Question

A comet is known to be traveling toward the earth at a speed of 255 km per second. It is observed to give light with a frequency of 642 x 1014 Hz. What frequency of light would the come be emitting if it were motionless? Express your answer to the nearest hundred trillion Hz.

Answer 1

Given:

The speed of the comet, u=255 km/s=255×10³ m/s

The observed frequency, f_o=642×10¹⁴ Hz

To find:

The frequency emitted by the comet.

Explanation:

The observed frequency is given by,

$f_o=\sqrt{\frac{c+u}{c-u}}f$

Where c is the speed of light and f is the frequency emitted by the comet.

On substituting the known values,

$\begin{gathered} 642\times10^{14}=\sqrt{\frac{3\times10^8+255\times10^3}{3\times10^8-255\times10^3}}\times f \\ \implies f=\frac{642\times10^{14}}{\sqrt{\frac{3\cdot10^{8}+255\cdot10^{3}}{3\cdot10^{8}-255\cdot10^{3}}}} \\ =641\times10^{14}\text{ Hz} \end{gathered}$

Final answer:

The frequency emitted by the comet is 641×10¹⁴ Hz