Sound as compression or rarefaction of air

[Fluxxx]

When a loudspeaker moves back and forth, sound is generated. The moving of the loudspeaker diaphragm causes condensation of air when it moves outward, and rarefaction of air when it moves inward. When this movement is happening at a certain frequency, we hear a sound. See for example this illustration:

https://www.physicsforums.com/attachments/sound-gif.84528/?temp_hash=012fb293b7e650bf392ecc98c949c953​

I was thinking about this and I understand we perceive the condensation/rarefaction as sound. But what happens if we have only one or the other? I.e. if we have a loudspeaker only moving from it's initial position outward ONCE, only condensation of air happens. In the illustration above, this would correspond to only one crest of the wave, but no trough.

Same question goes if the loudspeaker only moves backwards from it initial position once, so there's only rarefaction (one trough, no crest).

So my questions are:
1. If ONLY ONE condensation (one "crest") is happening, will we still perceive it as sound?
2. If ONLY ONE rarefaction (one "trough") is happening, will we still perceive it as sound?
3. If the answer is yes to any or both of question 1 and 2, are the sounds in 1 and 2 different from each other? If so, how?
4. If the answer is yes to any or both of question 1 and 2, are the sounds different from a sound that contains both condensation and rarefaction? If so, how?

 

[Vanadium 50]

If you have a crest without a trough, where did the extra material come from?

Your question is based on an impossible premise, I'm afraid.

 

[Fluxxx]

So what happens if the diaphragm of the loudspeaker only moves outward once from it's initial position? Wouldn't that create only condensation - i.e. only a crest?

 

[Vanadium 50]

The answer is still no. If you have an overpressure and not an underpressure, where does the extra material come from?

 

[jbriggs444]

The answer is still no. If you have an overpressure and not an underpressure, where does the extra material come from?

From half a wavelength (or less) over?

You move the speaker membrane in toward the room by some increment. The air displaced by this motion is a local excess. The pressure associated with this local excess causes material to move further into the room causing a local excess farther in. And so no. The phenomenon is called a wave. Ignoring dispersion, many wave shapes are possible. Including a wave form that consists of a single pulse above or below the baseline.

Of course, if one has a single pulse in the middle of an otherwise flat baseline, one might argue that the baseline amounts to a single infinitesimally deep trough.

Or am I failing to take your point?

 

[CWatters]

How about the pressure wave/pulse from an explosion?

 

[Vanadium 50]

How about the pressure wave/pulse from an explosion?

Makes for a poor loudspeaker. Too much harmonic distortion.

 

[CWatters]

I see no reason why you can't also create a negative pulse. For example by evacuating a cylinder slowly until it fails (or a diaphragm in the wall fails).

 

[boneh3ad]

The answer is still no. If you have an overpressure and not an underpressure, where does the extra material come from?

The premise almost works. You would have a pulse that quickly drops to ambient after the speaker finishes its movement. It would overshoot on its way to ambient, I'd wager, thus conserving mass. So in that sense it's still one wavelength, not half a wavelength as originally proposed.

 

[DaveC426913]

Regardless of half versus full wavelength arguments, a single pulse is tantamount to an infinite wavelength, which is a frequency of zero. We do not perceive sounds below 20Hz. Elephants can perceive sound down to 10Hz.

But 0Hz is not a sound. It is simply a shock wave. And I don't think it's physically possible to have one alone.

 

[jbriggs444]

Regardless of half versus full wavelength arguments, a single pulse is tantamount to an infinite wavelength, which is a frequency of zero. We do not perceive sounds below 20Hz. Elephants can perceive sound down to 10Hz. But 0Hz is not a sound.

Nonsense. A single pulse has Fourier components at infinitely many wavelengths.

 

[DaveC426913]

Nonsense. A single pulse has Fourier components at infinitely many wavelengths.

How does that negate anything I said?

 

[jbriggs444]

And how does that make it a sound?

Because it is a compression wave in air with a component at audible frequencies.

