Is nonlinear acoustics in mainstream physics?

[Squizzie]

TL;DR Summary

Looking for a physics text on sound or wave theory, explaining the circumstances where frequency and wavelength are not linearly proportional.

I have come across the term "nonlinear acoustics" in various technical reports and engineering texts, but have been unable to nail it down in a modern physics textbook.
It appears to relate to the transmission of pressure waves in which either the frequency and wavelength are not linearly dependent, or where the speed of the wave is dependent on the amplitude of the wave, i.e. the pressure.

I thought I had found it in Feynman, with:
"Both sound and light travel with a speed in air which is very nearly independent of frequency. Examples of wave propagation for which this independence is not true will be considered in Chapter 48." (my emphasis),
but was disappointed that the closest Chapter 48 came was the tantalising:
" Incidentally, we know that even when ω and k are not linearly proportional, the ratio ω/k is certainly the speed of propagation for the particular frequency and wave number."

I was unable to find a description of any case where where ω and k are not linearly proportional.

I know in BLAST WAVE Chapter 5, Hans Bethe proposed a "theory to provide a natural transition to the well-known acoustic theory, and to set in evidence the limitations of the latter." (referred elsewhere in the paper as the "semi-acoustic theory") and went on to develop a theory that was implemented in the "IBM runs" of that paper, but I am unable to find any evidence that it made its way into mainstream physics in the intervening 70-odd years.

As Feynman pointed out: "The principle of science, the definition, almost, is the following: The test of all knowledge is experiment. Experiment is the sole judge of scientific "truth.". I am concerned that there does not appear to be any experimental evidence for the existence of acoustic waves in which frequency and wavelength are not linearly dependent.

As mentioned, I have found references in journal articles, Wikipedia and some engineering texts, but can't find it in any mainstream physics textbooks. As this is a physics forum, I wonder if members can assist.

 

[Baluncore]

Linear acoustics is teachable as basic principles to all students.
Shock waves are a special case where acoustics becomes non-linear.

When acoustics becomes non-linear, the complexity rises, so it can confuse the student. Any material with physical hysteresis, or a loose bolt, will show a non-linear acoustic behaviour. That will generate harmonics due to waveform distortion, or cross modulation of incident waves. That is all too complex for a general text book chapter on acoustics. It would be more applicable to engineering, or a specialist ultrasonics or sonar text.

I would suggest a specialist text such as; Physical Acoustics, Principles and Methods. Volume II - Part B "Properties of polymers and non-linear acoustics", by Warren Perry Mason. 1965.

Non-linearity is widely discussed in electronics, so non-linearity is essential to learning there. When non-linearity is encountered in acoustics, the mathematics, and waveform principles, can migrate from the electronics chapters.

Unless you are a lecturer in acoustics, it is not your prerogative to change the syllabus for students. General text books have evolved to teach students quickly and cleanly. You must follow that well trodden path, or wander forever in the wilderness.

 

[Squizzie]

Shock waves are a special case where acoustics becomes non-linear.

And there's my difficulty.
I can't find any physics textbooks that

1. report any experimental evidence of that or
2. propose that as a theory.

I have quoted Bethe who proposed a theory 70 years ago, and can find engineering papers and texts that develop the theory, but none with any experimental evidence.
(It only took a couple of years for Einstein's theory of General Relativity to be validated using the orbit of Mercury )

 

[nasu]

The acoustic phonons modes in solids are dispersive for high frequency. The simple theory is described in any solid state textbook. Experimental measurements can be found in same textbooks and research papers.
For a more practical instance, transversal acoustic waves in bones are slightly dispersive too and there are papers reporting the possible correlation with osteoporosis.
Surface waves called Lamb waves are strongly dispersive (nonlinear).
Nonlinear modes are described in most acoustic books. It is not an ignored topic.

 

[renormalize]

...but none with any experimental evidence.

