I think I am going to move the discussion here so math is not clogging up the other thread. Here is a similar build from another thread that I could find, but our final results are a bit different, so I think it is possible there might be some mistakes somewhere buried in all that math. I have shown all my work and double checked it so I think my numbers are right.

Here are the relevant posts. It will require a lot of help from other players, and especially from the GM, to break the sound barrier, but I am pretty confident it is possible to do it RAW. And to expand on this, is there a way to go even faster? How about the light barrier (186,282 miles per second; 299,792 kilometers per second)? The fastest we can go right now is 8,400 feet per second, or about 1.5 miles per second, so we still have a very far way to go. The "easiest" mathematical solution I can think of is to wait for about 17 more official speed doubling items/feats/etc. to be released, so the equation is simply 1.5 * (2^17) = 196,608.

Quote from Kaboom979 >>

Quote from MilestoGo_24 >>

With haste cast on you with far step, assuming you have a speed of 30 feet, and being a 2nd-level fighter multiclass with action surge, you can move almost as fast as me running from my problems.

 I put together the hypothetical build of a Tabaxi Fighter(2),Totem Barb (5, elk), Monk (13) with haste caste on them, the mobile feat, and the boots of speed magic item. Assuming I did my calculations correctly, I found this bad boy could hit 384 mph in a one turn burst (3400 ft in a single turn). This build would be very difficult to pull off and probably wouldnt synergize well in any other aspect (plus it requires the DM to give you stuff), but it will get you as far away from your problems as you could desire. 

Quote from XXXGammaRay >>

Quote from Vince_Snetterton >>

Quote from XXXGammaRay >>

Quote from Vince_Snetterton >>

Quote from XXXGammaRay >>

I remember reading a build somewhere on Beyond that can break the sound barrier. I do not remember the exact build, but it seems pretty fun for a one shot.

 The sound barrier at sea level is approx 770 mph = 4,065,600 feet / hour = 1129 feet / sec = 11,290 feet / turn.

Good luck creating a build using RAW that can do hat. And yeah, I have seen some of the Hasted Tabaxi Monk power-gamer set ups.

I do not see how this is power gaming. If anything, this build would be about roleplaying the fastest athlete in the land. Optimization might not be a core part of roleplaying for you, but optimization is a core part of roleplaying for others. If anything, some level of optimization is essential to roleplay and immersion, since characters who want to be the best at something requires optimization as part of that roleplay. If someone wants to roleplay as the best Pallid elf CSI agent, that character is going to max out their Int and Wis and do everything possible to get expertise in Insight, Investigation, and Perception.

Tabaxi can double speed, so it is 30*2 = 60.
Boots of speed would be 30*2*2 = 120.
Haste would doubles speed, so 30*2*2*2 = 240.
Dash allows you to move again, so (30*2*2*2)*2 = 480.
Haste would allow another action, so (30*2*2*2)*3 = 720.
Mobile grants speed +10, so (40*2*2*2)*3 = 960.

Using class loadout from above:
Barbarian 5 would grant speed +10, so (50*2*2*2)*3 = 1,200.
Barbarian elk totem would grant speed +15 during rage, so (65*2*2*2)*3 = 1,560.
Fighter 2 would grant another action via action surge, so (65*2*2*2)*4 = 2,080.
Monk 13 would grant speed +20, so (85*2*2*2)*4 = 2,720.
Monk 13 would also allow bonus action to dash, so (85*2*2*2)*5 = 3,400.

Using a modified class loadout from above:
Barbarian 5 would grant speed +10, so (50*2*2*2)*3 = 1,200.
Barbarian elk totem would grant speed +15 during rage, so (65*2*2*2)*3 = 1,560.
Fighter 2 would grant another action via action surge, so (65*2*2*2)*4 = 2,080.
Monk 10 would grant speed +20, so (85*2*2*2)*4 = 2,720.
Monk 10 would also allow bonus action to dash, so (85*2*2*2)*5 = 3,400.
Wizard 3 Bladesinger via Bladesong grants speed +10, so (95*2*2*2)*5 = 3,800.

