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All I Know About Decibel (dB) - Part 2

As Part 1 introduces, we get decibel using the formula

l=10×logp1p2(dB) l = 10 \times log \frac{p_1}{p_2} (dB)

I'd blame my poor English ability that I didn't realise what the name decibel really meant for quite a few years. It's called deci-bel so apparently there's a Bel first.


The bel (B) and the smaller decibel (dB) are units of measurement of sound pressure level (SPL) invented by Bell Labs and named after him

from: Wikipedia

That's him! As stated, using deci-, people can make bel smaller, and meanwhile we have to add the 10×10 \times in the formula, to make bel become decibel.

You might notice that when talking about voltage and current, the formula becomes

20×logp1p2(dB) 20 \times log \frac{p_1}{p_2} (dB)

So why 20 here? I was very confused. I asked around and got this answer: For measuring something like a magnitude, we use 20×20 \times , otherwise for the power stuffs, use 10×10 \times ... Okay then it's time to test my English again: what kind of thing is a magnitude? And what is not? I reckon it's a correct but not so good answer.

Finally I met a guy, he took out a piece of paper and wrote some high school maths on it:

P=U×I=U×(U/R)=U2/R P=U \times I=U \times (U/R) = U^2 / R

Yeah that's Ohm's Law, I get it. Then if PrP_r and UrU_r are the references and UU is the voltage we are measuring, from the original 10×10 \times formula we have:

10×log(P/Pr) 10 \times log (P / P_r)
=10×log((U2/R)/(Ur2/R)) = 10 \times log ((U^2/R)/(U_r^2/R))
=10×log(U/Ur)2 = 10 \times log (U/U_r)^2
=2×10×log(U/Ur)=20×log(U/Ur) = 2 \times 10 \times log (U/U_r) = 20 \times log (U/U_r)

That's how 20×20 \times comes up. Same process for the current (Use P=I2×RP=I^2 \times R ). Maths can be scary, but useful.

from OZLab

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