Answer to Question #161984 in Optics for Ivo

Question

A driver travels northbound on a highway at a speed of 25.0m/s. A police car, travelling southbound at a speed of 40.0m/s, approaches with its siren producing sound at a frequency of 2500Hz

(a) What frequency does the driver observe as the police car approaches?

(b) What frequency does the driver detect after the police car passes him?

Answer 1

(a)

$$f_o=f_s(\dfrac{v+v_o}{v-v_s}),$$ $$f_o=2500\ Hz\cdot(\dfrac{343\ \dfrac{m}{s}+25\ \dfrac{m}{s}}{343\ \dfrac{m}{s}-40\ \dfrac{m}{s}})=3036.3\ Hz.$$

(b)

$$f_o=f_s(\dfrac{v-v_o}{v+v_s}),$$ $$f_o=2500\ Hz\cdot(\dfrac{343\ \dfrac{m}{s}-25\ \dfrac{m}{s}}{343\ \dfrac{m}{s}+40\ \dfrac{m}{s}})=2075.7\ Hz.$$