You are driving along a highway at 30.0 m/s when you hear a siren. You look in t

Question

You are driving along a highway at 30.0 m/s when you hear a siren. You look in the rear-view mirror and see a police car approaching you from behind with a constant speed. The frequency of the siren that you hear is 1300. Hz. Right after the police car passes you, the frequency of the siren that you hear is 1280. Hz. a) How fast was the police car moving? b) You are so nervous after the police car passes you that you pull off the road and stop. Then you hear another siren, this time from an ambulance approaching from behind. The frequency of its siren that you hear is 1400. Hz. Once it passes, the frequency is 1200. Hz. What is the actual frequency of the ambulance's siren? a) 32.6 m/s, b) 1292 Hz

Explanation / Answer

Fd = f(v-vr)/(v-vs)
1300 = f(343-30)/(343-vs)
1300(343-vs) = 313f
343-vs = 0.24076 f    ----(1)

Fd = f(v+vr)/(v+vs)
1280= f(343+30/(343+vs)
1280 (343+vs) = 373
343+vs = 0.2914 f    ----(2)

Eqn (1)+(2)

686 = 0.5322 f
f = 1289 Hz

343-vs = 0.24076*1289
vs = 343-310.36
vs = 32.64 m/s

1300*32.63 + 313 f = 445900

313 f = 403472.2

F = 1289 Hz

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