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