Question

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?

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

Answer 1

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

Explanation:

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