 

[DaveC426913]

(EDIT: changed the question)

Because it is a compression wave in air with a component at audible frequencies.

What frequency would that be? A single overpressure?

 

[jbriggs444]

(EDIT: changed the question)

What frequency would that be? A single overpressure?

Infinitely many, as already stated.

Edit: The question is ill-posed. You have to specify the wave form for the single pulse before its components are determined.

 

[DaveC426913]

Infinitely many, as already stated.

Are you asserting that a single overpressure would result in a person hearing a sound at all frequencies?

 

[jbriggs444]

Are you asserting that a single overpressure would result in a person hearing a sound at all frequencies?

Have you ever heard of Fourier analysis?

 

[DaveC426913]

Have you ever heard of Fourier analysis?

I have. I think you are caught up in the mathematics of the problem, and have lost sight of the question being asked, which is about perception.

Ears do not hear Fourier transformations. Ears require periodic pulses to interpret them as sounds.

 

[jbriggs444]

I have. I think you are caught up in the mathematics of the problem, and have lost sight of the question being asked, which is about perception.

Ears do not hear Fourier transformations. Ears require periodic pulses to interpret them as sounds.

Reference, please.

You have falsely claimed that a shock wave is 0 hz. I'd like a reference for that claim as well.

 

[DaveC426913]

The onus is on you to demonstrate the relevance of post #11 - Fourier transformation in the perception of sound. I think you've diverged onto a tangent. (My post 12 essentially says: "relevance?")

(Dang. Gotta step out. Won't be online for a few hours. But I'll be back.)

 

[DaveC426913]

Your post 11 claims that a shock wave is a "tantamount to" a frequency of zero. The onus is on you.

That is not what I said. I said the vice versa. That a single overpressure is tantamount to a shock wave (i.e. as opposed to a sound).

I then went on to say that it cannot be a REAL shockwave (I really did. Go check.)

The reason it can't be real is because a real shockwave will have harmomics (I did not elaborate to that extent. I think that omission is what you ran with.)

The OP is describing a hypothetical event, not a real event. I am saying that the hypothetical event is essentially an idealized shockwave - a single overpressure with no underpressure and no harmonics.

Fourier analysis will not apply to such a shape as the OP is describing.

 

[jbriggs444]

That is not what I said. I said the vice versa. That a single overpressure is tantamount to a shock wave.

I then went on to say that it cannot be a REAL shockwave (because a real shockwave will have harmomics - I did not explicitly say that).

The OP is describing a hypothetical event, not a real event. I am saying that the hypothetical event is essentially an ideal shockwave - a single overpressure with no underpressure and no harmonics. Fourier analysis will not apply to such as shape as the OP is describing.

Fair enough. My initial objection was to the use of the descriptive phrase "0 hz" when better phraseology might have been "no single definable wavelength". The above characterization makes things more clear.

So now I am trying to wrap myself around the notion that a single half wave pulse will not have harmonics. Possibly that is a matter of terminology with which I am unfamiliar. So try this...

It would seem clear to me that an aperiodic wave form, if expressible as a sum of periodic wave forms, must have components at infinitely many frequencies. If it has components at audible frequencies, these would excite detectors in the human inner ear. Clearly, a single half-wave is not a periodic function. So, barring the possibility that all such components are inaudibly faint or at inaudible frequencies, one would expect some excitation of the inner ear.

What am I missing with that argument?

 

[jerromyjon]

I see this as simply a change in pressure, similar to changing altitude in atmosphere. That is, if the front and rear of the speaker are isolated. If not, the compression on one side would dissipate into the decompression on the other side of the diaphragm. If the compression reaches your ear and is decompressed quickly enough (but not too quickly) wouldn't that constitute an audible wave?

 

[boneh3ad]

I have. I think you are caught up in the mathematics of the problem, and have lost sight of the question being asked, which is about perception.

Ears do not hear Fourier transformations. Ears require periodic pulses to interpret them as sounds.

