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In a follow up to my previous question: How does the X-59 acheive quiet supersonic flight?

Canards and a long narrow airframe were cited as design choices to prevent shock waves from coalescing. How does this design shape achieve this goal? How does this shape affect the flow field such that the shockwaves do not coalesce? I want to understand this in terms of the physics and aerodynamics of the shockwaves. It would be useful to see a side-by-side comparison to other supersonic aircraft like the Concorde.

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After a lot of digging around, I found this.

...the main noise-reduction technique is to redesign the aircraft to reshape the acoustic signature. A sonic boom consists of a double bang on the ground that is caused by two large pressure pulses. As the random shockwaves travel away from the aircraft at the speed of sound, they pile up and coalesce. The engineers aim to reshape the acoustic signature of the boom by preventing sonic waves piling up.

“You shape every aspect of the airplane to make the shockwaves as close to equal strength as you can. When they’re as evenly distributed as possible along the length of the airplane, changes in temperature are small and the waves don’t coalesce. When the signal reaches the ground, it’s smeared out. Instead of two loud bangs, there’s a pressure change and a soft thump,” says Peter Coen, NASA’s commercial supersonic technology project manager.

Source: Aerospace Testing International, Dec 2018: Supersonic testing: Boom or bust?

I realize this doesn't answer the question of the physics, but I thought i would stick within my paygrade. Someone else who better understands what the fluid is doing can tackle explaining that.

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