16.4 Moving Observer, Combined Motion, and Reflections

For a moving observer, the source still emits into still air with unchanged spacing around a stationary source. The observer's motion changes how fast fronts are encountered. Moving toward the source increases encounter rate; moving away decreases it.

Because the medium spacing is unchanged for stationary source cases, observer motion does not alter wavelength in the air itself. It alters only meeting rate with those fronts, which is exactly what frequency records.

This expression reduces to each special case immediately by setting one speed to zero. It is efficient but only if your sign convention is explicit. Write one short sign sentence before substitution to avoid mixing opposite conventions from different textbooks.

In reflected-sound setups, the moving object first acts as observer and then as source of the reflected wave. That creates two Doppler stages. This is the basis for velocity measurements in Doppler ultrasound and speed-detection radar analogs that use acoustic waves.