### Home > A2C > Chapter 11 > Lesson 11.3.2 > Problem11-150

11-150.

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?

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

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

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

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

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

$P = 20 · 10^{6} = 2 · 10^{7}$

3. What does 0 decibels mean?

The sound ratio is $1$.

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

$100$ times more pressure.