KinexiaLEARN PHYSICS

Doppler Effect — Receding Ambulance (Worked Example)

Medium
Problem

An ambulance siren emits 700 Hz while driving away at 25 m/s. What frequency does a stationary pedestrian hear? (v = 343 m/s)

Given

  • f = 700 Hz

  • vs = 25 m/s (receding)

  • v = 343 m/s

Find

The observed frequency f'.

Principle

Receding stretches wavefronts: f' = f·v/(v + vs) — lower pitch.

Formula

Solution

  1. Write the formula: f′=f⋅v/(v+vs)f' = f \cdot v/(v + v_s)

  2. Substitute: f′=700×343/(343+25)f' = 700 \times 343/(343 + 25)

  3. Denominator: 368368; f′=700×343/368f' = 700 \times 343/368

  4. Calculate: f′=652 Hzf' = 652\ \mathrm{Hz}

652 Hz

Unit check

Hz × (m/s ÷ m/s) = Hz. The speed ratio is dimensionless — frequency stays in hertz.

What this means physically

652 Hz — noticeably flatter than 700 Hz. The falling pitch of a passing siren is the Doppler effect announcing the ambulance is moving away.

Common mistake

Using minus for receding. Receding grows the denominator (v + vs) — check the sign against the physical expectation (lower pitch).