Logarithms are used to measure the “loudness” of sound. Decibels (dB) are logarithmic units used to descrbe a ratio of two levels of intensity or pressure. The difference between two levels of sound pressure (P₁ and P₂) is defined as _{$\large{10 \operatorname { log } ( \frac { P _ { 1 } } { P _ { 2 } } )}$}dB. Usually, when decibels are used to describe just one sound, it is assumed that that sound is being compared to a reference level of 20 micropascals.

1. How many decibels correspond to doubling the pressure of a sound?

   Answer (a):

   $10 \operatorname{log}\left(2\right) ≈ 3.0$

2. What is the sound pressure of a sound described as 60 dB?

   Hint (b):

   $10\cdot \text{log}\left(\frac{P}{20}\right)=60$

   $\text{log}\left(\frac{P}{20}\right)=6$

   $10^6=\frac{P}{20}$

   Answer (b):

   $P = 20 · 10^{6} = 2 · 10^{7}$

3. What does 0 decibels mean?

   Answer (c):

   The sound ratio is $1$.

4. How many times more pressure is in a sound of $40 \text{ dB}$ than of $20 \text{ dB}$?

   Answer (d):

   $100$ times more pressure.