# ID = 120 # All I Know About Decibel (dB) - Part 2

As Part 1 introduces, we get decibel using the formula

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

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 $$10 \times$$ in the formula, to make bel become decibel.

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

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

So why 20 here? I was very confused. I asked around and got this answer: For measuring something like a magnitude, we use $$20 \times$$, otherwise for the power stuffs, use $$10 \times$$... 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:

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

Yeah that's Ohm's Law, I get it. Then if $$P_r$$ and $$U_r$$ are the references and $$U$$ is the voltage we are measuring, from the original $$10 \times$$ formula we have:

$10 \times log (P / P_r)$

$= 10 \times log ((U^2/R)/(U_r^2/R))$

$= 10 \times log (U/U_r)^2$

$= 2 \times 10 \times log (U/U_r) = 20 \times log (U/U_r)$

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