Sound waves
Sound is a wave of pressure peaks and valleys
Waves carry energy; intensity = power per unit area
\[
I = \frac{P_{\rm pt.source}}{4 \pi r^2} \>, \quad \mbox{for a spherical wave}
\]
Decibel scale
\[
\beta = 10 \, \log \left( \frac{I}{I_0} \right) \>, \quad \mbox{in dB}
\]
Human hearing threshhold $I_0=10^{-12}\,\mbox{Wm}^{-2} = 0\,$dB
Doppler effect ($v = $ speed of sound, $f_s = $ source frequency)
-
source moving with $v_s$
\[
f = f_s \> \left( {1 \mp \frac{v_s}{v}} \right)^{-1}
\]
-
observer moving with $v_o$
\[
f = f_s \> \left( {1 \pm \frac{v_o}{v}} \right)
\]
-
both source and observer moving
\[
f = f_s \> \frac{1 \pm \frac{v_o}{v}}{1 \mp \frac{v_s}{v}} \qquad
\left\{ \begin{array}{l} \mbox{upper sign - toward} \\ \mbox{lower sign - away from} \end{array} \right.
\]
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