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I've been talking to a friend, and he said that it's impossible to travel at exactly the same speed as the speed of sound is. He argued that it's only possible to break through the sound barrier using enough acceleration, but it's impossible to maintain speed exactly equal to that of sound. Is it true? And if it's true, why?

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The notion of a "sound barrier" is a popular misconception. –  Ben Crowell Sep 8 '13 at 20:28

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It's true that at the speed of sound, you will have a huge amount of drag. The reason is that the air in front of you has to move out of the way, and if you are moving at the speed of sound, the pressure wave that pushes the air out of the way is moving at exactly the same speed as you. So in the continuum mechanics limit, you can't push the air out of the way, and you might as well be plowing into a brick wall.

But we don't live in a continuum mechanics universe, we live in a world made of atoms, and the atoms in a gas bounce off your airplane. At the speed of sound, you get a large finite push-back which is a barrier, and above this, you still have to do the work to push a mass of air out of the way equal to your plane's cross section with ballistic particles.

As you go faster, the amount of drag decreases, since the atomic collisions don't lead to a pile-up on the nose-cone. But if you look at wikipedia's plot here, the maximum drag at the supersonic transition is only a factor of 2 or 3 higher than the drag at higher supersonic speed, so it is possible to travel at Mach 1, it is just not very fuel efficient.

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I read something interesting. Once you start going faster than the speed of sound, the drag force can actually decrease with increasing speed. Maintaining constant speed in this regime would be tricky because if you accidentally apply a little too much force, you will go faster and drag will decrease, so your speed keeps increasing for a while. Of course, this instability could probably be controlled, but controlling your speed in this region isn't as simple as it is normally. And wikipedia makes it look like this happens just above mach 1. –  NowIGetToLearnWhatAHeadIs Nov 12 '13 at 4:12

No, this is not true. Unlike the speed of light, for example, there isn't anything particularly special about the speed of sound that would prevent you from traveling exactly at it. There isn't really anything else I can explain about it without knowing what reason your friend gave for making his argument.

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