Question

A police car siren emits a frequency of2010 Hz when stationary. When it isdriving toward a stationary car, the otherdriver hears a frequency of 2120 Hz.How fast is the police car driving?(Speed of sound = 343 m/s)(Unit = m/s)

Answer 1

17.797 m/s

Step-by-step explanation:

We can calculate the velocity of the car using the following equation:

`f_o=(f)/(1-(v_r)/(v))`

Where fo is the perceived frequency, f is the emitted frequency, vr is the speed of the car and v is the speed of the sound. So, replacing f = 2010 Hz, fo = 2120 Hz, and v = 343 m/s, we get:

`2120=(2010)/(1-(v_r)/(343))`

Solving for vr, we get:

`\begin{gathered} 2120(1-(v_r)/(343))=2010 \\ \\ 1-(v_r)/(343)=(2010)/(2120) \\ \\ 1-(v_r)/(343)=0.948 \\ \\ -(v_r)/(343)=0.948-1 \\ \\ -(v_r)/(343)=-0.0519 \\ \\ v_r=-0.0519(-343) \\ v_r=17.797\text{ m/s} \end{gathered}`

Therefore, the police car is driving at 17.797 m/s