Sound Intensity & Decibel Reference Cheat Sheet

Key Facts

• Sound intensity is power per unit area, given by $I = \frac{P}{A}$, where $I$ is in $\text{W/m}^2$.
• For a point source spreading uniformly, intensity follows $I = \frac{P}{4\pi r^2}$.
• The decibel level is $\beta = 10\log_{10}\left(\frac{I}{I_0}\right)$, where $I_0 = 1.0 \times 10^{-12}\,\text{W/m}^2$.
• Intensity can be found from decibel level using $I = I_0 10^{\frac{\beta}{10}}$.
• A change of $10\,\text{dB}$ means the intensity changes by a factor of $10$.
• A change of $3\,\text{dB}$ is approximately a factor of $2$ in intensity.
• Doubling the distance from a point source reduces intensity to $\frac{1}{4}$ of its original value.
• The difference between two sound levels is $\Delta \beta = 10\log_{10}\left(\frac{I_2}{I_1}\right)$.

Vocabulary

Sound intensity

Sound intensity is the sound power passing through each square meter of area, measured in $\text{W/m}^2$.

Decibel

A decibel is a logarithmic unit used to compare a sound intensity to a reference intensity.

Reference intensity

The reference intensity for sound in air is $I_0 = 1.0 \times 10^{-12}\,\text{W/m}^2$, about the threshold of human hearing.

Inverse square law

The inverse square law states that intensity from a point source decreases as $\frac{1}{r^2}$ as distance $r$ increases.

Logarithm

A logarithm gives the exponent needed to produce a number, such as $\log_{10}(1000) = 3$.

Threshold of hearing

The threshold of hearing is the quietest typical sound a human can detect, usually taken as $0\,\text{dB}$.