# Sound as compression or rarefaction of air

1. Jun 6, 2015

### 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 [Broken]​

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?

Last edited by a moderator: May 7, 2017
2. Jun 6, 2015

Staff Emeritus
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.

3. Jun 6, 2015

### 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?

4. Jun 6, 2015

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

5. Jun 6, 2015

### jbriggs444

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?

6. Jun 7, 2015

### CWatters

How about the pressure wave/pulse from an explosion?

7. Jun 7, 2015

Staff Emeritus
Makes for a poor loudspeaker. Too much harmonic distortion.

8. Jun 7, 2015

### 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).

9. Jun 7, 2015

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.

10. Jun 7, 2015

### 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.

11. Jun 7, 2015

### jbriggs444

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

12. Jun 7, 2015

### DaveC426913

How does that negate anything I said?

13. Jun 7, 2015

### jbriggs444

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

14. Jun 7, 2015

### DaveC426913

(EDIT: changed the question)
What frequency would that be? A single overpressure?

15. Jun 7, 2015

### jbriggs444

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.

16. Jun 7, 2015

### DaveC426913

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

17. Jun 7, 2015

### jbriggs444

Have you ever heard of Fourier analysis?

18. Jun 7, 2015

### DaveC426913

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.

19. Jun 7, 2015

### jbriggs444

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

20. Jun 7, 2015

### 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.)

21. Jun 7, 2015

### DaveC426913

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.

Last edited: Jun 7, 2015
22. Jun 7, 2015

### jbriggs444

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?

23. Jun 7, 2015

### 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?

24. Jun 7, 2015

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.

25. Jun 7, 2015

### DaveC426913

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.

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

This is what the OP is describing: