Question

A comet is known to be traveling at 286 km per second. It is observed to give light with a frequency of 633 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 data:

fs: frequency of source (comet); fs = ?

fo: frequency observed; fo = 633*10^14 Hz

vs: velocity of source (comet); vs = 286000 m/s

vo: velocity of observer; vo = 0 m/s

c: speed of light; c = 3*10^8 m/s

Doppler effect equation:

fo/fs = (c + vo)/(c + vs)

633*10^14/fs = (3*10^8)/(3*10^8 + 286000)

Solving for fs,

633*10^14 = fs*(3*10^8)/(3*10^8 + 286000)

(633*10^14)(3*10^8 + 286000)/(3*10^8) = fs

fs = 633.6*10^14 Hz, which is the true frequency of light the source emits

Answer: 633.6*10^14 Hz