Question

A comet is known to be traveling at 236 km per second. It is observed to give light with a frequency of 641 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

6.4 x 10¹⁶ Hz

Step-by-step explanation

Given:

• The speed of the source, vs = 236 km/s

,

• The speed of light, c = 300,000 km/s

,

• The observed frequency of the light, fo = 641 x 10¹⁴ Hz

Find:

• The frequency of the source, fs

To solve this problem, we have to apply the Doppler Effect formula for light,

`f_o=f_s\sqrt{(1-v_s/c)/(1+v_s/c)}`

Solving for fs,

`f_s=f_o\sqrt{(1+v_s/c)/(1-v_s/c)}`

Replace the known values and solve,

`f_s=641\cdot10^(14)Hz\cdot\sqrt{(1+(236km/s)/(300,000km/s))/(1-(236km/s)/(300,000km/s))}\approx6.4\cdot10^(16)Hz`

Hence, the emitted frequency of the comet's light is 6.4 x 10¹⁶ Hz.