Kyoko asked in Science & MathematicsPhysics · 5 months ago

help please?

A stationary speed gun emits a microwave beam at 2.1*10^10 Hz. it reflects off a car and returns 1030 hz higher. what is the speed of the car

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  • NCS
    Lv 7
    5 months ago
    Best answer

    Same technique as here:

    https://answers.yahoo.com/question/index?qid=20190...

    I get 7.4 m/s.

  • Vaman
    Lv 7
    5 months ago

    f(obs) = f(s)√[(c - v) / (c + v)] . c is very large as compared with v. So we can write it as = f(s) ( 1-v/c)^(1/2) = f(s) ( 1- v/(2c))

    f(0bs) - f(s) = - v/2c. If there is a positive shift, one can write it as + v/(2c). Now v= 1030*2 *3*10^8/(2.1*10^(10))=1030*2*3/2.1*10^(-2)=29.42 m/s

    =10.59km/h

    • Vaman
      Lv 7
      5 months agoReport

      Thanks. It is binomial expansion and keep the first two terms. Thanks for the comments.

  • Anonymous
    5 months ago

    Observed frequency, f(obs) = (2.1 x 10¹⁰) Hz + 1030 Hz

    source frequency, f(s) = (2.1 x 10¹⁰) Hz

    v = speed of car

    c = speed of microwave = speed of light = 3 x 10⁸ m/s

    f(obs) = f(s)√[(c - v) / (c + v)]

    f(obs)/f(s) =√[(c - v) / (c + v)]

    [f(obs)/f(s)]² =(c - v) / (c + v)

    [f(obs)/f(s)]²(c + v) =(c - v)

    c*[f(obs)/f(s)]² + v*[f(obs)/f(s)]² = c - v

    v + v*[f(obs)/f(s)]² = c - c*[f(obs)/f(s)]²

    v{ 1 + [f(obs)/f(s)]²} = c {1 - [f(obs)/f(s)]²}

    v = c {1 - [f(obs)/f(s)]²} / { 1 + [f(obs)/f(s)]²}

    v = 3 x 10⁸ {1 - [((2.1 x 10¹⁰) + 1030) / (2.1 x 10¹⁰)]²} / {1 + [((2.1 x 10¹⁰) + 1030) / (2.1 x 10¹⁰)]²}

    v = -14.7 m/s

    The negative sign denotes object is travelling towards the source

    • BigBird5 months agoReport

      You have not considered that the reflecting surface acts as both an observer and a source.

  • 5 months ago

    ...

    F = Fo (V+/-VL) / (V+/-Vs)

    VL (V of listener) is + if move toward source and vice versa

    Vs (V of source) is + if move away from listener and vice versa

    plain old V is speed of sound in the environment

    so

    2.100000103E10 = 2.1E10 (343/(343-V))

    343-V = 342.99998

    V = 0.0000168 m/s or 0.0000437 km/hr

    I think something is wrong with your given numbers

    When you get a good response,

    please consider giving a best answer.

    This is the only reward we get.

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  • Anonymous
    5 months ago

    378.2 mph. .

    • Lv 7
      5 months agoReport

      No, it is correct. My professor helped me with this question and she is from France!

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