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I stumbled onto this page

http://mylifeisaverage.com/story/1364811/

and the post states that they were

all making strings and shapes with these sets of 216 really small spherical earth magnets. What did I do? I strung them together and found the string's resonant frequency. It was 15 Hz

so I'm wondering how the poster could have figured this out?

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That is a story, nothing else! Read some more entys of that thread and think about it. –  Georg Mar 5 '11 at 16:27

3 Answers 3

up vote 2 down vote accepted

There's an interesting question in here if you look hard enough.

First of all, there's nothing special about the resonant frequency of something made of little magnets. It might as well be a piece of ordinary string, a metal bar, or whatever. In fact I think the fact that it's made of separate little magnets stuck together would give it a much lower Q factor than, for example, a metal bell, which would make the resonant frequency less clear and harder to measure.

But anyway, let's assume we have some object with a mechanical resonance around 15 Hz. How do we measure this frequency with no other equipment?

As a human, there are basically two ways you can observe something's vibration frequency. If the vibration is slow enough - below about 5 or maybe 10 Hz - you can just count the individual cycles. If I'm wiggling a jump rope at the resonance frequency and count 300 wiggles per minute, then the frequency is 300/(60 s) = 5 Hz.

The other way - which works well between about 50 Hz and 10,000 Hz - is to listen to the pitch of the vibrations and figure out the frequency of that musical pitch. If I listen to a bell and hear the pitch A above middle C, that means the frequency is 440 Hz (A 440). If, like me, you don't have perfect pitch, you'll need some reference pitch to compare it too, such as a piano, but once you figure out the closest note of the musical scale, you know the frequency to within 3%.

The interesting thing in this case is that 15 Hz is right in the middle of that awkward frequency range which is too fast to count, but too low to hear.

So how do you measure a frequency in this awkward range? If you have some simple lab equipment it becomes easy. For example, just shine a light on a photodiode and arrange it so that the edge of the vibrating object gets in the light path and casts a shadow. Then look at the photodiode signal on an oscilloscope and you'll see the vibrations at 15 Hz. (Interestingly, an ordinary TV camera would be a bad choice here because they take about 30 discrete frames a second, so 15 Hz is right around the Nyquist frequency and aliasing would make it impossible to tell if it were 13 Hz or 17 Hz, for example.)

But what if you don't have an oscilloscope, or video camera or anything like that? I think you would still be able to measure the resonance frequency by hand, you'd just have to be inventive. For example, you can try to excite the vibrations using subharmonics. If you give your string of magnets a sudden shove 3 times a second, for example, then your 3 Hz excitation signal has harmonics at 6 Hz, 9 Hz, 12 Hz, 15 Hz..., because it's not sinusoidal. So if you're able to show that you get a strong resonance at 3 Hz, but not at 2.9 Hz or 3.1 Hz, then you know that the resonant frequency is one of those harmonics. If you repeat that process with some different subharmonic (e.g. 5 Hz), then you can quickly narrow down the possibilities for the resonant frequency.

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Loved the explanation (+1) but personally I'm afraid I'd still have a hard time reaching for the > 5 Hz range, manually! –  Gerben Mar 6 '11 at 11:56

216 magnets suggest Neocube; I think such string could be just forced by electromagnet or simply by passing a AC current from a generator. While generator is able to produce arbitrary frequency, it is possible just to try to tune into a resonance and thus obtain the resonance frequency.

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You shake the arrangement of magnets, then let it sit and wiggle. You then count the number of wiggles per minute. Frequency in hertz is then $\frac{{\rm \# of wiggles}}{60 {\rm s}}$.

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Can you count 15 wiggles per second? Oh, I'm sorry, 900 wiggles per minute? I sure can't. –  Keenan Pepper Mar 5 '11 at 17:37
    
There are many ways to measure it: - Using a strobe light. - Recording the sound and analyzing it. - Making the string of magnets close a circuit at a certain point in its oscillation and measuring the frequency with an oscilloscope. - Video, though 15 Hz seems a bit too fast to make an accurate measurement with normal cameras. - ... –  mmc Mar 5 '11 at 18:00

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