Problem — Doppler, police car moving away

Problem

A police car with a siren at $500\;\text{Hz}$ moves away from a stationary pedestrian at a speed of $25\;\text{m/s}$. Calculate the frequency perceived by the pedestrian (speed of sound $340\;\text{m/s}$).

Solution

Setup. Source moving away, receiver stationary. The perceived frequency decreases; the denominator contains $v_0 + v$:

$f' = f\,\frac{v_0}{v_0 + v} = 500\cdot\frac{340}{340+25} = 500\cdot\frac{340}{365}$

$\ev{f' \approx 466\;\mathrm{Hz}}$

Consistent with experience: as it moves away, the siren sounds lower-pitched.

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Topics: Onde Concepts: Effetto Doppler