Ears effectively do hear the Fourier transform, as the cilia in your ears are all tuned to their own resonant frequency and sense that portion of a sound signal. The pulse may not have a single frequency in the sense of an infinite signal length, but it definitely has a characteristic frequency that corresponds to the pulse width (otherwise known as the pseudofrequency in the field of wavelet analysis). Your ear would absolutely be able to hear that provided it's amplitude was large enough and it was in your hearing range.

 

[DaveC426913]

So now I am trying to wrap myself around the notion that a single half wave pulse will not have harmonics. Possibly that is a matter of terminology with which I am unfamiliar.

I think that's the general consensus here: that the OP's conjecture of a single half pulse - without harmonics, let alone a without restorative half pulse - is highly unrealistic, if not downright physically impossible.

It would seem clear to me that an aperiodic wave form, if expressible as a sum of periodic wave forms,

What if it is not expressible as a sum though? Then the rest does not follow.This is what the OP is describing:

 

[jbriggs444]

I think that's the general consensus here: that the OP's conjecture of a single half pulse - without harmonics, let alone a without restorative half pulse - is highly unrealistic, if not downright physically impossible.

The condition of having an excitation of a single frequency only is not one that I see in the OP. Not being able to see the image in the OP, I had assumed a crest without a trough rather than a rising edge without a falling edge. Yes, I agree that a rising edge without a falling edge would be difficult or impossible to arrange since it implies a permanent change in ambient pressure over a wide area.

What if it is not expressible as a sum though? Then the rest does not follow.

Surely any suitably continuous waveform over a finite interval is approximately expressible as a such a sum.

 

[DaveC426913]

it definitely has a characteristic frequency that corresponds to the pulse width (otherwise known as the pseudofrequency in the field of wavelet analysis). Your ear would absolutely be able to hear that provided it's amplitude was large enough and it was in your hearing range.

It had never occurred to me that the ear would be sensitive to the pulse width.

 

[DaveC426913]

The condition of having an excitation of a single frequency only is not one that I see in the OP. Not being able to see the image in the OP, I had assumed a crest without a trough rather than a rising edge without a falling edge.

Frankly, I cannot see it either.

You're right. If it were a single overpressure, followed by a return to ambient, you would be able to determine the frequency and wavelength.

I read the OP as suggesting an overpressure without return (really, that's a quarter of a pulse). Subsequent posts suggest this is the general assumption.

 

[Fluxxx]

Sorry for not having posted here the last days, I was on a trip. I read your replies, and I feel like I should clarify my original question. I don't know why the image in the original post disappeared, as I uploaded it here as an attachment in the forum, are these attachments just temporary, i.e. disappear after a while? Anyway here's the image again, from an external url:

On the illustration there is the result of a loudspeaker vibrating forward (causing condensation) and back (causing rarefaction). I think the question might include several questions, so let's take them one by one.

1. Assume that the speaker, instead of moving forward and back (like regular when sound is heard) it is only moved forward ONCE. Since forward movement (i.e. x>0 from initial position, x=0) causes condensation and backward movement (x<0 from x=0) causes rarefaction, only one forward movement would cause only condensation, right?

2. If the above physical condition is not possible to create only a condensation, would there be another situation where it would be possible? DaveC and jbriggs suggests some kind of shock wave or pulse. Could such a shock wave/pulse be created physically?

View attachment 84586
This image is not correct, instead look at the illustration above, remove everything below the x-axis. Now you have two crests. Remove one of them. So there is what I am trying to determine, only one crest (condensation).

3. Hypothetical: Assuming such a pressure wave described above can be generated, how would it be perceived by our ears? Would we perceive it as sound or something else?

 

[DaveC426913]

1. Assume that the speaker, instead of moving forward and back (like regular when sound is heard) it is only moved forward ONCE. Since forward movement (i.e. x>0 from initial position, x=0) causes condensation and backward movement (x<0 from x=0) causes rarefaction, only one forward movement would cause only condensation, right?

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), the air itself would still return on its own because you would have a situation where there is a slightly higher pressure to diagram-right and a slightly lower pressure diagram-left. The air would move back to replace it.

 

[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.