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The Doppler effect is the change in observed frequency when the source, observer, or both move relative to the medium. The master formula: $f' = f(v \pm v_o)/(v \mp v_s)$, where $v$ is sound speed, $v_o$ is observer speed, and $v_s$ is source speed. Convention: upper signs for approaching (higher frequency), lower for receding (lower frequency). Observer terms go in the numerator, source terms in the denominator.

The physical mechanism differs for source and observer motion. When the source moves, it compresses (or stretches) the wavefronts, changing the wavelength in the medium: $\lambda' = (v \mp v_s)/f$. When the observer moves, the wavelength is unchanged but the observer intercepts wavefronts at a different rate.

This asymmetry means that $f(v+v_o)/v \neq fv/(v-v_s)$ even when $v_o = v_s$ — a distinctly classical phenomenon arising because sound propagates through a medium. For light in vacuum, only relative motion matters (relativistic Doppler). The classical Doppler formula breaks down when $v_s = v$: all wavefronts pile up into a shock wave (sonic boom, Mach cone with half-angle $\sin\theta = v/v_s$).