Physics » Sound and the Physics of Hearing » Sound Intensity and Sound Level

# Summarizing Sound Intensity and Sound Level

## Summary

• Intensity is the same for a sound wave as was defined for all waves; it is

$$I=\cfrac{P}{A},$$

where $$P$$ is the power crossing area $$A$$. The SI unit for $$I$$ is watts per meter squared. The intensity of a sound wave is also related to the pressure amplitude $$\Delta p$$

$$I=\cfrac{{(\Delta p)}^{2}}{2{\text{ρv}}_{w}},$$

where $$\rho$$ is the density of the medium in which the sound wave travels and $${v}_{w}$$ is the speed of sound in the medium.

• Sound intensity level in units of decibels (dB) is

$$\beta \phantom{\rule{0.25em}{0ex}}(\text{dB})=\text{10}\phantom{\rule{0.25em}{0ex}}{\text{log}}_{\text{10}}(\cfrac{I}{{I}_{0}}),$$

where $${I}_{0}={10}^{–12}\phantom{\rule{0.25em}{0ex}}W/{\text{m}}^{2}$$ is the threshold intensity of hearing.

## Glossary

### intensity

the power per unit area carried by a wave

### sound intensity level

a unitless quantity telling you the level of the sound relative to a fixed standard

### sound pressure level

the ratio of the pressure amplitude to a reference pressure