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.

Step-by-step explanation:

The observed frequency is given by,

`f_o=\sqrt{(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*10^(14)=\sqrt{(3*10^8+255*10^3)/(3*10^8-255*10^3)}* f \\ \implies f=\frac{642*10^(14)}{\sqrt{(3\cdot10^(8)+255\cdot10^(3))/(3\cdot10^(8)-255\cdot10^(3))}} \\ =641*10^(14)\text{ Hz} \end{gathered}`

Final answer:

The frequency emitted by the comet is 641×10¹⁴ Hz