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Air Absorption

The intensity of a plane wave is observed to decay exponentially according to

$\displaystyle I(x) = I_0\, e^{-x/\xi}
$

where

\begin{eqnarray*}
I_0 &=& \hbox{intensity at the plane source (\textit{e.g.}, a vibrating wall)}\\
I(x) &=& \hbox{intensity $x$\ meters from the plane-source}\\
\xi &=& \hbox{intensity decay constant ($1/e$\ distance in meters)}\\
& & \hbox{(depends on frequency, temperature, humidity}\\
& & \hbox{and pressure)}
\end{eqnarray*}

Relative Frequency in Hz
Humidity 1000 2000 3000 4000
40 5.6 16 30 105
50 5.6 12 26 90
60 5.6 12 24 73
70 5.6 12 22 63


$\textstyle \parbox{5in}{\emph{Attenuation} in dB per kilometer at 20\mbox{${}^{\circ}$}C and
standard atmospheric pressure.}$



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``Computational Acoustic Modeling with Digital Delay'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2015-04-29 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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