Sound as compression or rarefaction of air

[jbriggs444]

OK, so you are talking about a true half wavelength. Overpressure followed by return to ambient.

This is still not realistic/possible. Even if the diaphragm did not complete a full cycle (i.e. it only went from x=0 to x=1 and back to x=0)

That's a full cycle. We're talking about a half cycle. The diaphragm goes out and does not come back.

 

[Vanadium 50]

The diaphragm goes out and does not come back.

But the air does.

 

[jbriggs444]

But the air does.

No. It does not.

The compressed air is in a sound wave that is proceeding rightward at the speed of sound. It never comes back.

 

[Vanadium 50]

Leaving an underpressure behind the speaker dome for all eternity? I don't think so.

 

[jbriggs444]

Leaving an underpressure behind the speaker dome for all eternity? I don't think so.

If the speaker membrane is embedded in a hole in a wall for instance then the underpressure behind the membrane will propagate leftward at the speed of sound as well. Ideally, that situation is limited only by the walls of your laboratory. More realisticly, the sound pulse will disperse, diffract and reflect until nothing is left but the original ambient pressure, of course.

Until that happens, pressure at the speaker membrane is ambient. After that happens, pressure at the speaker membrane is ambient. What's the problem?

 

[jerromyjon]

So an increase in pressure will cause a wave of condensation.

It would overshoot on its way to ambient,

Meaning it will be followed by rarefaction causing an oscillation as it passes your ear.

 

[DaveC426913]

If the speaker membrane is embedded in a hole in a wall for instance then the underpressure behind the membrane will propagate leftward at the speed of sound as well. Ideally, that situation is limited only by the walls of your laboratory.

Ah but this is a different setup. You are adding constraints.

 

[jbriggs444]

Ah but this is a different setup. You are adding constraints.

May I take that as an agreement that it is possible to come up with a setup that will produce a pressure waveform in air that consists of a good approximation of a single positive pressure pulse?

 

[sophiecentaur]

This all boils down to the Fourier transform of a step change, with an infinite time at zero, followed by an infinite time at 1. The result is very dodgy and is the subject of much debate (See this and other links). Best not to get involved in the theoretical bits if you do not have a strong mathematical stomach but the resulting spectrum will have infinite extent and be a continuous function of frequency.
You have to look at the practical situation of a real loudspeaker and a real room. Once the speaker diaphragm has moved forward, there will be a net movement of air forwards / outwards. The impulse will partly dissipate itself against the walls at the first impact or there will be reflections and these will also dissipate until the net pressure in the room is a minuscule bit higher than it started, due to the reduced volume.
Also, afair, a 'shock' wave is what is produced when an object is moving supersonically. Most loudspeakers don't do that.

 

[Fluxxx]

Ah but this is a different setup. You are adding constraints.

In my opinion that is okay, since I'm trying to find a physical setup where this situation is possible. See question 2 in post #29.

This all boils down to the Fourier transform of a step change, with an infinite time at zero, followed by an infinite time at 1.

No it doesn't, then you misunderstood my question. It is not a Heaviside function we are talking about here, but a "half wave". See post #29 for a description. It's more like a pulse, but without points of discontinuity.

 

[sophiecentaur]

OK then. You describe the time function and the Fourier transform will give the spectrum. You can band pass filter the pressure pulse in any way you like but the spectrum will have a width which is related to the time over which the pulse is non zero. (Narrow pulse - broad spectrum and vice versa).
I am not sure what the question is actually about; it seems to be shifting around quite a lot. It is a mixture of basic theory and various practical aspects of a thought experiment.
What are we trying to achieve?

 

[Fluxxx]

Ok, the main question is whether a "half wave pulse" disturbance in air pressure would be perceived by the human ear as sound (and if so how would it sound?) or something else.

Then people started discussing whether it is physically possible to create such a pulse, which I also think is an interesting question but that's not the main question.

 

[jbriggs444]

Ok, the main question is whether a "half wave pulse" disturbance in air pressure would be perceived by the human ear as sound (and if so how would it sound?) or something else.

If such a pulse cannot be generated then the question of how it would be perceived becomes irrelevant. Like "what is the sound of one hand clapping". Accordingly, the responses suggesting that no such pulse can be generated seem legitimately on point.

The idea that the human ear (and brain) could perceive such a disturbance at all without perceiving it as a sound seems far fetched and highly speculative. Fortunately, no one has gone in that direction.

We've had a couple of responses indicating the cilia in the inner ear can, at least in principle, be stimulated by a single pulse. If a single pulse is audible at all then, in my opinion, it would sound like a click, a pop or a bang.

 

[DarioC]

Ok, I will leave out the sarcasm this time, apparently the monitors have a limited sense of humor. You could generate a single pulse wave with a piston or a say a piece of plywood tipped on one end on a hard floor and then dropped. Would make a foof sound.

If anyone is really interested I could hook up a microphone and a scope and see what the wave form looks like from the plywood sheet. Don't think I want to get into the piston part, though it would likely be better. Wonder if the microphone would lie to me as it has moving parts.

I do have all the equipment required, and a large area aircraft hangar with an unused sheet of plywood in it.

May just do it anyway.

another edit: In response to your rephrasing of the question at 5:30 above: If you could generate a pressure pulse whether your ears would hear it would depend (as someone said, I think) on the rise and fall time of the pulse. If too slow, like being in a chamber and having the air pressure increased slowly and then released slowly would not be heard by your ears as sound.

Interestingly enough I have a cloud chamber I built and the pop-off valve on it that releases the pressure in the chamber makes a "chuff" sound when opened quickly. Has a leading "squeek" component also, but the chuff is midpoint in the very fast pressure release phase. Might be our pulse there. Thinking about that.

 

[jerromyjon]

Ok, the main question is whether a "half wave pulse" disturbance in air pressure would be perceived by the human ear as sound (and if so how would it sound?) or something else.

I was considering ear-bud headphones but then I became concerned with the health of my hearing which is beginning to decline already. I figured if I could supply the right amount of current to extend the diaphragm slightly and stop it would narrow the environment.