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Applying the Doppler Effect to the breaking of the sound barrier would have allowed scientists to predict that a shockwave (a "boom") would be created before pilots began actually breaking the sound barrier. The Doppler Effect was discovered in 1842, long before planes could break the sound barrier.

When pilots began to break the sound barrier and create those booms, where scientist baffled and confused? Or, were they expecting that boom / shockwave?

Before Chuck Yeager, planes were breaking the sound barrier and creating booms but they then were crashing because the airframe / wings could not withstand the force of supersonic flight. So, no one knows when the first booms were noted by scientists. I just wonder how long it took for this very unexpected phenomenon to be figured-out. Or, was it even predicted because of the Doppler Effect?

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    Humans produced sonic booms long before there was a realized concept about the speed of sound, or that exceeding it produced. sonic boom. The tip of a whip travels faster than the speed of sound when cracked. While this was confirmed later (Wikipedia says 1958) than bullets or shells breaking mach 1, it was done many years preceding. I doubt that anyone would have figured out that the sound comes from breaking the speed of sound, specifically, unless someone first figured out what a sonic boom was. – bobsburner Dec 24 '19 at 11:00
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    An important innovation of supersonic flight regarding sonic booms, is that the engines of supersonic planes were the first powerful sound sources to travel faster than sound. A supersonic bullet or whip tip doesn't produce any sound of its own and therefore they can't produce any loud sonic boom comparable to that of an aircraft. – Pere Dec 24 '19 at 17:49
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    @Pere It is no clear to me how much of the sound energy reaching the ground in a boom comes from engine noise as opposed to the air pushed aside by the passage of the airplane. As a non-specialist I have to rely on expert authority. Do you have citations I should know about? – kimchi lover Dec 24 '19 at 18:48
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    @Pere No, the sound of the engines does not add to the sound of the sonic boom in any appreciable way. When the Space Shuttle was in operation and would return to Earth, it was gliding with no engines running but would make a sonic boom as it entered dense atmosphere. Compare that to fighter jets exceeding the sound barrier both heard from the ground. The sound of the engines is not always noticeable if there is any background noise, but the sound of a sonic boom will literally shake the ground. – krb Dec 25 '19 at 1:20
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    Aviation stack exchange says a lot about sonic booms; the answer to aviation.stackexchange.com/questions/17357/… seems to bear out what krb said. – kimchi lover Dec 25 '19 at 14:53
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Yes, and no. A 2003 survey paper "Sonic Boom Research: History and Future" by Plotkin and Maglieri says they were predicted by Mach in the 1870s, were known as "ballistic waves" when caused by artillery shells. (See also this and this, which have some historical references, but none obviously connected with Yeager's flight. They do cite a seminal 1946 paper A Determination of the Wave Forms and Laws of Propagation and Dissipation of Ballistic Shock Wave by Du Mond, et al., and the experimental work it reports, using small calibre AA projectiles, including the .50 machine gun bullet the X-1 was modeled on.)

There is an article "Crack of the bullet" in the 1923 Infantry Journal explaining that if a bullet leaves the muzzle faster than the speed of sound "... the flight of the projectile causes a cone shaped wave...", and that this phenomenon had been studied beginning in 1886.

This article is a translation of a 1921 article in Revue d'Artillerie; in late 19th century France ballistics research was carried out seriously by competent scientists. Presumably the article popularizes what was known from this research. (I heard a lecture by David Aubin on 19th century ballistics in France but have not read his paper.)

So the theory of the sonic boom was known, and examples heard, long before Yeager's flight. Plotkin and Maglieri state (in the one page not paywalled away from view) that it took a while to realize that aircraft-caused sonic booms were the same thing as the ballistic wave. So there seems to have been a period of scientific bafflement, but perhaps not as intense or as long as the OP seems to imply.

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    Incidentally, this was an era when France prided itself on having the world's best engineers. So the definitive research being done in French is not only unsurprising, but expected. – T.E.D. Dec 24 '19 at 17:38
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    @T.E.D. Presumably so, but not proven on the evidence I've sketched above. – kimchi lover Dec 24 '19 at 17:42
  • @T.E.D. That is very intriguing. Could you please recommend any further reading or books on French engineering from that era? I'd love to learn more about this! – Qasim Dec 27 '19 at 4:46
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    @Qasim - I first read about it myself in David McColough's The Path Between the Seas. Only the first few chapters cover French engineering in any kind of detail, but the rest is also worth reading for the story of how Germ theory first got put into action (shockingly against strenuous objection). – T.E.D. Dec 27 '19 at 6:35
  • Note that the fact that pressure waves limit the speed you can travel in a medium was known long before in ship design. The ultimate for boats is to move out of that medium - hydroplaning on top of the water. But the traditional solution is the same for boats and planes - make the body longer and skinnier. The main difference, and the thing that confused aircraft designers at first, was that boats don't have control surfaces (wings) that hit the waves – slebetman Dec 27 '19 at 9:23

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