Sound Intensity - Acoustic Intensity

Acoustic Intensity

The intensity is the product of the sound pressure and the particle velocity

\vec{I} = p \vec{v}

Notice that both v and I are vectors, which means that both have a direction as well as a magnitude. The direction of the intensity is the average direction in which the energy is flowing. For instantaneous acoustic pressure pinst(t) and particle velocity v(t) the average acoustic intensity during time T is given by

I = \frac{1}{T} \int_{0}^{T}p_\mathrm{inst}(t) v(t)\,dt

The SI units of intensity are W/m2 (watts per square metre). For a plane progressive wave we have:

I = \frac{p^2}{Z} = Z v^2 = \xi^2 \omega^2 Z = \frac{a^2 Z}{\omega^2} = E c = \frac{P_{ac}}{A}

where:

Symbol Units Meaning
p pascals RMS sound pressure
f hertz frequency
ξ m, metres particle displacement
c m/s speed of sound
v m/s particle velocity
ω = 2πf radians/s angular frequency
ρ kg/m3 density of air
Z = c ρ N·s/m³ characteristic acoustic impedance
a m/s² particle acceleration
I W/m² sound intensity
E W·s/m³ sound energy density
Pac W, watts sound power or acoustic power
A m² area

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Famous quotes containing the word intensity:

    “We may say that feelings have two kinds of intensity. One is the intensity of the feeling itself, by which loud sounds are distinguished from faint ones, luminous colors from dark ones, highly chromatic colors from almost neutral tints, etc. The other is the intensity of consciousness that lays hold of the feeling, which makes the ticking of a watch actually heard infinitely more vivid than a cannon shot remembered to have been heard a few minutes ago.”
    —Charles Sanders Peirce (1839–1914)