Hifumi's Study Notesnotesphysicscegep3Doppler effect

Doppler effect

Tags

phys/wave

cegep/3

Word count

127 words

Reading time

1 minute

When a wave source / observer is moving, the perceived frequency is affected.

f^{'} = \frac{v \pm v_{o}}{v \mp v_{s}} f

[!example] Receding light source is red shifted, approaching light source is blue shifted.

Examples

Standing at a crosswalk, you hear a frequency of 560 Hz from the siren of an approaching ambulance. After the ambulance passes, you hear the frequency of the siren as 480 Hz. Determine the ambulance’s speed from these observations. Use the speed of sound for normal air conditions.

\begin{aligned} {\begin{cases} f^{'} & = 560 = \frac{v}{v - v_{s}} f \\ f^{″} & = 480 = \frac{v}{v + v_{s}} f \end{cases} \\ f = \frac{560 (v - v_{s})}{v} & = \frac{480 (v + v_{s})}{v} \\ 560 v - 560 v_{s} & = 480 v + 480 v_{s} \\ v_{s} & = \frac{1}{13} v \approx 26.4 m / s \end{aligned}

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