### Home > A2C > Chapter Ch11 > Lesson 11.3.2 > Problem11-150

11-150.
1. 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 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. Homework Help ✎

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

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

3. What does 0 decibels mean?

4. How many times more pressure is in a sound of 40 dB than of 20 dB?

10 log(2) ≈ 3.0

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

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

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

P = 20 · 106 = 2 · 107

The sound ratio is 1.

100 times more pressure.