized Gaussian wave-packets.
  4. Mar 10, 2014 #3


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    They're not.

    Most textbooks focus on sinusoidal waves, at least at the introductory level, because:

    • They're easy to generate, using e.g. a resonant LC circuit.
    • They're easy to analyze mathematically.
    • One can construct or analyze any shape wave as a superposition (sum) of sinusoidal ones, using the methods of Fourier analysis.


    Maxwell's equations are linear differential equations. The sum of any two solutions is itself a solution.
  5. Mar 10, 2014 #4

    Simon Bridge

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    Welcome to PF;
    Square waves can, in principle, be transmitted as described - but in practice the wave interacts with "stuff" en route. What with diffraction, attenuation, and dispersion, the received wave is unlikely to be very square.

    You will be aware that a changing electric field gets you a magnetic field, and that a changing magnetic field gets you an electric field?

    You can set this up to be self-sustaining if you vary the E field in such a way that the resulting varying B field will produce the original varying E field. The shape that does that is a sine wave.

    Why is it a sine wave - basically because "thems the rules". That is just how E and B fields are related to each other. (There's a deeper physics underlying the wave-model you are using.)

    OTOH: you can construct all kinds of waves and pulses from sine waves so the overall wave form need not look anything like a sine wave. So: while not all EM waves are sinusoidal, sine waves are special. Which is why fourier analysis is so useful.

    [edit] wow - between the three of us we seem to have covered the bases.
    @fandi.bataineh: any of this useful?
  6. Mar 10, 2014 #5


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  7. Mar 11, 2014 #6
    @Simon Bridge - yes all replies were useful to me, thank you all

    but i still wonder about something; in the field of wireless communications (analog and digital); the information is always carried by a sinusoidal wave (called the carrier, and MUST be sinusoidal) by means of modulation (in analog communications) or keying (in digital communications), so why this is done?

    whereas in wired -digital- communications; pulses are directly sent over cables without being loaded to any sinusoidal carrier wave (the most common example is ethernet technology), so what makes it possible -or effecient- to send pulses over wires but not over wireless channels?
  8. Mar 11, 2014 #7

    Simon Bridge

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    Historically wireless transmission was by pulses too - messages sent by morse code on, basically, short bursts of static (by todays standards). It didnt last that long. iirc the Titanic sent it's famous mayday using a spark-gap transmitter that basically did this: the areal went the length of the ship and the EMF could kill seagulls.

    But imagine lots of these operating close together: all the signals would tend to drown each other out and there were other problems due to having a combination of fundamentals to make the pulse - the pulse that arrives tends not to be much like the one that was sent. Anyway, you'd never get it past Health and Safety.

    When the technology got better, everyone started sending tones that the morse key switched on and off.

    If you look at waves in nature - they tend to try to be sine waves. When you displace a string at a point, it initially makes a triangle shape. Release it and that does not persist - it can for a while if the setup is very careful to avoid losses (sound, heat, drag, etc) but, normally, after a few oscillations, it's a sine wave - usually at the fundamental frequency. This is the self-sustaining shape - it lasts lots longer for the same energy input.

    Using a pure harmonic as a carrier wave allows the receiver to be tuned to the signal that you want. That's important in crowded airwaves. You also get a longer range and sine wave are easier and cheaper to make than other kinds of wave.

    Hopefully you can see that a lot of the concerns are not so important down a wire. The signals down wire are changes in electric field - the magnetic field tends not to be used so much and the charges in the wire are used to sustain the signal. Even so - wire signals often need to be "buffered" every so often so the pulses keep something like their shape - either that or the wire is kept very short. OTOH: see how computer data networks work.

    It's a big subject. This description is by no means complete, but it should give you an idea.

    When you start out learning about this stuff, you deal a lot with pure sine waves, as the others said, because the math is easy. As you advance you start to deal more with other kinds of signal - and different strategies to get information from A to Z intact.
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