A fire truck\'s siren emits sound of frequency 350 Hz which travels at a speed o

Question

A fire truck's siren emits sound of frequency 350 Hz which travels at a speed of 40 kph is followed by an ambulance which travels at a rate of 60 kph sounds it siren at a frequency of 400 Hz. A cyclist riding his bicycle is travelling in the same direction at a rate of 30 kph is in between the truck and the ambulance. Consider 347 m/s as the speed of sound in air. What are the

a.) frequency heard by the cyclist caused by the truck?

b.)frequency heard by the cyclist caused by the ambulance?

c.) beat frequency heard by the cyclist in the situation mentioned above?

Explanation / Answer

given

speed of fire truck is 40 kmph = 11.111 m/s , frequency f_f = 350 Hz

speed of ambulance is 60 kmph = 16.66 m/s , frequency f_a = 400 Hz

cyclist speed is 30 kmph = 8.33 m/s in between truck and ambulance

the speed of sound is v = 347 m/s

a) frequency heard by the cyclist caused by the truck is

from Doppler effect f' = f ( (v-/+v0) / (v -/+ vs))

here the observer reference frame the truck is moving away from him so that the observer can hear the less frequency so the formula becomes

f' = f((v-v0)/(v+vs) )

f' = 350((347 -8.33)/(347+11.111)) Hz

f' = 331 Hz

b)frequency heard by the cyclist caused by the ambulance

here ambulance approaching the observer so

f' = f((v-v0)/(v-vs) )

f' = 350((347 -8.33)/(347-16.66)) Hz

f' = 358.82 Hz = 359 Hz

c) the beat freqeucy is f = df = 359-331 = 28

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