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Resonance and harmonics

  1. May 24, 2012 #1
    If I have a oscillator that has an infinite number of harmonics, what decides which harmonics are excited? Is it whatever frequency inputs I drive into the system, and the system damps out frequencies that don't match the harmonics or is it possible that driving at only one harmonic frequency, every harmonic would be excited in the system? If this is the case how do the intensities distribute?
  2. jcsd
  3. May 24, 2012 #2
    Are you saying that you have an electrical oscillator that is outputting a signal that contains infinite harmonics, or are you describing something like a tuning fork and asserting that it has an infinite number of resonant frequencies?
  4. May 24, 2012 #3
    something like an electrical oscillator..let me refine my question a little better. If I drive my electrical oscillator at a certain frequency continuously, my feeling is the output would reflect only that frequency and none of the harmonics. On the other hand, if I drove the oscillator at a certain frequency for a finite amount of time, and then looked at the system later on will there be an infinite number of harmonics present or will the harmonics present be band-limited somehow? I know that in a stove IR radiation might be set up as a standing wave, but if all the harmonics were present then my stove would contain uv, and x-rays, and gamma-rays, and that does not happen. I am trying to reconcile the frequency limit in the stove vs. the seeming lack of a frequency limit on say a string fixed at two ends.
  5. May 24, 2012 #4
    Forgive me but how do you drive an electrical oscillator?
  6. May 24, 2012 #5
    write the second order diff eq for an RLC circuit set it equal to a forcing function, the output will be the convolution of the RLC impulse response with the forcing function, I am looking at oscillators that have an infinite number of modes available to them, perhaps I am using the wrong terminology. I am not looking at systems with a single resonance mode available to them.
  7. May 24, 2012 #6
    OK, but that is not an electrical oscillator.

    You can drive an mechanical oscillator, but with an electrical one, you set up the circuit, switch on and it either oscillates or it doesn't.

    Please be more precise in your question.
  8. May 24, 2012 #7


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    1/√(LC) defines the single frequency that a simple LC circuit will resonate at. If you include some non linearity in the circuit then you can obtain resonances with harmonics of the fundamental, I reckon.
  9. May 24, 2012 #8


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    You are forgetting that simple mathematical models are not the same as reality. For example when the wavelength of the vibrations of the string is the same size as the diameter of the string, the model you learned about in "dynamics 101" doesn't make any sense.

    It's easy to make an electrical oscillator that produces a square wave, or an approximate triangle (sawtooth) wave, both of which contain large numbers of harmonics. There are lots of practical applications of this.

    Nonlinear mechanical systems can also have a wide variety of behavours, but often they are designed to suppress the effects rather than "enhance" them.
  10. May 24, 2012 #9
    What you are asking about is actually a famous failure of classical physics that had a prominent role in the development of quantum mechanics. It was known as the "ultraviolet catastrophe" around the turn of the century. According to classical thermodynamics and electromagnetics there should be, as you suggested, an infinite number of standing wave frequencies in a black body, each with a certain portion of the total energy. The total predicted energy was infinite (look up Rayleigh-Jeans law).

    The only place I have seen this come up in the electronics field is when we talk about thermal noise of -174dBm/Hz. On the surface this seems to imply that every circuit we build has an infinite amount of noise power if we take the frequency up to infinity. In reality, this -174dbm/Hz comes from classical thermodynamics and, thus, is only valid below ultraviolet. And, thankfully, we do not need electronics to function at ultraviolet frequencies.
    Last edited: May 24, 2012
  11. May 25, 2012 #10


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    In a mechanical system, the harmonics arise because of alternatives modes of oscillation. The fundamental frequency of a string fixed at the ends is with the string as one half wavelength: the only static points are the endpoints. For the first harmonic, the string is one wavelength; the centre is now an additional fixed point.
    To get harmonics from electrical circuits you will need extra modes of oscillation. I've no idea whether that is/can be done. But you can certainly produce harmonics by post-processing the signal nonlinearly, e.g. put it through a rectifier.
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