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Wavepatterns and harmonics

  1. May 22, 2004 #1
    so IN THEORY, there should be an oscillation pattern that yields the hydrogen spectrum ?
  2. jcsd
  3. Jun 5, 2004 #2

    This is an interesting issue...could you please rephrase your question though before I can give you my answer...

    I mean more generally, can you describe what you mean when you say

    Going back to a very basic idea...if you could set up a wave equation the spherical harmonics of which when analyzed with the radial wavefunction should be able to explain fine structure in the hydrogen spectrum (this seems to deviate from your original question but still, the hydrogen spectrum analysis is characterized by fine structure and not by the classical approach which fails to explain orbital degeneracy and fails to account for the experimentally observed spectrum). When you say, "yields the hydrogen spectrum", you probably mean this mathematically:

    Can we get a function to reprsent this oscillation pattern?

    Please correct me if I am wrong...

  4. Jun 5, 2004 #3
    It could be represented by a Fourier sum, right ? ..

    My intent with the thread was to

    first, conclude that the hydrogen spectrum could be produced by a classical electromagnetic wave (i.e. discrete spectrum does not contradict the wave theory of light (might not be obvious to everyone)).

    second, discuss how such waves could be emitted and what sources could produce 'em.

    third, explain my idea on this matter and discuss it.

    I believe my idea is much more basic than this. Think about this:
    A charge is oscillating sinusodial along the y-axis. Sinusodial waves are emitted perpendicular to the oscillation. What do the waves emitted at all other angles look like ? Are they sinusodial ? If not, what do they look like and what kind of spectrum would they produce ?
  5. Jun 5, 2004 #4
    Hello Hydr0matic

    Thanks for rephrasing your original question...interesting idea.

    Usually, if a the graph is viewed from a different angle, you see its projection and obviously not the original thing as it was being produced.

  6. Jun 5, 2004 #5
    That's a Hertz dipole. If you're far enough away (distance>>oscillation amplitude), the radiation is harmonic in all directions. What changes is intensity (max. at the "equator", min. at the "poles").
  7. Jan 3, 2005 #6
    This is basically my point, yes - the angle of emission. A simple harmonic oscillator will emit a sinusodial wave perpendicular to it's direction of oscillation, and the amplitude of the wave is dependant on the angle between the emitted wave and the oscillator.

    BUT, what about the waves not emitted perpendicular ? Are they sinusodial ?
  8. Jan 5, 2005 #7
    They're obviously not sinusodial. Because, at an angle not perpendicular to the direction of oscillation, the relative oscillation is both vertical and horisontal.

    So what kind of spectrum will these non-sinusodial waves produce ?

    What do the waves emitted at different angles have in common ?

    Do anyone else think this sounds interesting ? or should I just shut up ? :smile:
  9. Jan 5, 2005 #8


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    For the radiation emitted by a sinusoidally oscillating electric dipole, see for example Griffiths, Introduction to Electrodynamics, chapter 9. The formula is simplest in spherical coordinates. of course, so let the dipole oscillate along the z-axis with angular frequency [tex]\omega[/tex], with maximum dipole moment [tex]p_0[/tex]:

    [tex] \bold E = -\frac {\mu_0 p_0 \omega^2}{4 \pi} \left(\frac {\sin \theta}{r}\right) \cos [\omega (t - r/c)] \hat \theta [/tex]

    The direction of the electric field is only in the polar direction, which is the direction of longitude lines on a globe. There is no radial or azimuthal component. The field is perpendicular to the direction of propagation (the radial direction) at all points.

    Similarly, the magnetic field is only in the azimuthal direction, which is the direction of latitude lines on a globe. There is no radial or polar component. This field is also perpendicular to the direction of propagation at all points.

    And the oscillation is always sinusoidal in time.
  10. Jan 5, 2005 #9
    Thanx jtbell.. I realize I haven't been that clear in my posts. I'm specifically talking about the radiation emitted by an oscillating electric monopole.

    Again I'm unclear. With "direction of oscillation" I meant the axle along which the monopole is oscillating.

