Question

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 470 Hz ; as the truck recedes, you hear a tone of 400 Hz .Howmuch time will it take for the truck to get from your position to the fire 5.0 km away, assuming it maintainsa constant speed?

Answer 1

Answer:

time = 182.68 s

Explanation:

given data

truck approaches = 470 Hz

truck recedes =  400 Hz

position away =  5.0 km

solution

if V is the speed of sound in air and v is the speed to truck

f is the frequency of sound

when truck approach

f1 = $\frac{V+v}{V} f$  

and when truck recede

f2 = $\frac{V+v}{V} f$  

so here we can say

$\frac{f1}{f2} = \frac{V+v}{V-v}$   ...........1

$\frac{470}{400} = \frac{340.278+v}{340.278-v}$  

v = 27.37 m/s

so here 5 km

S = u×t  + 0.5 ×a×t²  ...........2

5 × 10³ = 27.37 t + 0

t = 182.68 s