So then there_ is_ a 100Hz component in the resulting magnetic field.
This was what I had expected.
Did I not phrase my original question properly?
I point out again, the coil is bifilar. IOW the opposing 200Hz and
300Hz currents are in adjacent windings.If I held a pickup coil a few inches away, connected to a CRO, what would the waveform look like, and what would a spectrum analysis show?
What Bill describes above?
Ken Morrow
says that the idea was around from around 1912. I came up with it for myself in 1963 or 1964, and - unsurprisingly - the Wikipedia dates for modern discussions of the approach start with "The Feynman Lectures on Physics" in 1964.
Harry Messel and I were just plugged into the same zeitgeist.
the electric fields of moving charges. I was never taught that - Wheeler's book came out a bit after the time I worked it out for myself as an underg raduate, but when I talked about my insight with other people, it seemed th at the idea was well known, but not helpful enough to get talked about in u ndergraduate courses.
Purcell does the Lorentz contraction thing in his Berkeley series E&M text. (1965..
Very nice, but I think it might cause more confusion in undergrads.
george H.
No. None.
Because you hadn't thought about what was going on.
So each separate coil is grounded at the not-driven end. That wasn't obvious in the way you posted your original question.
It doesn't make much difference to my point. The magnetic field inside the bifilar pair of coils will reflect the influence of both currents, and the relevant trigonometrical identity
means that it will still look like a 500Hz waveform 100% modulated at 100Hz.
You'd have got the same effect (and wasted less current) by driving a single coil between the two sources.
The spectrum analyser will show the the 300Hz and the 200Hz components, and nothing else - 100% modulation completely suppresses the centre frequency.
It's been in the upper-level undergraduate physics track since at least the 1940s. I have a copy of the first edition of Stratton's "Electromagnetic Theory", published in 1941, and it's in there. Being a chemist, you probably didn't take the upper-level class.
Cheers
Phil Hobbs
No, there isn't. If you put a Hall sensor in the field, and look at its output on a baseband spectrum analyzer (or a sound card plus Daqarta), you'll see two peaks, neither of which is at 100 Hz.
If you rectify the Hall sensor's output, you'll get 100 Hz, all right.
Your confusion is between _beats_ and _frequency components_. If you've ever tuned a guitar, you know that it's the beats you listen to, but they're at a frequency of only a few hertz, which is far below any frequency component that you can hear.
Cheers
Phil Hobbs
Difference frequencies are plainly audble, because we can sense intervals of silence. I guess that's equivalent to observing two mixed sines over a short time window, or rectification, or something.
Worse, having got my secondary schooling in Tasmania, I got stuck into the non-calculus stream of first year physics in Victoria, and got so bored wit h it that I didn't take second year physics.
I rather regretted it when I found out that the second year physics thermod ynamics was a lot better taught than the second year chemistry thermodynami cs, but since then I've found that text-books work a lot better than lectur ers in telling me what I need to know. None of the - limited number - of ph ysics texts that I've ever found it useful to consult has pushed the relati vistic explanation for magnetism, which strikes me as odd, but then again a lot of physics lecturers don't seem to be all that interested in consilien ce.
a
e non-calculus stream of first year physics in Victoria, and got so bored w ith it that I didn't take second year physics.
odynamics was a lot better taught than the second year chemistry thermodyna mics, but since then I've found that text-books work a lot better than lect urers in telling me what I need to know. None of the - limited number - of physics texts that I've ever found it useful to consult has pushed the rela tivistic explanation for magnetism, which strikes me as odd, but then again a lot of physics lecturers don't seem to be all that interested in consili ence.
The Berkeley Series on physics has some nice texts. Besides Purcell, I liked Reif on Thermal physics... I called it "little Reif"
George H.
** Too true.
Most I came across at Sydney Uni lacked a clear grasp of the topics they were attempting to teach undergrads. I recall a lot of messy math written on blackboards in white chalk and regular use of "fudge factors" when the detail became too hard to handle.
... Phil
I think I see what you mean. The two differing frequencies are in the circuit, but the beat occurs only in the surrounding medium.
Ken Morrow
** So called "beat frequencies" will be evident in any medium where the two frequencies are simultaneously present - including a piece of wire.
If the medium can carry or pass one frequency without the generation of any harmonics, then it can also pass two or more with the same result.
.... Phil
It's got nothing to do with the medium, it's just high school math. If you use your favourite math program to plot
y=sin(x) + sin(1.01 x) over a few hundred cycles, you'll see what we're talking about. Big strong beats, but no component at the beat frequency.
Cheers
Phil Hobbs
--- The "beat" occurring because of the interaction of two signals propagating in a linear medium will be the because of the generation of minima and maxima due to simple algebraic addition and subtraction of the signal amplitudes in time, since no heterodynes will be generated.
Since our ear is a non-linear detector, it's [almost] mandatory that signals of different frequencies entering an ear at the same time mix, and produce heterodynes.
I'll perform an experiment some time tomorrow using two single-tone sources feeding separate loudspeakers, with the loudspeakers aimed at a single ear to see/hear what happens.
I'll use something like 300Hz and 700Hz to see if I can get what should be a clearly discernible 1000Hz at the high end, and I'll post what I find. John Fields
no, the beat frequency is an illusion, you'd need to use a envelope detector to get a real 100 hz output.
I found an online simulator:
spectrum analyser will show 200Hz and 300Hz only.
** That does not accord with observation.
Mid frequency tones from a sine wave generator played through a high quality loudspeaker ( ie the Quad electrostatic) sound quite pure and the addition of harmonics as small as 0.1% by voltage (-60dB or 1ppm by power) can be detected by most listeners.
Part of the explanation is the ear has a great many detectors, each operating in a small frequency band. Sure, they do not respond to amplitude in a perfectly linear fashion but neither do they generate audible harmonics or sum and difference products.
** It's a poor scientist who experiments on himself ...** You might like to do a little Google research before embarking on that voyage of discovery ....
.... Phil
The general explanation seems to be that the ear bones in front of the cochlea "RTA" are quite non-linear at high audio levels, generating harmonic and intermodulation distortion.
This would also explain why you can simulate big pipes on a small pipe organ, by playing two pipes simultaneously, with a frequency difference that would have been created by a big pipe.
Apparently the ear bone nonlinearity performs some kind rectification (envelope detection) on the combined beat waveform from the two smaller pipes..
** With SPLs over 110dB, harmonics are generated in the ear canal and other ear parts on the way to the "detectors". But at any comfortable sound level, human hearing is pretty much IM free.
** That is famous psycho acoustic phenomenon of human hearing that is not particularly SPL dependant. When the harmonic structure of a low tone is present, the low tone is perceived to exist by most listeners.
Been exploited by pipe organists for centuries...
.... Phil
Barbershop quartets, not quite so long.
Mark L. Fergerson
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