    True. Which is why all waves emitted by the monopole have the same wavelength. BUT, if we were to represent a wave emitted by the monopole with a line - again, one that's not emitted perpendicular - the line would not be sinusodial. I.e. all waves, except for the ones emitted perpendicular, will be "unpure", as Tyger put it.
    They will not produce the single "pure" discrete line in a spectrum that the perfectly sinusodial would.
    So the question is, what would they produce ?
  11. Jan 5, 2005 #10


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    If the charged particle is oscillating "horizontally and vertically" and both are at the same frequencey then it will generate (monochromatic) elliptically polarized radiation at the same frequency and possibly harmonics of the fundamental. This will not resemble the hydrogen spectrum. At extreme amplitudes it might resemble synchrotron radiation.
  12. Jan 5, 2005 #11


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    I would suggest a review of the history of atomic spectra might be useful. What you will find is: classical physics could not explain nor generate the type of motion that would produce discrete spectra. Further, the mechanics of a radiating charge require that the charge lose energy. As a result, Rutherford's atom could not exist, contrary to experiment.

    This vexing problem drove crazy many of the finest minds at the turn of the 20th century. Then Bohr, with a stroke of extraordinary genius, proposed a simple model that opened the door to the quantum theory of atoms -- which quite nicely explains discrete spectra with all of its physical subtleties.

    Reilly Atkinson
  13. Jan 5, 2005 #12
    I've expressed myself vaguely again. My apologies. A monopole oscillating along a straight axle will not generate this elliptically polarized radiation, I believe. Only a circular motion would, correct ? By "horizontally and vertically" I meant the relative movement of the oscillator, viewed from an angle not perpendicular to it's direction of oscillation. (horizontally is not the right word since the movement relative to the non-perpendicular wave is towards/away from - i.e. z-axle).

    An oscillating monopole moving along a straight axle - would it or would it not produce harmonics of the fundamental at any angle except perpendicular and along the axle (0°)?

    Follow up question - Am I right in guessing that the non-perpendicular waves would basically consist of one half a period where the wave is blueshifted, and one half a period where the wave is redshifted ? (i.e. during one half of the period the monopole is moving towards the emitted wave, and the other half it's moving away from it).

    Please, I know I don't exactly come off as a physics professor, but don't insult my intelligence. I'm not finished yet. There's a reason why I'm taking this step by step. Just blurting it out would result in gibberish worthy of a crackpot, since I'm obviously not expressing myself clear enough half of the time. Let me get to the end before you chop my legs off :wink:

    Thanx reilly, but I know my history quite well. What you're saying about classical physics is simply not true - discrete spectra does not contradict the wave theory of light..
    Concerning Rutherford's atom - I agree, it could not exist. But I'm not talking about an electron circulating a proton. I'm simply discussing an oscillating monopole. If what I believe is correct, the most fundamental discrete spectrum is simply a result of the simplest oscillating motion.
  14. Jan 6, 2005 #13


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    I was only trying to help out. I look forward to your "real" question. :-)
  15. Jan 6, 2005 #14
    I know, I'm sorry. I appreciate your help.

    Once we establish what kind of harmonics the monopole radiates, there's only one thing left to explain..

    You suggested that the non-perpendicular waves would produce more than a one line spectrum, correct ? .. Do you have an idea how the spectrum might look, perhaps ?
  16. Jan 7, 2005 #15


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    Hydr0matic -- You are correct that there's nothing in the wave theory of light that precludes discrete spectra -- think for a moment about the actual quantum theory of radiation -- based on Maxwell's equations, which in first order QM perturbation theory is virtually identical to classical E&M.

    The problem is with the motion of the charges, which should be evident from Bohr's and subsequent theories. I assume that by monopole you mean a single charge. If so, then I refer you to any graduate level E&M text, Jackson, Panofsky and Phillips, Landau and Lef****z, or whatever. There you will find first that if a charge oscillates at frequency f, the emitted radiation will have frequency f and only f. Second, an oscillating charge will have a full set of multipoles -- dipole, quadrapole, and so forth -- which determine the angular distribution of radiation. To get discrete spectral lines with f1, f2, and so forth requires charges oscillating at f1, f2 and so on. And there's the rub: what kind of motion will produce discrete spectra? Quantum "motion", which, by fiat, allows discontinuous "motion".

    Your real mission, should you chose to accept it, is to figure out how a classical motion can generate discrete spectra, and how to make the charge complex absorb only certain frequencies. Your problem is with the source, not the radiated fields. And, you will also need to explain Rutherford's expt. with your theory. Good luck.

    Reilly Atkinson

    PS If your monopole is not a single charge, what is it?
  17. Jan 7, 2005 #16
    First of all, thank you thank you thank you!.. for getting this discussion somewhere.. I really appreciate it.

