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 660 nm appear green to him, with a wavelength of 555 nm. The police officer writes out a traffic citation for speeding. How fast was the physicist traveling, according to his own testimony?

Answer 1

Speed of physicist car is 0.036c or 1.08 x 10⁷ m/s .

Step-by-step explanation:

Doppler Effect is defined as the change in frequency or wavelength of the wave as the source or/and observer moving away or towards each other.

In this case, the Doppler effect equation in terms of wavelength is :

`\lambda_(s) = \lambda_(o)\sqrt{(1-(v)/(c) )/(1+(v)/(c) ) }` ......(1)

Here
`\lambda_(s)` is source wavelength,
`\lambda_(o)` is observed wavelength, v is speed of the observer and c is the speed of light.

Given :

Source wavelength,
`\lambda_(s)` = 660 nm = 660 x 10⁻⁹ m

Observed wavelength,
`\lambda_(0)` = 555 nm = 555 x 10⁻⁹ m

Substitute these values in the equation (1).

`555*10^(-9) } = 660*10^(-9) \sqrt{(1-(v)/(c) )/(1+(v)/(c) ) }`

`\sqrt{(1-(v)/(c) )/(1+(v)/(c) ) } = 0.84`

`{(1-(v)/(c) )/(1+(v)/(c) ) } = (0.84)^(2) = 0.7056`

`1-(v)/(c)=0.7056+0.7056(v)/(c)`

`(v)/(c)=(0.2944)/(8.056)`

`v = 0.036c=0.036*3*10^(8)`

v = 1.08 x 10⁷ m/s