Respuesta :
The speed of the car is 12 m/s.
Explanation:
As in the present problem, the frequency emitted by the source (f) is given as 570 Hz and the Doppler frequency or the frequency heard by the observer (f') is given as 590 Hz. So there is an increase in the frequency which confirms that the car is moving towards the observer. Then, the speed of the car can be obtained by substituting the known parameters in the Doppler shift frequency formula.
As the observer is stationary, the speed of observer is zero, so the numerator will only have the speed of sound which is 343 m/s. And as the car is coming towards the observer, the speed of car should be subtracted from the speed of sound in the denominator.
[tex]f'=\frac{v}{v-v_{s} }*f[/tex]
[tex]590=\frac{343}{343-v_{s} }*570[/tex]
[tex]343-v_{s} = \frac{343}{590} * 570 = 331[/tex]
[tex]v_{s} = 343-331=12 m/s.[/tex]
So, the speed of the car is 12 m/s.
