Hearing the siren of an approaching fire truck, you pull over to side of the road and stop. as the truck approaches, you hear a tone of 460 hz; as the truck recedes, you hear a tone of 410 hz. how much time will it take to jet from your position to the fire 5.00 km away, assuming it maintains a constant speed?

The truck will reach there in 250 seconds.

Explanation:

The frequency due to doppler effect, when the observer is stationary and the source is moving towards it is

=

where v= velocity of sound in air

= velocity of source of sound

f= frequency of sound and

= frequency oberved due to Doppler effect

= 460------------------------------------------( 1 )

The frequency due to doppler effect, when the observer is stationary and the source is moving away from it

=

where v= velocity of sound in air

= velocity of source of sound

f= frequency of sound and

= frequency oberved due to Doppler effect

= 410-------------------------------------------( 2 )

Dividing ( 1 ) by ( 2 )

41v + 41 = 46v  - 46

87= 5v

=

Velocity of Sound (v)= 348 m/s

=20 m/s

Therefore, the truck is moving at 20 m/s.

Distance= 5000 m

Time=

Time= 250 s

Time = 4 min 10 sec