Shock cones, boat wakes & compressibility

8:30>> Uh so like it'll it'll like like it'll be wider or more narrow based on >> based on how fast you're going. It's kind of like the wake on a boat, right? It's the same same principle is like the the waves in the water are moving at a certain speed, but your boat is piercing through that disturbance faster than the waves can proliferate. Yes. Right. And what ends up in in water, you're not getting this compressibility thing because it's it's just water. It's in it's in it's a two-dimensional sort of surface in three dimensions. So, it can dissipate its energy in this like Z direction, right? But but in sound, the energy has nowhere to go. And so, you're just piling up these air particles one on top of the other, right? >> So, that's the pressure wave that you

9:11get when you go supersonic. >> Okay. >> Okay. We figured that out. Obviously, we have the we have the F-16s and all of these like really nice military jets. We have the Concord that used to be a >> the only commercial supersonic jet. >> Yeah. >> That has not been replicated at scale yet. >> Since Yeah. I think there's there's recent things coming out of Boeing and NASA that are trying to resurface that and they're trying to make a version of the Concord without the sonic boom >> without sonic boom >> which is going to be very cool. There is I do know and I because they're abusing me with advertising on X. There is a uh startup >> uh that is doing supersonic

9:53jet uh they're building their own supersonic jet platform outside of the primes. >> I'm not saying they're accomplishing it, >> but that's what the advertising is putting forth. I mean nowadays with like the the access to computation and AI and all that stuff, I wouldn't be surprised if a if a small rag tag team of engineers like cracks Yeah. >> you know certain problems, >> which is fair. >> So, so that would be very interesting. So, okay, we've gotten to supersonic, right? >> Yes. >> Then there's something called hypersonic. The definition of hypersonic is greater than Mach 5. So, five times the speed of sound. >> Five times the speed of sound. Got it. And there the air behaves even more differently. >> Okay. The physics turns into a different

10:35animal altogether. >> It's kind of like levels in a video game. And like when you get to level two, it's it's harder than level one. >> It is harder than level one. And now we're here in level two, right? What ends up happening is the physics of the air starts mattering. Before you could just treat it as an ideal gas. Ideal gas meaning a bunch of point particles that are bumping around. Sure. Like even even the speed of sound you can derive that actually um you know in in physics at Princeton physics um one of the problems on the final for statistical mechanics was to derive the speed of sound from

11:16first principles. And I remember being like, "Thank goodness." Because like half an hour before the test, I saw this derivation and I was like, "I'm just going to memorize it." And and then and then it came up on the test. I was like, "Dude, I got this." And I just like and just like wrote it down >> and and then some of my classmates afterwards was like, "What the hell was that?" And I was like, uh, you know, I just randomly happened up on that page and I was like, this is something that I should probably just know how to do. >> Yeah. >> In case. And it it was the exact problem. Oh my gosh, I love that. >> That's so >> it's it's a really cool problem where you basically treat the particles like billiard balls, like an ideal gas. And

11:57you start asking like how how the the dissipation, how these billiard balls will >> bump into each other to create the effect of sound. Yep. And then and then how fast that sound is going to go in terms of temperature, density, and things like that of the air, right? And the mass of the particles even Yeah. Yeah. There's like there's there's terms that go into that derivation. >> So, >> Yep. >> Um, all that is fine before hypersonic, >> right? >> Okay. When you get to hypersonic, then you start caring about what is the air made out of. >> Yes. >> It's not pointlike particles. Most of it is nitrogen and oxygen. Okay. >> And those are diatomic particles. Okay. Right. Diatomic molecu molecules.

12:38>> Yes. >> So diatomic molecules means you've got two atoms. Nitrogen is an N2. >> Oxygen is an O2. >> Yep. >> And those guys have other degrees of freedom. They don't just move. >> They also vibrate >> and they also rotate. >> Okay. So there's other ways in which energy can affect them. So, and so the