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

Answer:

17.797 m/s

Explanation:

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

$f_o=\frac{f}{1-\frac{v_r}{v}}$

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:

$2120=\frac{2010}{1-\frac{v_r}{343}}$

Solving for vr, we get:

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

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