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