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 hzhz ; as the truck recedes, you hear a tone of 420 hzhz . How much time will it take for the truck to get from your position to the fire 5.0km away, assuming it maintains a constant speed? Express your answer using two significant figures.

Answer 1

The time taken by the truck to get to the required position 5 km away from the fire is 261.55 s.

Tone at which the truck approaches at = 470 hz

Tone at which the truck recedes = 420 hz

Distance = 5.0 Km away

Speed = constant

Speed of sound = v

Speed of air = V

Frequency of sound = f

Frequency when truck approaches = f₁ =

= f₁ = [( V + v) / V ] X f

Frequency when the truck recedes = f₂ =

= f₂ = [( V - v) / V ] X f

Thus, equating both equations =

= f₁ / f₂ = (V + v) / (V - v)

= 470/420 = (340.278 + v) / (340.278 - v )

= [ 470 X 340.278 ] - 470v = [ 420 X 340.278 ] + 420v

= 159930.66 - 470v = 142916.76 + 420v

= 17013.9 = 890v

= v = 19.117 m/s

The time taken = t =

= s = ut + (1/2)at²

= 5 X 10³ = 0 + (19.117 X t)

= t = 261.55 s

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