Sound Intensity Equations

Time and Frequency Domain implementations assume two microphone method.

General Equation

Ir = p · u r

 

from Euler

u = - 1 ∫ δp dt
ρ δr

 

Time Domain Implementation

p = pA + pB
2
u ≈ - 1 ∫ pB - pA dt
ρ Δr
I ≈ - pA + pB ∫(pB - pA)dt
2ρΔr

 

Frequency Domain Implementation

I ≈ Im GAB
ρΔrω

 

I = Intensity

 

p = pressure

 

u = particle velocity

 

r = direction of u

 

ρ = fluid density

 

pA, pB= p @ mics A and B

 

Δr = distance between mics

 

GAB= Cross Spectrum between A and B

 

Im = Imaginary Part

 

ω = angular frequency (radians/sec)

 
 
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