Multiple-Concept Example 6 reviews the concepts that play a rolein this problem.

Question

Multiple-Concept Example 6 reviews the concepts that play a rolein this problem. A speeder is pulling directly away and increasinghis distance from a police car that is moving at 24 m/s withrespect to the ground. The radar gun in the police car emits anelectromagnetic wave with a frequency of 6.3 x 109 Hz.The wave reflects from the speeder's car and returns to the policecar, where its frequency is measured to be 330 Hz less than theemitted frequency. Find the speeder's speed with respect to theground.

Chapter 24, Problem 32

Explanation / Answer

   for this we use the doppler effect fromwhich the doppler frequency for an electromagnetic
   radiation is given by    fo = fs[1 ±(vrel / c)]    where vrel is the relativespeed between the source and the observer of the radiation    according to our pbm as the distance betweenthe police car and the speeders car is increasing    so the doppler frequency will changeto    fo - fs = -fs (vrel / c)    from the given problem after the wavereflects from the speeders car it returns to thepolice car    then its frequency will befo'    so the second doppler shift is    fo' - fo=  - fo (vrel /c)      adding the above tow equations we get    (fo - fs) +(fo' - fo) = - fo(vrel / c) - fs (vrel / c)    fo' - fo =- [fo (vrel / c) + fs(vrel / c)]               =- 2 fs (vrel / c)    but fo ˜ fs    so we get    fs - fo' ˜2 fs (vrel / c)    the relative speed will be    vrel = [(fs -fo') / 2 fs] c          = [330Hz / 2 (6.3 x 109 Hz)] (3 x 108 m /s)             =....... m / s    the speeders speed with respect to theground will be    vspeeder = vrel +vpolice                 =  vrel + 24 m / s                = ........ m / s

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