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)

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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