I mean ‘sound’ in the sense of ‘pressure wave’ here; I’m not asking what the highest frequency audible to humans or any other animals or even current detection equipment is. I’m wondering if there is a limit based on the specific conditions of the transmitting medium. For the purposes of example, assume sea-level air at a temperature of 300 K.
Let’s say there’s some piston producing the sound. Assume for now that the piston is infinitely rigid and can move as fast as we want it to, and has a reasonably large cross-section. I understand those assumptions may not be trivial to the question, but I’ll start with them for now.
So, the way I thought sound was produced was that the piston (which starts in) pushes out. All the air molecules in front of it are pushed together until the piston stops and reverses. Most of them are now moving in the same direction as the piston (call it forward), and spread into the space in front of the piston. Collisions with other molecules will tend to push those ones forward, so the energy gets transferred along. While that happens, though, the piston was moving backwards. Now there’s an abhorrent vacuum. A number of air molecules will enter this space simply because it’s there and they happened to be going in that direction. So when the piston starts moving forward again, they’ll be the ones that get pushed together just like the ones at the start.
Hopefully that wasn’t too unclear. Using that as my basis, I think there would be an upper limit on how quickly the piston could move and still produce a wave. It could go in and out so quickly that less than one molecule on average would be affected … I’m not sure if that would count as a wave or not. There’d only be intermittent wavefronts. Of course, maybe that is itself detectable, but if it were, would it be possible to tell the difference between one ‘hypersonic’ wave and another?
I’m running in circles a bit here so I think I should cut it short and hope someone can straighten me out. Especially about how sound is produced. The animation shown here is confusing me. I’m not sure that it is intended to be accurate, but there are some particles just moving back and forth apart from any others (see the very bottom left or right for examples).
If I had to make an educated guess, I would say that the upper limit would be when your piston has to start moving at the speed of sound to produce the frequency. Whether or not the resulting shockwaves would produce a higher frequency, I dunno.
Heat is the vibration of molecules. When you push them around you heat them up to, in theory past the point where it’s not “air” anymore, but some kind of plasma that would melt whatever might be close enough to hear it directly. Is it sound anymore? I don’t think so.
I suppose you could say that immediatly outside the fireball of a nuclear blast is the loudest possible sound
The brief answer is that there is indeed an upper limit on the sound velocity in any given medium. I can’t seem to find my old texts at the moment, but I do know that there is an intrinsic upper limit related to the density of the material. I’ll see if I can dig up some comprehensible references tomorrow.
This is a more difficult question than you think. What we are talking about are “particles” known as phonons. When we asking if there is a characteristic lower-limit wavelength for these particles the answer is yes, classically… no quantum mechanically. It has to do with the way the mathematics works out, but basically when you look at the phonons, they are limited by something called the Dubye (sp?) frequency behaving classically.
Phonons, by the way, are not just observed by ears. It is somewhat similar to photons being not just observed by the eye. There is a much larger range that we are not able to detect with our limited organs, indeed all frequencies are allowed above the limit.
If you want to know what this wavelength boundary is, it’s simple. It’s just twice the spacing between atoms. If you get a wavelength that’s smaller than this, then it is representable by a different longer wavelength classically (this is left as an exercise for the reader)!
Well, I suppose I have answers at least but it really is more difficult than I thought. I’d never heard of phonons before. I don’t think I’m going to understand it much past the idea of a quantum of acoustic energy, but that makes a lot of sense at least. Thanks to all, especially JSPrinceton. (By the way, I found the correct spelling to be Debye for the ‘classical’ frequency limit).
"**Explain why phonons have an upper limit in their possible frequency (unlike photons).
High frequency means small wavelength. With light, the wavelengths can get as small as they want to, as far as we can tell. But with a phonon, or sound wave, the wavelength can’t get any smaller than twice the lattice spacing. That would be a vibration which looks like this: //////" **
Apparently you can get up into the megahertz range with some materials
[C15.05] Propagation of Acoustic Waves through a Phononic Lattice
R.E. Vines, J.P. Wolfe (University of Illinois at Urbana-Champaign)
“Surface acoustic waves can be continuously scanned in propagation direction for the study of anisotropic structures such as composite materials and fabricated lattices. Using line-source transducers and a rotating sample, we have observed the transmission of megahertz waves through such periodic structures. A two-dimensional lattice of polymer cylinders in an aluminum base provides a ‘phononic lattice’ which displays frequency dispersion and acoustic bandgaps.” etc
Whoa. I feel like an idiot now. I just realized, after stopping merrily in to see what the news was, that I answered completely the wrong question, eh? hangs head in shame