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

`6.59* 10^7m/s`

Step-by-step 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

`(\lambda)/(\lambda')=\sqrt{(1+(v)/(c))/(1-(v)/(c))}`

Where
`c=3* 10^8m/s`

Substitute the values

`(635)/(510)=\sqrt{(1+(v)/(c))/(1-(v)/(c))}`

`1.25=\sqrt{(1+(v)/(c))/(1-(v)/(c))}`

Squaring on both sides

`1.5625=(1+(v)/(c))/(1-(v)/(c))`

`1.5625-1.5625(v)/(c)=1+(v)/(c)`

`1.5625-1=(v)/(c)+1.5625(v)/(c)=(v)/(c)(1+1.5625)`

`0.5625=2.5625(v)/(c)`

`v=(0.5625c)/(2.5625)=(0.5625* 3* 10^8)/(2.5625)`

`v=6.59* 10^7m/s`