Problem — Approaching siren (1 kHz)

Problem

An ambulance siren emits a sound of frequency $1{,}0\;\text{kHz}$. The ambulance approaches a stationary observer at $30\;\text{m/s}$. What frequency does the observer perceive? ($v_\text{sound} = 340\;\text{m/s}$)

Solution

Setup. Source approaching, receiver stationary: $f' = f\,\dfrac{v}{v - v_s}$, with $f = 1000\;\text{Hz}$:

$f' = 1000\cdot\frac{340}{340 - 30} = 1000\cdot\frac{340}{310} \approx 1097\;\mathrm{Hz}$

$\ev{f' \approx 1{,}1\;\mathrm{kHz}}$

Links

Topics: Onde Concepts: Effetto Doppler