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March 26, 2017

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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 G3 tone (196 Hz). The instant the car passes by, he hears the sound as a distinct D3 tone (147 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 340 m/s.)

  • physics - ,

    196=f1/(340-Vcar)
    147=f(1/(340+vcar)

    dividing the first equation by the second

    196/147=(340+vcar)/(340-Vcar)

    4/3 (340-Vcar)=340+Vcar

    1/3 340=7/3 Vcar

    vcar=340/7=you do it... m/s That is almost 109mph

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