W8-02 Doppler Effect

This lecture, part of a physics course, derives the relativistic Doppler effect for electromagnetic waves. The instructor begins by reviewing the key results of special relativity from the previous lecture. He then introduces the Doppler effect as the change in frequency of waves due to relative motion between source and observer, using the example of a train whistle. The main derivation considers a source moving with velocity v relative to the Earth frame, emitting waves of frequency ν0 in its own rest frame. The time interval between successive wave crests in the source frame is the proper time Δt0 = 1/ν0. Due to time dilation, the Earth observer measures a longer time interval Δt = Δt0 / sqrt(1 - v^2/c^2) between emissions. However, the observer also sees the source moving, so the distance between crests is altered. The derivation carefully calculates the arrival times of successive crests at the observer, accounting for the source’s motion. The final result is the relativistic Doppler formula: ν = ν0 * sqrt((1 - v/c)/(1 + v/c)) for a source moving away from the observer. The lecture concludes by mentioning the cosmological redshift, where distant galaxies moving away show a frequency shift, providing evidence for the expanding universe.