In the relativistic Doppler effect, beta (β) represents velocity divided by the speed of light.
It is defined as β = v/c, where v is the relative velocity between source and observer and c is the speed of light. Because no massive object can reach or exceed c, the magnitude of β remains below 1 for ordinary physical motion. A slow-moving object has a very small beta; an object traveling at 90% of light speed has β = 0.9.
Beta appears in the relativistic Doppler formulas because velocities near light speed cannot be handled accurately with classical mechanics alone. Relativity accounts for both motion-related frequency change and time dilation. For motion directly away from an observer, the received light is shifted toward lower frequencies, or redshift; motion toward the observer produces blueshift.
Beta is easy to confuse with gamma. Gamma, written γ, is the Lorentz factor, γ = 1/√(1 − β²), and measures the strength of relativistic time-dilation effects. Delta and alpha are not the standard dimensionless velocity parameter in this formula.