Were the first sonic booms predicted?
score:46
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 (See also this and this, which have some historical references, but none obviously connected with Yeager's flight.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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