A girl is riding her bike down the street at a speed of 3.5m/s[E] when she hears a fire truck with a siren emitting a sound with a frequency of 425Hz. The girl detects a frequency of 475Hz. The air temperature is 28°C. Is the fire truck moving towards or?

Question

away from the girl? What is the speed of the truck? (Sorry the question is too long)

1031 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-26T06:19:03

The truck is moving away from the girl at $=37.42ms^-1$

This is an example of the Dopler's effect

The speed of sound at $28^@C$ is

$c=331+0.6*28=347.8ms^-1$

The observed frequency is $f=475Hz$

The emitted frequency is $f_0=425Hz$

Therefore,

$Deltaf=f-f_0=475-425=50Hz$

Apply the equation

$Deltaf=(Deltav)/cf_0$

The velocity of the receiver relative to the source is $=Deltav$

Therefore,

$Deltav=c/f_0Deltaf=347.8*50/425=40.92ms^-1$

But

$Deltav=v_r-v_s=40.92$

$v_r=3.5ms^-1$

$v_s=3.5-40.92=-37.42ms^-1$

As $v_s<0$ , the truck is moving away from the girl