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 \[ f = f_s \> \frac{1 \pm \frac{v_o}{v}}{1 \mp \frac{v_s}{v}} \qquad \left\{ \begin{array}{l} \mbox{upper sign - toward} \\ \mbox{lower sign - away from} \end{array} \right. \]