The human ear responds [[Logarithms|logarithmically]] to increases in both Volume and [[Frequency]]. The 'Volume' is referred to as the dynamic [[Codomain|range]] and frequency refers to "pitch". $\huge P \approx kA^{2} $ An increase in power of a audio signal from $P_{0}$ to $P_{1}$ results in the ratio $\frac{P_{1}}{P_{0}}$ which can be encoded as $10^{x}$, where $x$ is measured in [[Bel|bels]]. $\huge x \,\pu{ b } = \log_{10} \frac{P_{1}}{P_{0}} $ Or, $\huge \frac{x}{10} \pu{ db } = 10\log_{10} \frac{P_{1}}{P_{0}} $ $\huge \begin{align} \frac{P_{1}}{P_{0}} &= \frac{kA_{1}^{2}}{kA_{0}^{2}} \\ &= \left( \frac{A_{1}}{A_{0}} \right)^{2} \\ x \pu{ db }&= 10 \log_{10} \left( \frac{A_{1}}{A_{0}} \right)^{2}\\ x \pu{ db }&= 20 \log_{10} \frac{A_{1}}{A_{0}} \end{align} $ >[!note] Rule of Thumb >A coincidence, an ampltiude ratio of 2 is approximately an increase of 6 [[Bel|Decibels]].