Question

A driver travels northbound on a highway at a speed of 25.0 m/s. A police car, traveling southbound at a rate of 40.0 m/s, approaches with its siren producing sound at a frequency of 2500 Hz. (a) What frequency does the driver observe as the police car comes? (b) What frequency does the driver detect after the police car passes him? (c) Repeat parts (a) and (b) for the case when the police car is behind the driver and travels northbound.

Answer 1

Answer:

a) The frequency the driver observes as the police car comes = 3036.3 Hz

b) The frequency the driver detects as the police car passes him = 2075.7 Hz

Explanation:

The Frequency of the sound, fs = 2500 Hz

The speed of sound in air, v = 343 m/s

The speed of the driver Northbound, vo = 25 m/s

The speed of the driver Southbound, vs = 40 m/s

a) The frequency the driver observes as the police car comes is calculated below

$\begin{gathered} f_0=f_s(\frac{v+v_0}{v-v_s}) \\ \\ f_0=2500(\frac{343+25}{343-40}) \\ \\ f_0=3036.3Hz \end{gathered}$

b) The frequency the driver detects after the police car passes him is calculated below

$\begin{gathered} f_0=f_s(\frac{v-v_0}{v+v_s}) \\ \\ f_0=2500(\frac{343-25}{343+40}) \\ \\ f_0=2075.7\text{ Hz} \end{gathered}$