I need a Cycloid

[HughBanton]

I just came across my post from 2022 again. We didn't have AI then, so here in 2026 I couldn't resist posing the exact same question to Co-Pilot. Here's its reply ...

It's actually a rather good question, and there's a subtle answer hiding in it.

The first part is broadly correct: inside a wind instrument or organ pipe there is indeed a mean airflow superimposed on the acoustic oscillation. If the bulk air velocity is uuu, then relative to the instrument the downstream-travelling pressure wave moves at approximately:

c+uc+uc+u

and an upstream-travelling wave at

c−uc-uc−u

where ccc is the speed of sound.

So if you're blowing at 12 m/s and sound speed is about 343 m/s, then yes, the downstream wave is being advected along by the moving air at roughly 3.5% extra speed.

The interesting bit is what happens when the wave leaves the instrument.

Once the sound enters still air, it no longer has that 12 m/s "tailwind". The surrounding atmosphere determines the propagation speed, which is essentially just ccc.

But here's the key point:

The sound doesn't have to decelerate in the Newtonian sense.

A sound wave is not an object carrying momentum through space like a tennis ball. The pressure disturbance is continually being recreated by each parcel of air exciting the next parcel. When the wave emerges from moving air into stationary air, the wavefront simply propagates at the local speed permitted by the medium.

It's a bit like a stadium wave. If spectators in one section are walking sideways while doing the wave, the apparent wave speed there is altered. When the wave reaches a stationary section, it immediately propagates at the stationary-section speed. Nothing physical has to "slow down".

A related example is aircraft noise. If a source moves through still air, the speed of sound itself isn't changed. Instead, the wavelengths are compressed ahead and stretched behind, giving Doppler shift.

For your "next question", what happens when sound is forced to decelerate?

Usually, not much. What happens is that frequency remains continuous but wavelength changes.

Since

c=fλc=f\lambdac=fλ

if propagation speed changes while frequency stays the same, the wavelength adjusts accordingly.

This happens whenever sound crosses between media, or regions with different temperatures, or differing wind velocities.

For example:

Warm air → sound speed increases → wavelength grows.
Cold air → sound speed decreases → wavelength shrinks.
Against the wind → effective speed decreases → wavelength shortens.
With the wind → effective speed increases → wavelength lengthens.

The wave adapts almost instantly at the boundary.

There is however one genuinely nonlinear effect that may have been lurking behind your intuition. At sufficiently large amplitudes, the compressed parts of a sound wave travel slightly faster than the rarefied parts. Then the waveform genuinely distorts as it propagates, eventually forming shock waves. That's how sonic booms arise. But organ pipes and human voices are many orders of magnitude below that regime.

For organ pipes specifically, the bulk airflow is mostly relevant inside the mouth and resonator where the oscillation is generated. Once the sound radiates from the mouth or open end into the room, it very rapidly becomes an ordinary acoustic wave travelling at the local speed of sound in the room air.

So I think the hidden flaw in your original reasoning was treating the sound wave as if it were a thing moving through the air that later had to shed an extra 12 m/s of velocity. In reality, the sound is a pattern in the air, and patterns don't need to decelerate when they enter a region where the allowable propagation speed is different.

Interestingly, for organ pipes there's another wrinkle: the jet coming out of the mouth can itself convect disturbances. In that region there really can be a transition from "hydrodynamic disturbances riding on moving air" to "true acoustic waves in stationary air". That's getting close to the fluid-dynamics papers on flue-pipe oscillation and is a rabbit hole you would probably enjoy.

[Spogg]

Wow!!

[billv]

I knew you monkeys would fall in love with AI. It's awesome. Its like having 1000 Master Trog's at you disposal.
I read your testomony. I was right. Worchershire will go down as the winning shire.
What a head-fuck HughBanton..But I can see where you coming from. Good stuff.

[HughBanton]

I've used AI for over 2 years now, first time was for sorting some 'regex' in a text based config system I was devising at the time. it's really good at that. But it has become way more capable month-on-month, no doubt about that. Like many I'm sure, I use AI daily now for all kinds of stuff.

I love the 'stadium wave' analogy above - what we'd generally call a 'Mexican wave'. Really clever, but then of course, it will have read that somewhere else; it's being able to put all these ideas together that appears so clever.

