What is a complex frequency?

Discussion in 'Physics & Math' started by arfa brane, Mar 4, 2020.

  1. James R Just this guy, you know? Staff Member

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    That's only because part of the wave is usually reflected at the boundary. Energy is conserved, so the total incident energy is shared between the reflected and transmitted portions.

    I don't understand. Which book is this? Got a quote?

    For water waves, the speed depends on the depth of the water and on the wavelength of the waves, as well as the acceleration due to gravity. In other words, water waves are dispersive, moreso in deep water than in shallow water.

    I don't see how this follows from anything that went before.
     
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  3. arfa brane call me arf Valued Senior Member

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    Well, I do. Moreover the connection is more of a relation; there's a relation between an oscillating mass and an inductor with an oscillating current, which is shown by the different equations of motion being similar. Which means, the differential equations have the same form.

    The book in question also extends this relation to deBroglie waves, and gives an example of a potential barrier for electrons. There's also the well-understood, indeed designed, tunneling effect in semiconductors. The space-charge region in a semiconductor diode represents a potential barrier for electrons.

    So, a connection between the gravitational field and the electromagnetic field, is the way a weight oscillates at the end of a string compared to the way a current oscillates in an LRC circuit. I note that a free oscillation in the latter case has the constraint that, if L or C are zero, spontaneous oscillation isn't possible. I think that's interesting just because, an LR or RC circuit only generates an exponential current decay, and, to see an exponential decay in a string pendulum you have to leave it oscillating.
     
    Last edited: Mar 29, 2020
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  5. arfa brane call me arf Valued Senior Member

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    Conservation of energy I think is a way to prove that a wave(form) is continuous at a boundary. Continuity means a differentiable function of , , , some variables, of which there must be at least one.
     
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  7. James R Just this guy, you know? Staff Member

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    arfa brane:

    So you're saying that wave motion is described with the same sort of mathematics, whether we're talking about water waves or electromagnetic waves or gravity waves? Is that the kind of "connection" you're talking about?

    Oscillations are oscillations, so we'd expect similar maths to apply to all kinds of oscillations, wouldn't we? Same for waves.
     
  8. arfa brane call me arf Valued Senior Member

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    Something like that. Except for the way a potential barrier is physically realised and how this differs between for example, electromagnetic and gravity waves.
     
  9. Write4U Valued Senior Member

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    These coupled oscillators may be of interest.



    and sideways (circular?)

     
    Last edited: Mar 30, 2020
  10. arfa brane call me arf Valued Senior Member

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    The Wilberforce pendulum



    Is a coupled system which nicely illustrates the storing of energy in rotational vs extensional spring motion.
    It's tuned so the additional small weights have the 'right' moments of inertia.

    If you can relate one of these to an LRC circuit that would be nice too.
     
    Last edited: Apr 1, 2020
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  11. arfa brane call me arf Valued Senior Member

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    And I just remembered that a magnetic compass is an example of an oscillating system; the needle has mass but is at an equilibrium so it doesn't accelerate due to gravity, it accelerates due the magnetic field around it.

    So that's a direct way to map the acceleration of a mass, to an initial displacement; you see an exponential decay of a sinusoid, and the damping also comes from the magnetic field, not the gravitational field.
    So the time it takes for the free oscillations to decay to zero depends on how strong the compass magnet is.

    Is there a current, or a voltage, i.e. is a magnetic compass an electronic device?
     
    Last edited: Apr 18, 2020
  12. exchemist Valued Senior Member

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    Magnetic compasses have been in use since medieval times.
     
  13. arfa brane call me arf Valued Senior Member

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    Really?

    That's sort of interesting. Sort of.
     
  14. exchemist Valued Senior Member

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    So, if they could be said to be "electronic" in some sense, it would have to be "but not as we know it, Jim", wouldn't it?

    Electrons are involved, though, perhaps unsurprisingly.
     
  15. arfa brane call me arf Valued Senior Member

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    The circuit (for a magnetic compass) has an oscillation of magnetic, not electric, potential. An oscillating magnet does have moving charges, but they're magnetic not electric, i.e. the magnetised length of steel/iron has no net electric charge.
    I'm pretty sure you can still use magnetic potential in some formula for SHM of a rotating magnet, in an external magnetic field.
     
  16. exchemist Valued Senior Member

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    A compass requires only a magnetised pointer mounted on a bearing that allows it to align with the Earth's field.

    There is no circuit.

    The moving charges in a permanent magnet are electric charges, viz. the electrons the material is made from. There is no such thing as magnetic charge - at least, not until such time as magnetic monopoles may be discovered, which they have not been.

    If the bearing is not damped in some way, the pointer will oscillate as it tries to align itself, due to the force created by the lack of alignment of its own field with that of the Earth. Modern compasses are often in an oil bath to damp these oscillation out quickly, so that magnetic North can quickly be determined by the navigator.

    I don't think the oscillation will be SHM, since the restoring force won't be proportional to displacement from equilibrium. I would need to look up the force relation for magnetic fields to check what it is, as a function of angle between the two fields.
     
  17. arfa brane call me arf Valued Senior Member

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    There is so a circuit; it looks like the one you can draw to represent an oscillating mass, it has an input and an output, with stuff in between.
    You confuse the meaning of my use of the word charge, with electric charge. Magnetic charge in my meaning is what can be related to a causal input; a change in the angle between the magnet and an external magnetic field.
    It is SHM, just not eternal. Like I said, the external field damps the free oscillations.
     
  18. exchemist Valued Senior Member

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    OK I've looked this up. The torque on a magnetic moment μ, at an angle φ to a field B is: μ B Sin φ. So it is not true SHM, as the restoring force is not proportional to displacement from the equilibrium position.

    However, as with a pendulum, for small angles where Sin φ ~ φ, it can be treated as approximately SHM.

    I'll leave you to your idiosyncratic use of terms.
     
    Last edited: Apr 19, 2020

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