Waldeck Schützer

Supersonic motion: waves pile up into a sonic boom

A moving source sends out a pulse every sixth of a second; each pulse spreads as a circle of radius c (t-t_i) around the place where it was emitted (sound speed c=343 m/s, one unit is 100 m, slowed down). Ahead of the source the circles crowd together, so a listener there hears a higher pitch, f_obs=f_0/(1-Mcosθ), where M=v/c is the Mach number. At M=1 the circles pile up at the source; for M>1 they have a common envelope, the Mach cone, with half-angle sinα=1/M: a listener on the cone receives many pulses at the same instant, which is the sonic boom (the right graph counts pulses heard per second and spikes there). Drag the listener, change M, and press the sound tick for the whoosh and…

Formula: sinα=(1)/(M)

Open it and play with the settings: https://www.dm.ufscar.br/profs/waldeck/en/art.html?item=sonic#sketches-2

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