Question

An ambulance with a siren emitting a whine at 1570 Hz overtakes and passes a cyclist pedaling a bike at 2.45 m/s. After being passed, the cyclist hears a frequency of 1560 Hz. How fast is the ambulance moving? (Take the speed of sound in air to be 343 m/s.)

Answer 1

The speed of the ambulance is 4.66 m/s.

Step-by-step explanation:

Given that,

The siren emitting a whine at 1570 Hz

The cyclist pedaling a bike at 2.45 m/s

The cyclist hears a frequency of 1560 Hz

We know that,

Speed of sound wave

`v = 343\ m/s`

We calculate the speed of the ambulance

Using Doppler effect,

`f'=f*(v+v_(o))/(v+v_(s))`

Where,

`f'`= frequency of ambulance siren

`f`= cyclist hears the frequency

`v_(s)`=speed of source

`v_(v)`= speed of observer

Put the value in to the formula

`v_(s)=f*(v+v_(o))/(f')-v`

`v_(s)=1570*(343-2.45)/(1560)-343`

`v_(s)=4.66\ m/s`

Hence, The speed of the ambulance is 4.66 m/s.