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?