A driver travels northbound on a highway at a speed of 26.0 m/s. A police car, t

Question

A driver travels northbound on a highway at a speed of 26.0 m/s. A police car, traveling southbound at a speed of 32.0 m/s, approaches with its siren producing sound at a frequency of 2450 Hz.

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

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

(c) Repeat parts (a) and (b) for the case when the police car is traveling northbound.

while police car overtakes_____ Hz

after police car passes______Hz

Explanation / Answer

given

speed of obsorver, vo = 26 m/s

speed of source, vs = 32 m/s

f = 2450 hz

let speed of sound, v = 340 m/s

a) Use Doppler's effect equation

As the police car approches,

frequency heard by listener, f' = f*(v + vo)/(v - Vs)

= 2450*(340 + 26)/(340 - 32)

= 2911.4 hz

B) after police car passes,

frequency heard by listener, f' = f*(v - vo)/(v + Vs)

= 2450*(340 - 26)/(340 + 32)

= 2068 hz

C) As the police car approches,

frequency heard by listener, f' = f*(v - vo)/(v - Vs)

= 2450*(340 - 26)/(340 - 32)

= 2497.7 hz

d) after police car passes,

frequency heard by listener, f' = f*(v + vo)/(v + Vs)

= 2450*(340 + 26)/(340 + 32)

= 2410 hz

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