An ambulance siren emits sound at 680 Hz while approaching a stationary observer at 20 m/s. The speed of sound is 340 m/s. Calculate the frequency the observer hears.

Vibrations & Waves Challenge #2 — Doppler Effect

The Doppler shift
of a siren.

Vibrations & Waves Medium

Problem

An ambulance drives towards you at 20 m/s, its siren emitting a steady 680 Hz. The speed of sound in air is 340 m/s. Calculate the frequency you hear as it approaches.

Source frequency\( f = 680\ \mathrm{Hz} \)
Source speed\( v_s = 20\ \mathrm{m/s} \)
Speed of sound\( v = 340\ \mathrm{m/s} \)
Answer inhertz

You are stationary; only the source moves.

Hint: an approaching source squeezes the waves, so the denominator shrinks: \( f' = f \cdot \tfrac{v}{v - v_s} \). If your answer came out lower than 680 Hz, the sign went the wrong way.

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The Doppler shiftof a siren.

Problem

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The Doppler shift
of a siren.