Why is the speed of sound the limit to which air can be accelerated in a nozzle without a diverging section? Why sound...

Why is the speed of sound the limit to which air can be accelerated in a nozzle without a diverging section? Why sound, instead of, say, electromagnetic waves, or some arbitrary constant determining the "speed limit" of particles?

What is the relationship between sound (pressure waves) and matter with respect to velocity?

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Molecules don't travel as electromagnetic waves.

The speed of sound is the limit because that is how fast the particles travel.

What kind of non-answer is that?

Molecules don't travel as pressure waves, either, not in this context. We are talking about a mass flow of air that cannot be accelerated past a certain point without a change in geometry, due to a handful of equations, choked flow, etc etc.

My question is why is that certain point related to "the speed of sound", or the speed at which an infinitesimally small pressure wave would propagate itself through a medium. Why sound? What's the special relationship with sound and the mass flow we are trying to accelerate?

Because the nozzle is effectively the same as a pressure wave traveling through the medium.

Imagine the air is stationary and the nozzle is moving, the physics are exactly the same and so is the wave.

Perhaps it's down to the sound waves and the air which is "transmitting" these sound waves suddenly travelling at the same speed and sort of crashing with each other. Maybe akin to feedback of some sort.

So it's because we treat the matter as it moves similar to a wave? I suspected that had something to do with it. Does this have anything to do with wave-particle duality, or is it unrelated?

You're looking at it backwards. Sound is just the acceleration of particles caused by fluctuations in pressure, so of course that's going to be the limit. The acceleration limit is the reason sound travels at the speed it does, not the other way around.

>Does this have anything to do with wave-particle duality, or is it unrelated?
Unrelated, Wave particle duality is some seriously weird shit that doesn't really make sense to me even though I know it is true.

Ohhh...I thought sound was the pressure difference (wave) itself. Sound is the actual acceleration of particles due to the pressure wave?

Because if you start with a medium at rest and introduce a small disturbance, the information about that disturbance, the energy introduced, will radiate away through the medium as a pressure wave. The speed of that wave is the speed of sound. These waves are nice and simple, near equilibrium, small disturbances, don't interact with each other.

If an object moves subsonic through air, its presence will be felt/heard before it arrives and the disturbance it creates is radiated away in all directions.

When something moves supersonic through air, it slams into unsuspecting air with no warning and keeps ramscooping everything in its path, which creates a huge shock wave. It breaks all the nice near-equilibrium small-disturbance stuff because it is moving faster than the medium can handle information.

A wave is a disturbance in a medium. The medium is composed of matter - atoms, molecules, etc - but these are bound to each other and are not transmitted by the wave.

Imagine a lot of people holding hands in a straight line, the wave is more or less each person doing an "ola", i.e., each one jumps in a certain time but they never jump one in front of the other. This is a transversal wave, but you get the idea. The wave is not the people, it is the disturbance of the medium composed by people and is the thing travelling.

Now, a wave in a medium is kinda the carrier of interaction in that medium (waves transmit energy and momenta, but not matter) and thus its maximal speed limits the speed of interactions related to that medium.

So the air in the nozzle can only attain a speed limited by the speed of sound in the air, because waves in the air are soundwaves.

Electromagnetic waves are special because they can propagate without a medium composed of atoms, molecules, like the vaccum, but the nozzle dynamics, so to say, is not related to electromagnetic waves/radiation, but is related to the interactions between the molecules of the air.

Okay...so then why does a simple change in geometry change the ability of the air to bypass the speed of the wave? Aside from the differential equation of area and velocity, I know how it works mathematically.

Also, OP here, it hurts that in both Phys I and II our crappy professors fell behind and skipped the wave motion/acoustics sections.

there's a separate course for that at my skool, I did it

>Ohhh...I thought sound was the pressure difference (wave) itself. Sound is the actual acceleration of particles due to the pressure wave?

It's both. Sound doesn't exist without a medium for sound to move through. In science, it's generally easier to talk about and manipulate the pressure wave itself, so that's generally how it's explained, but in reality, sound is just particles moving through space in a very particular oscillatory fashion.

Aww man. Acoustics is a really neat subject. That does suck

Good explanation here.

The speed of sound is the maximum average speed molecules in a continuum can move without creating a pressure discontinuity /shock wave (which incidentally, only moves slightly faster than a sound wave.)

A sonic boom is caused by the buildup of energy in a wave.

>the maximum average speed molecules in a continuum

maximum 'average relative speed' not 'average speed'

mechanical air waves cannot move faster than sound. when particles themselves move faster than sound, they eventually collide into sound waves and cannot penetrate them without turning into plasma. this happens at sufficiently high reynold's numbers but not in the context of a fighter jet engine

so air only moves the fastest at the speed of sound because the speed of sound stops air from moving faster

I like the derivation for speed of sound.

dp/du = rho*u

sleek physics

Interesting to note that *sound* waves cannot move slower than the speed of sound either...

they only move at the speed of sound, which depends on the molecular properties of the medium.

Compressibility of the medium, related to pressure and stuff
I don't know the actual equation

grc.nasa.gov/www/k-12/airplane/snddrv.html

dm/dt = rho u A, m = mass, rho = density, u = velocity, A =area

Plus momentum equation:

du/dt =1/rho * dp/dx, p=pressure, x= distance

use those 2 to derive speed of sound