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

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