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6 Doppler effect

The observed frequency changes when source and observer move relative to each other: higher when approaching, lower when receding. Doppler (general) f' = f × (v ± v<sub>o</sub>) / (v ∓ v<sub>s</sub>) v = speed of sound. Top signs = approaching. v_o = observer speed, v_s = source speed.

Getting the signs right

  • Approaching (getting closer) ⟹ f′ is higher. Pick signs to make the fraction bigger.
  • Receding ⟹ f′ is lower. Signs that make the fraction smaller.
  • Observer term is on top; source term on the bottom.
Worked example Passing ambulance A siren (f = 800 Hz) approaches a stationary observer at v_s = 30 m s⁻¹. Speed of sound = 340 m s⁻¹. Find f′. Observer stationary (v_o = 0), source approaching → f' = f · v/(v − v_s). f' = 800 × 340 / (340 − 30) = 800 × 340/310. f' = 877 Hz. ✓ f' ≈ 877 Hz (higher, as expected while approaching).

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