    This is exactly where the misconception lies. Yes! - all radiation will have frequency f, and yes, all waves will have the same wavelength from top to top. BUT, any wave not emitted perpedicular will not be sinusodial. I cannot stress the importance of this fact more. Lightwaves are not limited to sinusodial oscillation! As a result, a wave that clearly appears to have a certain frequency when viewed as a whole, might actually consist mainly of other frequencies.
    An analogy is temperature - we say an object has a certain temperature, but in fact, that temperature might not exist anywhere within that object, i.e. different parts of the object might have different temperatures.

    Have a look at these waveforms:

    The first one is supposed to be sinusodial but it's not quite "pointy" enough. Never mind.
    Take a look at waveforms 2 & 3 - they both have the same frequency and wavelength as the first one. Yet, clearly they are not the same waves. The second one has a mid-phase acceleration to it, and the third one has additional z-oscillation.
    The third type is the one I've been discussing in this thread, emitted by oscillating monopoles.
    This wave illustrates my point about the appearance of a certain frequency, but with other "internal" frequencies. As you can see the troughs of the wave have been shifted to the left creating what appears to be (roughly) two separate parts - one blueshifted and one redshifted.

    To avoid being unclear about too much I'll stop here for now..

    Am I completely clueless in the above explanation, or am I on to something ?
  18. Jan 7, 2005 #17


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    Since you raised the issue, yes, with all due respect, you are clueless about radiation. If you will take the time to study just a bit you'll certainly be forced to change your tune about the relation between particle oscillatory frequencies and radiation frequencies. You are dealing with material that's been examined with extraordinary vigilence for well over a century, and has stood the test of time. The onus is on you to give a clear and compelling argument why most of us are wrong. a good place to start is to explain the wave forms you have drawn -- what are they, how were they derived.

    Reilly Atkinson
  19. Jan 8, 2005 #18

    while you are correct in saying that a perceived frequency may contain other frequencies, you have not demonstrated this with the 3 waveforms on your link.

    you have left out the direction of the wave, which when viewed at right angles, can be seen in its' true form - symmetry. the 3 forms you showed are the same wave viewed at different angles, and the perception of the same wave changes. a donut viewed at 90' is a line, at 45' an oval, and at 0' (or 180') is a circle; but these are all just different perceptions of the same donut. the fourier form is still symmetrical.

  20. Jan 8, 2005 #19
    :wink: Maybe I am, I'll find out soon enough..

    I didn't realize I was saying something that was so outrageous ? Take a look at the quotes I started this thread with. Tyger said any wave that isn't sinusodial will produce harmonics, he even claims it to be an exact answer. If he's wrong, why haven't anyone pointed that out ?
    The fact of the matter is, I'm not saying anything at all that isn't in line with classical EM ..(the physics, not the beliefs).

    They weren't, I drew 'em just to illustrate my point about waves that have the same apparent frequency and wavelength still being very different from each other.

    I realize they are just lines on a surface, but... Try to look beyond the poor representation and focus on what I'm trying to say.

    The waves are all viewed from the same angle, the only thing that changes is the motion of the charge on the left. They are three separate examples of oscillatory motion producing different waves with the same apparent wavelength.

    Let's say you are observing an oscillating monopole right in front of you and you can see it's oscillatory motion (ignore the scale differences). Just standing there watching the oscillator swing up and down along the y-axle, you notice the sinusodial wave hitting you has the same frequency as the oscillating motion of the monopole.
    Now, the monopole starts moving away from you along the z-axle while it's oscillating. Instantly you notice a redshift in the waves hitting you. The monopole then slows down and starts moving towards you again - a blueshift occurs.
    The monopole repeats this motion back and forth along the z-axle and you realize the z-motion obviously has an effect on the radiated waves. An effect, more known as the Doppler effect.
    Now, what would happen if the z-motion of the monopole back and forth would get smaller and smaller, turning into what could be considered as an oscillatory motion along the z-axle ? Would the Doppler effect suddenly disappear ? .. Would the motion along the z-axle suddenly stop having an effect on the waves you see ? ..

    If you only answer one question in your next reply, let it be this:
    Are all waves radiated by an oscillating charge sinusodial ?

    Then read Tyger's quote again ...
  21. Jan 8, 2005 #20
    This was not my intent with the illustration. The waveforms are completely independent of each other, and they are all viewed from the same angle - perpendicular to the direction of the waves. The only thing that changes is the oscillatory motion of the charge on the left.

    Thanx T.Roc... Would you also confirm my suspicion that the non-perpendicular waves radiated by an oscillating monopole, contains such other frequencies ? ... (other than the percieved frequency f of the monopole).
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