Sound Intensity#
The intensity of a sound wave is defined as
the relation between particle velocity
which expresses the observation that particle have a mass that will resist a change in speed under the influence of an applied force (inertial reaction).
planewave#
Assume a plane wave that propagates in the x-direction
Euler equation
in x-direction
results in particle velocity
The paricle velocity is obtained by integration and using the Euler approximation to the pressure gradient one gets
Using
Using next the Fourier synthesis
and with
and therefore
we obtain
Assume the temporal ingration
evaluates to one if and only if
or
Approximating the sound pressure and pressure gradient by pressure measurements of 2 sensors labeled (1,2)
With
or
and finally the spectral sound intensity along sensor pair (1,2) is approximated by