Problem 14.50 Hearing the siren of an approaching fire truck, you pull over to t
ID: 1268062 • Letter: P
Question
Problem 14.50
Hearing the siren of an approaching fire truck, you pull over to the side of the road and stop. As the truck approaches, you hear a tone of 470Hz ; as the truck recedes, you hear a tone of 420Hz .
Part A
How much time will it take for the truck to get from your position to the fire 5.5km away, assuming it maintains a constant speed?
Express your answer using two significant figures.
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Problem 14.50
Hearing the siren of an approaching fire truck, you pull over to the side of the road and stop. As the truck approaches, you hear a tone of 470Hz ; as the truck recedes, you hear a tone of 420Hz .
Part A
How much time will it take for the truck to get from your position to the fire 5.5km away, assuming it maintains a constant speed?
Express your answer using two significant figures.
t = sSubmitMy AnswersGive Up
Explanation / Answer
For the approaching
f' = f(v)/(v - vs)
470 = 343f/(343 - vs) - Cross multiply
470(343 - vs) = 343f
161210 - 470vs = 343f
f = 470 - 1.37vs
For the receding
f' = f(v)/(v + vs)
420 = 343f/(343 + vs) - cross multiply
144060 + 420vs = 343f
f = 420 + 1.224vs
Set the f's equal
470 - 1.37vs = 420 + 1.224vs
50 = 2.59vs
vs = 19.3 m/s
Finally apply d = vt
5500 = 19.3(t)
t = 290 sec