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.