The Humming Arrow

A Doppler Card — one tone, one track, one formula. The ticks are the crests; the bracket is the ruler. Listen to the geometry.
λ ahead λ behind AHEAD of the arrow: blue ticks crowd — short wavelength, high pitch BEHIND the arrow: tan ticks spread — long wavelength, low pitch you listen here observed pitch (Hz) vs time — dashed line = the arrow's true note
Press LAUNCH — the arrow takes a steady tone across the sky.
Speeds and distances are exaggerated for legibility; the ratios obey the true formula. The ticks mark each wavefront's crest as it crosses the flight line; the brackets measure the gaps between them. Schematic, not to scale. Hover the arrow, ticks, observer, stars, or the trace for terse notes and sources.