A policeman with a very good ear and a good understanding of the Doppler effect

Question

A policeman with a very good ear and a good understanding of the Doppler effect stands on the shoulder of a freeway assisting a crew in a 40-mph work zone. He notices a car approaching that is honking its horn. As the car gets closer, the policeman hears the sound of the horn as a distinct E4 tone (330 Hz). The instant the car passes by, he hears the sound as a distinct C4 tone (262 Hz). He immediately jumps on his motorcycle, stops the car, and gives the motorist a speeding ticket. How fast was this car going? (Assume that the speed of sound is 343 m/s.)

Explanation / Answer

speed of sound = 343 m/s speed of sound = frequency*wavelength wavelength = speed of sound/frequency velocity/speed of sound = the change in wavelength/original wavelength velocity = (343 m/s)*(0.694 m - 0.779 m)/0.694 m velocity = 42.27 m/s = 94.55 miles per hour

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