An ambulance with a siren emitting a whine at 1600 Hz overtakes and passes a cyc

Question

An ambulance with a siren emitting a whine at 1600 Hz overtakes and passes a cyclist pedalling a bike at 2.44 m/s. While the ambulance is in front of the cyclist, they hear a frequency of 1S90 Hz. (A) How fast is the ambulance moving? (B) The cyclist stops at a stop sign while the ambulance continues forward, what is the frequency from the ambulance the cyclist hears? The ambulance stops at the hospital and emits the siren with a power of 30.0 W isotropic ally A small microphone intercepts the sound in an area of 0.750 cm^2. 200 m from the source Calculate (C) the sound intensity there and (0) the power intercepted by the microphone.

Explanation / Answer

A) Using Doppler's effect:

f = (V + Vr)f0 / (V + Vs)

V = speed of wave = 340 m/s

Vr = speed of receiver = 2.44 m/s

Vs = speed of source = Va

1590 = (340 + 2.44)(1600) / (340 + Va)

340 + Va = 344.6

Va = 4.6 m/s

b) now Vr = 0

f = (340)(1600) / (340 + 4.6)

f = 1578.6 Hz

c) Intensity at distance r, I = P / (4 pi r^2)

I = 30 / (4 pi 200^2) = 5.968 x 10^-5 W/m^2

d) POwer = Intensity x area

    = 5.968 x 10^-5 x (0.750 x 10^-4 m^2) =4.476 x 10^-9 W

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