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alexandr402 [8]
3 years ago
7

A physicist drives through a stop light. When he is pulled over, he tells the police officer that the Doppler shift made the red

light of wavelength 635 nm appear green to him, with a wavelength of 510 nm. The police officer writes out a traffic citation for speeding. How fast was the physicist traveling, according to his own testimony
Physics
1 answer:
Colt1911 [192]3 years ago
8 0

Answer:

6.59\times 10^7m/s

Explanation:

We are given that

Wavelength of red light=\lambda=635nm

Wavelength of  green light=\lambda'=510 nm

We have to find the speed of physicist traveling according to his own testimony.

We know that

\frac{\lambda}{\lambda'}=\sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}

Where c=3\times 10^8m/s

Substitute the values

\frac{635}{510}=\sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}

1.25=\sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}

Squaring on both sides

1.5625=\frac{1+\frac{v}{c}}{1-\frac{v}{c}}

1.5625-1.5625\frac{v}{c}=1+\frac{v}{c}

1.5625-1=\frac{v}{c}+1.5625\frac{v}{c}=\frac{v}{c}(1+1.5625)

0.5625=2.5625\frac{v}{c}

v=\frac{0.5625c}{2.5625}=\frac{0.5625\times 3\times 10^8}{2.5625}

v=6.59\times 10^7m/s

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