5. The siren on an ambulance produces a frequency of 460 Hz and is traveling tow

Question

5. 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

Here ,

f0 = 460 Hz
speed of sound , vs = 343 m/s

a) let the speed of ambulance is v

f = 510 Hz

510 = f0 * (v + vs)/vs

510 = 460 * (343 + v)/343

solving for v

v = 37.3 m/s

the speed of ambulance is 37.3 m/s

b)

relative speed of ambulance and car , v = 20 + 28 m/s

v = 48 m/s

for the frequency heard = f0 * (v + vs)/vs

frequency heard = 460 * (343 + 48)/343

frequency heard = 524.3 Hz

the frequency heard by the person in the car is 524.3 Hz

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