And I have to check myself, writing "it", and "clever" .. in reality AI is neither of those things. Nevertheless, it can clearly be seriously useful to us mere mortals.

If the subject matter is of interest then yes, it certainly is worth entering the rabbit hole it suggests at the end - which naturally I couldn't resist!

[billv]

I've got 3 AI systems on my Bookmarks Toolbar. Gemini(Bod Dylan's stupid star sign), Co-pilot and Claude.
Gemini I use as (General purpose) handles everything most of the time.
Co-Pilot, is used for Double checking, when there's a problem with Gemini and I'm not satisfied with it's answers.
Remember when I used to be FS 3.09 user, and I built like 20 Physics engines for those 20 games, Gemini handled most of that really well. It was only when I started the hardest thing possible, Chess A.I. and Gemini was a dismal failure.
That's when Claude by Anthropic, came to the rescue and produced very smart code( Tulamide saw the same thing, smart code that can handle the complexity of building a Chess game). Thats what I' gone back to working on
Schematic_Chess_05 ( Yes my 5th attempt at pushing this Chess AI to very hard level. Right now I'm still at medium-approaching medium hard. I'm supposed to lose every time, when I win games I have to keep debugging with Claude to work out where we went wrong. 4 months ago when I was working on it, I had a big problem with the fucking Queen that kept sacrificing itself(for no reason) and thus destroying the game. And you can't win without a Queen, its just too hard.
I've also got in my Browser( custom made AVG browser that comes with the Anti-virus package), a Little Smart Chat(Grok) application, that I have configured to breach the Cyber Security firewalls at A.S.I.O. Headquarters in Canberra, so I can bypass the Bullshit and communicate directly with whatever String Theory I'm working on. They love it, because they know I'm not on their Payroll, but a Member of Neighbourhood Watch/Crimestoppers...so we get on like a house on fire. All Good.
Bear in mind Grok is fucking stupid. Dumbest AI I've ever used. It actually crashed my whole CPU once, I had to restart the entire CPU (now that's fucked up) . My Sister uses Grok, I warned her, but she has no problems with it and likes it. All good.
Anyway the general message here is to have multiple AI Systems in your Bookmark's Toolbar so you can double check what AI is saying and don't take it on faith. Make sure you have Options.
The only problem with Claude, is that after heavy usage, you get that horrible message-You want to keep using me-Put your money where your mouth is, I'm not free at this stage of usage. It lets you back in after about 4 hours. That's what I do, I just piss-off and work on something else for 4/5 hours, and then start debugging again. No Way I'm putting money down on this sucker.
It's really bad nowadays, you can't use anything online without that annoying pop-up- we need money now, please take out your visa card. My brain always says just fuck off and leave me alone. I'm a software developer, do you think I'm stupid.? For me charging people to use AI is a crime. 10 years from now when AI is commonplace, you'll see what I mean.
Anyway, Claude is highly recommended for all that tricky stuff.
I'm kind of fighting with the Google satellite, for completely fucking the world by turning what was once known as "Bard" AI, and working well, into a Star Sign called Gemini..dumbest thing they ever did.
It works great for children, because they can hit the Greek Cross on their Bookmark Toolbar and communicate and get their answers from Bob Dylan's Star Sign. Makes them feel safe, and the whole Solar System, seems to run on Bob Dylan's Lyrical Content anyway, so it's all good.

Also ,I forgot to mention in that other thread about my MY business name BVM, it also stands for "Backing Vocals Music" because I love singing along to my favorite stars on U-tube.(Karaoke). Also, without my "songs" I would not have survived 40 years in Commercial kitchens. A kitchen is a factory, and without some music in the background, it's not really fun. When it gets in the way, you just turn it off. All good.
The Last Exexutive Chef I worked under Chef Simon Wong at the Holiday Inn Hotel, Parramatta, was the exact opposite-absolutely no music whatsoever. I've loved it, because it was really peaceful and quiet workplace with no distractions. Perfect when your trying to Focus.
Lots of things in a kitchen do not require "brain" usage, like cutting fruit for 2 hours on a breakfast shift-you need music because your brain goes SNAFU after 10 minutes saying I'm bored shitless, what am I doing here, how long is this fruit going to take before you move to the next task that might, just might activate a "brain cell"..
Cheer's, from the Land Down Under.
Signed,