Common Properties between Doppler Effect of Sound and Light

Sound's Doppler effect and light's Doppler effect share several qualitative features. (A) Wherever there is genuine relative motion between a listener/observer and a source -- whether of sound or of light -- the recorded frequency always differs from the emitted frequency. (B) The recorded frequency is always HIGHER than the emitted frequency whenever there is relative APPROACH. (C) The recorded frequency is always LOWER than the emitted frequency whenever there is relative RECEDE.

(D) Whenever the source's or the listener's speed ($v_s$ or $v_L$) is much smaller than the wave's own propagation speed v (the speed of sound, or of light), the exact formulas above simplify neatly using a single RELATIVE speed $v_r$ in place of tracking $v_s$ and $v_L$ separately: $n=n_0\left(1\pm\dfrac{v_r}{v}\right)$, so the Doppler SHIFT itself (the change in recorded frequency, $\Delta n=|n-n_0|$) is given by $\dfrac{\Delta n}{n_0}=\dfrac{v_r}{v}$, with the plus sign used for relative approach and the minus sign for relative recede; the exactly analogous statement holds for the recorded change in WAVELENGTH, $\Delta\lambda/\lambda$. …