Physics
Physics
Problem
A stationary observer standing beside a road measures the frequency of an ambulance siren as 1.20 kHz while the ambulance approaches and 0.800 kHz just after it passes. The speed of sound in air is 343 m/s. Determine the speed of the ambulance.Intuitive explanation
This is a Doppler shift problem where motion compresses or stretches sound waves. The key insight is that you have two frequency measurements—one when the source approaches (higher frequency) and one when it recedes (lower frequency)—which gives you two equations in two unknowns: the ambulance speed and the true siren frequency. Set up the Doppler formula for each case, then solve the system by taking their ratio to eliminate the source frequency.
Intuitive explanation
This is a Doppler shift problem where motion compresses or stretches sound waves. The key insight is that you have two frequency measurements—one when the source approaches (higher frequency) and one when it recedes (lower frequency)—which gives you two equations in two unknowns: the ambulance speed and the true siren frequency. Set up the Doppler formula for each case, then solve the system by taking their ratio to eliminate the source frequency.