Question

You are driving along a highway at 35.0 m/s when you hear the siren of a police car approaching you from behind at constant speed and you perceive the frequency as 1340 Hz. You are relieved that he is in pursuit of a different driver when he continues past you, but now you perceive the frequency as 1300 Hz. What is the speed of the police car? The speed of sound in air is 343m/s. possible answers are: A. 40.1, B. 38.4, C. 39.2, D. 30, E. 41.7 m/s.

Answer 1

Answer:

D ) 30 m/s

Explanation:

This change in frequency observation occur due to doppler effect

$f_(observed)=\frac{V_(wave)+-V_(receiver) }{V_(wave)+-V_(source)} *f_(original)$

When the police is coming to you , you hear a higher frequency-----------(1)

$f_(observed)=\frac{V_(wave)+V_(receiver) }{V_(wave)-V_(source)} *f_(original)\\1340=\frac{343+35 }{343-V_(police)} *f_(original)$

when the police is passing you , you hear a lesser frequency---------------(2)

$f_(observed)=\frac{V_(wave)-V_(receiver) }{V_(wave)+V_(source)} *f_(original)\\1300=\frac{343-35 }{343+V_(police)} *f_(original)$

divide (1)/(2)

$\frac{1340}{1300} =\frac{(343+35)*(343+V)}{(343-35)*(343-V)}\\\frac{1340}{1300} =\frac{378*(343+V)}{308*(343-V)}\\ V=30 m/s$