Sonic Boom / Mach Cone

A point source moves at constant speed v through a uniform, stationary medium with c = 343 m/s. M = v/c. For M > 1 the envelope of the spherical wavefronts has half-angle μ = asin(1/M), measured from the backwards flight axis; Mach 2 gives 30°. At or below Mach 1 there is no open Mach cone. The envelope grows only as far as the available emission history permits.

The camera follows the source, which stays at the red arrow. A wave emitted at time b is centred at v(b−t) relative to the source and has radius c(t−b). Blue great circles represent spherical fronts emitted every 0.1 s; only the latest 1.6 s are retained. The amber envelope is truncated to fit the view without changing its angle. Grid spacing is 100 m; x is the physical source position in the stationary frame, starting at x=0 when t=0.

Show prepares the first paused view. Afterwards valid Mach or speed edits update it directly and pause playback without resetting the camera; invalid text clears the output without moving focus. Reset restores Mach 1.8, speed 617.4 m/s, time 1.2 s and the initial camera. Scrub time or play at half speed up to 4 model seconds; replay at the end starts at zero. Drag to orbit; Ctrl/Meta plus wheel zooms, plain wheel scrolls the page. Only the exact Mach/speed input text and the time explicitly selected with the slider are retained, including empty or invalid numeric drafts. Animated time, geometry, playback and camera are not saved. Returning to the tool waits for Show. The previous numeric speed/time and older semicolon speed format are migrated as initial input choices.

This is wavefront geometry, not a compressible-flow or pressure simulation. It does not predict shock strength, sound level, aircraft shape, real atmospheric propagation or a recorded sonic boom. Source: NASA Glenn: Mach angle.