Doppler Equation ^🔗

$$ \begin{aligned} & f’ = f\frac{v_{w}}{v_{w} \pm v_{s}} \end{aligned} $$

• $v_{w}$: the velocity of the wave in the medium ($ms^{-1}$)
• $v_{s}$: the velocity of the source ($ms^{-1}$)
• $f$: the actual emitted frequency of the wave produced by the source ($Hz$)
• $f’$: the observed frequency of the wave ($Hz$)

Pātai: What is the $\pm$ symbol? ^🔗

• Literally: plus OR minus
• In words: $v_{w} \pm v_{s}$ means the velocity of the wave relative to the source
• Approaching: $f’ = f\frac{v_{w}}{v_{w} - v_{s}}$ because the wave and source are moving in the same direction, the wave appears to be moving slower relative to the source
  • Wavefront is compressed, wavelength is shorter, frequency is higher, pitch is higher
• Receding: $f’ = f\frac{v_{w}}{v_{w} + v_{s}}$ because the wave and source are moving in opposite directions, the wave appears to be moving faster relative to the source
  • Wavefront is expanded, wavelength is longer, frequency is less, pitch is lower

Doppler Skill 1: Calculating $f'$ ^🔗

• Activity 6A Q1, Q2

Breaking the Sound Barrier ^🔗