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In uk.d-i-y, Dave Plowman wrote:
Well, regardless of where you start the scale, the bel must be a
'quantity' based on something as any unit is.
Actually no - it's a "dimensionless" unit, 'cuz it expresses the
ratio of one measurement [in this case of a sound level] to another
measurement of the same thing. So the 'base of the unit' as you
put is divided away to nuttin'. And hence the insistence of the
pedants on saying "you can't give a value in decibels without
also giving the reference value"; they're right in an anal sort of
way, but for common level measurements there's a widely accepted
reference level - for audible sound pressure 0dB is "person with
good hearing (barely) can't hear it [but if it's made a bit louder
they will]; for audio levels it's 0.775V into 600 ohms if I recall
correctly. To express a wide range of ratios with smaller numbers,
we then take the logarithm of the ratio, so that a difference in
level of 1000 times is 3 bels (1000 being 10*10*10 - three tens),
a difference in level of one-hundredth is -2 bels (1/100 being
1/(10*10) - two tens on the bottom). And in a final twist to
confuse the unwary (maybe for marketing reasons? gawd knows) we
use the decibel, tenth-of-a-bel, for common use; so a ratio of
100 gets called 20dB, a ratio of a million is 60dB, and a doubling
is just about 3dB, since the base-10 log of 2 is about 0.3010 from
memory (you can tell I went to school when log tables were still
standard issue - but only just!).
It's as if we measured speeds as a ratio to some Standard, say a
British Standard Walking Speed of 4mph. Then a speed of 30mph would
get called "7.5", a speed of 1mph would be called "0.25", and so on.
If the Metrication Council then demanded we recalibrate the
British Standard Walking Speed to be expressed as 6.437376 km/h,
the 30mph = 48.28032 kp/h would still be called "7.5" (wot with
48.280832 being 7.5 times bigger'n 6.437376). The underlying
arbirtrary unit has been divided out, leaving the "dimensionless"
ratio.
HTH, Stefek
Almost correct - I think? Except 0dB in audio is actually 0dBm which equates
to 1mW into a resistive load, by convention accepted as 600R unless
otherwise stated. 1mW into 600R is almost exactly 775mV.
--
Woody