While driving a car, you hear an ambulance siren and pull to the side of the roa

ID: 1396271 • Letter: W

Question

While driving a car, you hear an ambulance siren and pull to the side of the road

and stop. Your friend happens to have a guitar-tuning app on her smart phone

that can measure sound frequency and she measures the frequency of the siren

to be 808 Hz as the ambulance approaches. After the ambulance passes, she

measures the frequency of the siren to be 708 Hz. Assume that the speed of

sound in air is 340 m/s.

a) What is the speed of the ambulance? [Hint: write down an equation for the

frequency you would hear when the ambulance approaches you. Write down

a second equation for the frequency you would hear when the ambulance is

moving away from you. You should now have two equations with two

unknowns. These equations can be used to answer the question.] Show

your work.

b) What is the frequency of the siren observed by a stationary listener when the

ambulance siren is also stationary?

given frequency of ambulance as it approaches = f1 = 808 Hz

given frequency of ambulance as it leaves = f2 = 708 Hz

speed of sound= v = 340 m/s

from Doppler effect

as the ambulance approaches the frequecy f1 = ((v-vo)*fo)/(v-vs) ....(1)

vo = speed of the observer = 0

vs = speed of the ambulance

as the ambulance leaves

f2 = ((v-vo)*fo)/(v+vs)...........(2)

from 1 & 2

f1/ f2 = (v+vs)/(v-vs)

808/708 = (340+vs)/(340-vs)

1.141*340 - 1.141*vs = 340 + vs

340*0.141 = 2.141*vs

vs = 22.4 m/s <------answer

++++++++++++++++

part(b)

from 1

808 = ((340-0)*fo)/(340-22.4)

fo = 754.7 Hz = 754 Hz <---answer

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