= Acoustic Doppler measurement
{title2=$v=c(1-f_s/f_o)$}
UNSW School of Physics documents a <Doppler effect> experiment using a buzzer based on <piezoelectricity>, powered by a taped-on $9\,\mathrm V$ <battery>, and a computer's built-in <microphone>. Audacity records the <acoustic wave>. First record the stationary source to establish its baseline <frequency>; then attach it to a bicycle passing the stationary <microphone>. The published <spectrogram> shows a rapid decrease in <frequency> during passage.<Measuring velocities using the Doppler Shift at UNSW School of Physics>[UNSW, Measuring velocities using the Doppler Shift: Introduction, Figs. 1–2; Circular Motion, Measurements (2)–(3); Linear Motion:Bicycle, Moving Source]{ref}
For numerical readout, select an approaching or receding interval, display its <frequency spectrum> using Plot Spectrum, and read the interpolated Peak <frequency>. The protocol recommends repeating with slightly different selections to test stability, and working outdoors to reduce reflections and <standing waves>. Longer windows refine <frequency> spacing while averaging over more motion. The baseline controls for the source's actual tone; repeated selections expose analysis-window sensitivity.<Measuring velocities using the Doppler Shift at UNSW School of Physics>[UNSW, Introduction, final paragraph; Circular Motion, spectrogram resolution discussion; Linear Motion:Bicycle, Plot Spectrum and Peak instructions]{ref}
Under nearly collinear constant-speed approach, infer $v=c(1-f_s/f_o)$ from the <classical Doppler effect for sound>. For recession the positive speed is $v=c(f_s/f_o-1)$. These inversions need a specified <speed of sound>. An offset path changes the projection, as in <Doppler frequency along a trajectory>; neither inversion measures the full speed near closest passage. The protocol's controls cannot remove arbitrary <acceleration>, background <measurement noise> or unresolved reflected paths. No new measurements are claimed here.
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