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Explore When Do You Hear a Supersonic Jet's Sonic Boom? #physics #soundbarrier #science with 70,216 views, 546 likes, and 2 comments. Experience the impact of this video content that has captured audience attention.

A jet goes supersonic 9.8 km above you, and you hear nothing yet: the sonic boom reaches the ground about 19.7 s after the jet has passed overhead. What the reel shows: a fighter jet at full afterburner accelerating from Mach 0.90 to Mach 1.40 over a desert range at dusk, at the altitude and speed of NASA's SonicBAT test flights (9.8 km, 32,000 ft, Mach 1.40). At Mach 1 its sound can't get ahead of it and piles up. Faster, the pile-up trails behind as a cone, a Mach cone, whose angle is set by sin μ = 1/M: at Mach 1.40, sin μ = 1/1.40, so μ = 45.6°. The cone's foot first touches the ground far behind the jet. Three people stand on the range; each starts a stopwatch as the jet flies over, and each stops it when the boom arrives: 19.7 s after the jet passed. Nobody hears one bang at the moment of Mach 1. The boom is heard all along the ground track, wherever the cone sweeps over. Why: the sound the jet sends out can't outrun it, so each pulse is left behind and they pile along a line, the cone. That cone sweeps the ground as the jet flies on, and a listener hears the boom only when it reaches them. In air of one temperature the wait would be t = h√(M² − 1)/(Mc). Real air is colder high up, so the cone bends and lands sooner. Simplified: the wait comes from tracing the cone through air that cools with height (the standard atmosphere), so it is 19.7 s, where the one-temperature formula gives 22.7 s, 15 % more. The jet, the people and the stopwatches are drawn far bigger than they are, the distances are true. Time is sped up (the stopwatches count real seconds). Left out: the ground's echo, wind, and the boom's two shocks, 0.12 s apart, drawn as one line. The full list is in the pinned comment. Sources: OpenStax University Physics Volume 1, sections 17.7 and 17.8 (shock waves, the Mach cone). NASA SonicBAT, Edwards, July 2016 (Haering et al.): the test point. GAO/NSIAD-96-98: an F/A-18C's acceleration at maximum thrust. Carlson, NASA TP-1122: the N-wave of a sonic boom. ISO 2533: the standard atmosphere.

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