Problem — Doppler, ambulance approaching

Problem

Doppler effect. An ambulance with a siren of frequency $f_s = 500\;\text{Hz}$ approaches a stationary observer with speed $v_s = 30\;\text{m/s}$. Sound travels at $v = 340\;\text{m/s}$. Calculate the frequency perceived by the observer.

Solution

Setup. Source approaching, receiver stationary. The wavefronts “bunch up”, the frequency increases; $v - v_s$ appears in the denominator:

$f' = f_s\,\frac{v}{v - v_s} = 500\cdot\frac{340}{340 - 30} = 500\cdot\frac{340}{310}$

$\ev{f' \approx 550\;\mathrm{Hz}}$

The observer hears the siren getting higher-pitched as long as the ambulance approaches; as it passes, the frequency drops abruptly.

Linked atoms

Argomenti: Waves Concetti: Doppler effect