Relativistic Doppler Effect Formula

The normal Doppler shift for waves such as sound which move with velocities v much less than the speed of light. For light and other electromagnetic waves, the relationship must be modified to be consistent with the Lorentz transformation. The Doppler effect is observed with visible light and all other electromagnetic waves. It relates the frequency observed by an observer in motion and the frequency emitted by the source. The formula is given by,

frequency observed = (frequency emitted) √((1+velocity/speed of light)/(1-velocity/speed of light))

The equation is:

f_O = f_E√ ((1+v/c)/(1-v/c))

Where:

f_O: Frequency observed

f_E: Frequency emitted

c: speed of light

v: velocity of the observer respect to the source

Relativistic Doppler Effect Formula Questions:

1) A bus is moving towards john at 1.5 *10⁸ m/s. The bus flashes the headlight on john of frequency 4200 Hz. At what frequency will john receive the light?

Answer:

From the formula of the frequency, using the observer velocity v = 1.5*10⁸ m/s = 0.5 c , and emitted frequency f = 4200 Hz

f_O = f√ ((1+0.5c/c)/(1-0.5c/c))

f_O = f√ (3) = 4200 Hz * 1.73 =8140.6 Hz