Question

A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. The frequency of the sound emitted by the siren on the police car is 500 Hz and the speed of sound in air is 343 m/s.

(a) What is the frequency heard by an observer in the truck as the police car approaches the truck?

(b) What is the frequency heard by an observer in the truck after the police car passes the truck?

(c) If the truck and the police car were moving in the same direction with the police car behind the truck, what frequency would an observer in the truck hear?

Answer 1

(a) What is the frequency heard by an observer in the truck as the police car approaches the truck?

using a formula, we have

f₀ = f_s [(v + v₀) / (v - v_s)

f₀ = (500 Hz) {[(343 m/s) + (36 m/s)] / [(343 m/s) - (45 m/s)]}

f₀ = (500 Hz) [(379 m/s) / (298 m/s)

f₀ = 635.9 Hz

(b) What is the frequency heard by an observer in the truck after the police car passes the truck?

using a formula, we have

f₀ = f_s [(v + v₀) / (v - v_s)

f₀ = (500 Hz) {[(343 m/s) + (-36 m/s)] / [(343 m/s) - (-45 m/s)]}

f₀ = (500 Hz) [(307 m/s) / (388 m/s)]

f₀ = 395.6 Hz

(c) If the truck and police car were moving in the same direction with the police car behind truck, then frequency heared by an observer in the truck will be given as :

f = [(635.9 Hz) - (395.6 Hz)]

f = 240.3 Hz