Question #161984

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?


1
Expert's answer
2021-02-22T10:28:44-0500

(a)

fo=fs(v+vovvs),f_o=f_s(\dfrac{v+v_o}{v-v_s}),fo=2500 Hz(343 ms+25 ms343 ms40 ms)=3036.3 Hz.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)

fo=fs(vvov+vs),f_o=f_s(\dfrac{v-v_o}{v+v_s}),fo=2500 Hz(343 ms25 ms343 ms+40 ms)=2075.7 Hz.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.

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