Key Concepts

• • f_obs = f₀ · v / (v − vₛ) for a stationary observer, source speed vₛ (positive = approaching)
• • Approaching source: wavefronts bunch up → higher observed frequency (blue shift)
• • Receding source: wavefronts stretch out → lower frequency (red shift)
• • As vₛ → v (Mach 1), f_obs → ∞ — the sonic boom scenario
• • Astronomers use red-shift of light to measure galaxy recession velocities (Hubble's law)