The PC fan tachometer gives out 2 pulses per rotation. It doesn't work with all multimeters, as I've tried it a couple of times on cheaper equipment and got nonsense results (like a fan spinning at 50.000RPM or so
) but I have created custom measuring circuits that would count the number of pulses per second or time the interval between two rising edges of the pulse, and it worked...
EDIT: You should always put the GND wire on the GND port, even if it works without it, for more precise measurement. Since the voltage is a difference of electrical potential, as long as the GND lead is on something *constant*, for the purposes of frequency measurement, it might not make a difference, but the electrical potential of air, or your hand, might not be constant, so holding the wire or leaving it hanging around might easily skew the results.
Also, remember when calculating the speed that the motherboard can actually make considerable mistakes when measuring the RPM. This has to do with the way most of those things work. They count the total number of pulses per second and then calculate the RPM. This means that if the count is 'off' by just 1 (for the purposes of this example, let's say it's 1 less) on a 3000RPM fan, that'll equate to a calculated RPM of 2790RPM. Depending on the update speed of the measurement, this "step" may be anything between 30RPM and 300RPM (faster updating measurement is less precise). Your instrument, on the other hand, measures the frequency, down to the decimal, so it's indeed a lot more precise since the PC has no means of measuring 'half a pulse'.
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