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10-79.

Logarithms are used to measure the “loudness” of sound. Decibels (dB) are logarithmic units used to describe a ratio of two levels of intensity or pressure. The difference between two levels of sound pressure ($P_{1}$ and $P_{2}$) is defined as $10\log(\frac{P_1}{P_2})$ 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 (a measure of pressure). Homework Help ✎

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

$10 \text{log}\left(2\right) ≈ 3.0$

2. What is the sound pressure of a noise 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 $40$ dB than of $20$ dB?

$100$ times more pressure.