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

Answer:

The speed of the ambulance is 4.66 m/s.

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,

$f'=f\times\dfrac{v+v_{o}}{v+v_{s}}$

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

$v_{s}=f\times\dfrac{v+v_{o}}{f'}-v$

$v_{s}=1570\times\dfrac{343-2.45}{1560}-343$

$v_{s}=4.66\ m/s$

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