Question

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

Answer 1

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

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

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

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

$0.5625=2.5625\frac{v}{c}$

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

$v=6.59\times 10^7m/s$