The siren on an ambulance produces a frequency of 460 Hz and is traveling toward

Question

The siren on an ambulance produces a frequency of 460 Hz and is traveling towards a hospital. Given the speed of sound is 343 m/s.

a. A person at the hospital hears a frequency of 510 Hz coming from the ambulance. What is the speed of the ambulance?

b. A person is driving in a car towards the hospital at speed of 20 m/s and in the opposite direction of the ambulance which is traveling toward the hospital at 28 m/s. (The ambulance and car are driving toward each other and towards the hospital). What is the frequency heard by the person on the car?

Explanation / Answer

doppler effect

f = [(c + vr)/(c + vs)]*fo

where

c is the velocity of waves in the medium;

vr is the velocity of the receiver relative to the medium; positive if the receiver is moving towards the source (and negative in the other direction);

vs is the velocity of the source relative to the medium; positive if the source is moving away from the receiver (and negative in the other direction).

a)

510 = [(343 + 0)/(343 + vs)]*460

343 + vs = 343*460/510 = 309.37

vs = 309.37 - 343 = - 33.63 m/s

the speed of the ambulance = 33.63 m/s

b)

f = [(343 + 20)/(343 - 28)]*460

f = 530.09 Hz

the frequency heard by the person on the car = 530.09 Hz

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