Question

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?

Answer 1

Answer:

253.65259 seconds

Explanation:

f' = Approaching frequency = 460 Hz

f = Receding frequency = 410 Hz

v = Speed of sound in air = 343 m/s

v' = Speed of truck

Doppler effect

$\frac{f'}{f}=\frac{v+v'}{v-v'}\\\Rightarrow 460\left(343-v'\right)=410\left(343+v'\right)\\\Rightarrow 157780-460v'-157780=140630+410v'-157780\\\Rightarrow v'=19.712\ m/s$

The distance is 5 km

Time = Distance / Speed

$Time=\frac{5000}{19.712}=253.65259\ s$

Time will it take to hear the jet from your position is 253.65259 seconds

Answer 2

The time takes to hear the jet is 253.6 seconds

given information:

Approaching frequency f' = 460 Hz

Receding frequency f = 410 Hz

speed of sound in air v = 343 m/s

Let the speed of truck be v'

distance traveled d = 5km = 5000m

Doppler effect:

Doppler effect is the effect of change in frequency of sound as the observer and the source move towards or away from each other. Mathematically:

$f'=f\frac{(v+v')}{(v-v')}\\\\f'(v-v')=f(v+v')\\\\460(343-v')=410(v+v')\\\\v'=19.7m/s$

Hence the speed of the truck is 19.7 m/s

Now the time taken to cover the distance d = 5000m:

$t=\frac{5000}{19.7}s \\\\t=253.6s$

Time taken to hear the jet from the given position is 253.6 seconds

Learn more about Doppler Effect:

https://brainly.com/question/1330077?referrer=searchResults