The security alarm on a parked car goes off and produces a frequency of 960 Hz. The speed of sound is 343 m/s. As you drive toward this park

Question

The security alarm on a parked car goes off and produces a frequency of 960 Hz. The speed of sound is 343 m/s. As you drive toward this parked car, pass it, and drive away, you observe the frequency to change by 75 Hz. At what speed are you driving

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Nem 5 years 2021-08-01T01:32:43+00:00 1 Answers 248 views 1

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  1. Acacia
    0
    2021-08-01T01:34:11+00:00
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    Answer: 13.4\ m/s

    Explanation:

    Given

    The frequency of the source is f_o=960\ Hz

    Change in frequency is 75\ Hz

    Speed of sound c=343\ m/s

    Suppose v is the velocity of the observer

    Doppler frequency is given by

    f'=f_o\left(\dfrac{c\pm v_o}{c\pm v_s}\right)

    Here, the source is at rest

    While approaching source, frequency is

    f_1=f_o\left(\dfrac{c+v}{c}\right)\quad \ldots(i)

    While leaving, frequency is

    f_2=f_o\left(\dfrac{c-v}{c}\right)\quad \ldots(ii)

    The difference in the frequency is

    \Rightarrow f_1-f_2=75\\\\\Rightarrow f_o\left(\dfrac{c+v}{c}\right)-f_o\left(\dfrac{c-v}{c}\right)=75\\\\\Rightarrow f_o\left(\dfrac{2v}{c}\right)=75\\\\\Rightarrow v=\dfrac{75\times 343}{2\times 960}\\\\\Rightarrow v=13.39\approx 13.4\ m/s

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