Kyoko asked in Science & MathematicsPhysics · 5 months ago

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

Same technique as here:

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

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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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