Further modifications:
Boon of Speed grants speed +30.
Artifact #1 grants speed +10.
Artifact #2 grants speed +10.
Longstrider grants speed +10.
Transmuter's Stone from wizard grants speed +10.
Potion of Swiftness from artificer grants speed +10.
Mantle of Inspiration from bard allows reaction to move.
Totalling all that up, (175*2*2*2)*6 = 8,400.

8,400*10*60 = 5,040,000 feet per hour ~ 954 miles per hour

With some help from friends and divine intervention from a friendly GM, a Tabaxi can turn into a sonic hedgehog.

 So, forgetting that some of those modifiers might not multiply, but stack (that is an entire argument I am not going to get into), I believe you double-counted Boots of Speed.

Other that, let's see, your triple-classed 20th level char, that is attuned to TWO Artifacts, plus the Boots of Speed, and assuming there was a Bard, Wizard, possibly an Artificer present, AND the DM handed the char a +30 to speed, and assuming you did not double-count Boots of Speed (which you did), sure, you can break the speed of sound.

But no, the char can't do it alone.

Please point out exactly where Boots of Speed is being double counted and where exactly do things not multiply. You can highlight and bold things, and it is easy to point out where I could have made a mistake since I showed my work step by step. If saying no to players is fun, saying no to a fellow GM is not all that different, and you are doing it with facts too.

The goal post is doing it RAW, not doing it alone with further arbitrary limits that you make up on the spot. Breaking the sound barrier requiring a team effort (including the GM) is exactly the kind of fun roleplaying D&D can be about. Breaking the sound barrier might not be fun for you, but for groups sick and tired of imitating Tolkien and parroting stereotypes, something as simple as breaking the sound barrier is a fun refreshing campaign to break the monotony.

Considering abilities that boost your speed in the game don't factor in any of that stuff, no it won't. All this exercise takes is finding as many force multipliers as possible. 

Dissonant Whispers allows you to move your speed as a reaction. I think finding a way to get that to work in the build is key to maximizing the full movement potential.

Edit: Didn't see mantle of inspiration in the calculations. Last time I thought about a build like this Glamour Bards were not a thing. Mantle is definitely the better reaction based movement.

forget air resistance, gravity, and all the other real world stuff...even without it, its all pure speculation and homebrew as the order of operations just isn't defined.

Quote from HeathSmith >>

forget air resistance, gravity, and all the other real world stuff...even without it, its all pure speculation and homebrew as the order of operations just isn't defined.

 the generic answer to the first part of your response is "Magic." The second part of your response is entirely correct, as I don't think the developers of D&D considered that people would actually want or have a use for this.

Quote from Vince_Snetterton >>

I have made my comments on this. But if you are going to open up a thread devoted to this concept, you better add "how fast can you go in a vacuum?".

If a falling humanoid has a terminal velocity far less than the speed of sound because of the friction due to air, that same kind of friction applies to horizontal movement. Yes, I am aware that the char is applying a horizontal force vector with every step, which re-accelerates the char against the constant drag due to air.

But it will take some serious physics to calculate what a max speed is at sea level with air present.

I do not think RAW cares about speed in a vacuum. Adding in real world physics would be homebrew, and that would violate sticking with RAW.

Quote from HeathSmith >>

forget air resistance, gravity, and all the other real world stuff...even without it, its all pure speculation and homebrew as the order of operations just isn't defined.

While I do not think the order of operations is explicitly stated, I think all the stuff that says "walking speed increases by X" gets added to the base speed first, and then stuff like doubling speed from Boots of Speed gets applied. Although not all speed increasing effects are permanent, all the speed doubling effects are temporary, and I do not think it makes sense for the speed doubling effects to pick and choose which portion of the speed increases gets doubled and which do not.