A fire tracks siren with frequency f_s and constant speed v_s and an observer in

Question

A fire tracks siren with frequency f_s and constant speed v_s and an observer in the car with constant speed v_o approaching toward each other from distance L(in opposite direction). The observer hearing the sound of siren with frequency f_o as it approaching to the observer. The ratio of the f_o/f_s = 1.25. The car and fire track then pass each other and after 20 second the same distance L they are away from each other. At this time the ratio of the frequency is f_o/f_s = 0.819.they (speed of the sound 343 m/s). Determined the speed of the car and fire track. Determine the distance L. If the frequency of the siren 800 Hz find the wavelength of the sound in all the cases?

Explanation / Answer

This is a problem of Doppler effect

f' = f (1± Vo/V ) moving observer

f' = f (1/(1-+ Vs/V)) moving source

f'= f ((V + Vo) / (V- Vs) ) source and moving observer

Data

fo/fs = 1.25 Approaching

fo / fs = 0.819 pulling away

Part a)

f'/f= ((V + Vo) / (V- Vs) ) = 1.25

f'/f = ((V - Vo) / (V + Vs) ) = 0.819

We have two equations and two unknowns, so we can solve the system of equations

V + Vo = 1.25 ( V – Vs)

V – Vo = 0.819 ( V + Vs)

2V = 2.069 V – 0.431 Vs

Vs = 343 (2.069 -2) / 0.431

Vs = 54.91 m/s

V + Vo = 1.25 ( V – Vs)

Vo = V ( 1.25-1) – 1.25 Vs

Vo = 343 0.25 – 1.25 54.91

Vo = 85.75 – 68.64

Vo = 17.11 m/s

Part b)

t = 20 s

V =d/t

Distance traveled per vehicle

d1 = Vc t

d2 = Vf t

vehicles as the total distance away is the sum

dt = d1 +d2

dt = Vc t +Vf t = t ( Vc+Vf)

dt = 20 (17.11 + 54.91)

dt = 1440.4 m

Part c)

f= 800 Hz

f'/f = 1.25

f' = 1.25 f

f'= 1.25 800

f'= 1000 Hz

f'/f =0.819

f'= 800 0.819

f'= 655.2 Hz

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