Question

A speeder tries to explain to the police that the yellow warning lights she was approaching on the side of the road looked green to her because of the Doppler shift. How fast would she have been traveling if yellow light of wavelength 575.9 nm had been shifted to green with a wavelength of 564.2 nm

Answer 1

Answer:

The speed of the speeder is $8.348x10^6m/s$.

Explanation:

Spectral lines will be shifted to the blue part of the spectrum if the source of the observed light is moving toward the observer, or to the red part of the spectrum when is moving away from the observer (that is known as the Doppler effect).

That shift can be used to find the velocity of the object (in this case the speeder) by means of the Doppler velocity.

$v = c\frac{\Delta \lambda}{\lambda_{0}}$   (1)

Where $\Delta \lambda$ is the wavelength shift, $\lambda_{0}$ is the wavelength at rest, v is the velocity of the source and c is the speed of light.

$v = c(\frac{\lambda_{0}-\lambda_{measured}}{\lambda_{0}})$

For this case $\lambda_{measured}$ is equal to 564.2 nm and $\lambda_{0}$ is equal to 575.9 nm.

$v = (3x10^8m/s)(\frac{575.9 nm - 564.2 nm}{564.2 nm)})$

   

$v = 8.348x10^6m/s$

Hence, the speed of the speeder is $8.348x10^6m/s$.