The sound “barrier” is just the speed of sound, specifically when it pertains to an object accelerating to and past it.
The air suddenly can’t get pushed out the way in the same way any more. It’s way easier to explain with a gif than in words:
What you see (sometimes, and it can also happen without breaking the sound “barrier”), is water vapor condensing out the air due to the pressure drop immediately behind the shockwave.
As for it being a barrier, drag increases sharply as you approach the speed of sound, and drops off after passing it (although never back to where it was when you where doing only 80% or so the speed of sound. This means that while aircraft might struggle to reach the speed of sound, they can frequently accelerate after passing it. There is also some incorrect maths you can do where the speed of sound has infinite drag, it’s wrong, but it created a bit of a reputation before anyone either knew why it was wrong, or had actually travelled faster.
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