Your focus on physics textbooks is far too narrow to find the info you seek on shocks and blast waves. You need to consult monographs, conference proceedings, military research reports, and of course, published journal articles. Here are a just a few randomly selected references from a couple of minutes of googling:

• Blast wave kinematics: theory, experiments, and applications
• A new blast wave scaling
• Experimental Methods of Shock Wave Research: Measurement of the Physical Properties of Blast Waves
• Approximate Blast Wave Theory and Experimental Data for Shock Trajectories in Linear Explosive‐Driven Shock Tubes
• Theoretical and Experimental Studies on Blast Wave Propagation in Air
• SELF-CONSISTENT BLAST WAVE PARAMETERS
• Theoretical and experimental study of cylindrical shock and heterogeneous detonation waves

Experimental data on shocks and blast-waves are available dating back nearly a century or more.

 

[Frabjous]

Check out Acoustics by Pierce
https://www.amazon.com/Acoustics-In...Applications/dp/3030112136/?tag=pfamazon01-20

Here are a couple of pages from Randall
https://www.amazon.com/Introduction-Acoustics-Dover-Books-Physics/dp/0486442519/?tag=pfamazon01-20

 

[Squizzie]

Check out Acoustics by Pierce
https://www.amazon.com/Acoustics-In...Applications/dp/3030112136/?tag=pfamazon01-20

Here are a couple of pages from Randall
https://www.amazon.com/Introduction-Acoustics-Dover-Books-Physics/dp/0486442519/?tag=pfamazon01-20
View attachment 337648View attachment 337649

Interesting.
I can get to a copy of Pierce in a couple of days when the State library opens.

It's going to take me a couple of weeks to access Randall (Not in State Library, University library closed over Christmas, Amazon offering 2-week delivery of paperback. On order.)
Re Randall: Could I ask you to show the derivation of the bulk modulus

from your extract please? Perhaps post the relevant section of Chapter 2?

And could I ask if nonlinear acoustics is a phenomenon of an ideal gas?

 

[renormalize]

And could I ask if nonlinear acoustics is a phenomenon of an ideal gas?

Absolutely yes. See for example, pg. 89 of https://apps.dtic.mil/sti/tr/pdf/ADA371866.pdf:

 

[Baluncore]

And could I ask if nonlinear acoustics is a phenomenon of an ideal gas?

Negative absolute pressures are not possible in a gas, so high amplitude waveforms can suffer distortion, which is a non-linear phenomenon.

 

[Squizzie]

Negative absolute pressures are not possible in a gas, so high amplitude waveforms can suffer distortion, which is a non-linear phenomenon.

Is that a "Yes" or aa "No" to my question which was:

And could I ask if nonlinear acoustics is a phenomenon of an ideal gas?

 

[Baluncore]

Is that a "Yes" or aa "No" to my question which was:

It will depend on the circumstances, and the interpretation of your question.

Yes, it is possible for an ideal gas to be non-linear, after all, it can support a shock wave, or fluid cavitation. But then no, ideal gasses are assumed to be linear for small amplitude sound waves.

 

[Frabjous]

Interesting.
I can get to a copy of Pierce in a couple of days when the State library opens.

It's going to take me a couple of weeks to access Randall (Not in State Library, University library closed over Christmas, Amazon offering 2-week delivery of paperback. On order.)
Re Randall: Could I ask you to show the derivation of the bulk modulus View attachment 337692 from your extract please? Perhaps post the relevant section of Chapter 2?View attachment 337690

And could I ask if nonlinear acoustics is a phenomenon of an ideal gas?

Here you go.



Randall does not have that much on nonlinear acoustics. You might want to look at the TOC before ordering. I posted the sample because it told the story at an intuitive level.

Nonlinear acoustics includes ideal gases for “large“ amplitude waves. Standard acoustics is for “small” amplitude waves. There are different nonlinear formulations depending on the specific application.

 

[Frabjous]

Absolutely yes. See for example, pg. 89 of https://apps.dtic.mil/sti/tr/pdf/ADA371866.pdf:

The OP should look at all of Hamilton‘s stuff at this meeting.

The above pdf has the transcript of his presentation.
Various papers are here.
https://apps.dtic.mil/sti/pdfs/ADA371868.pdf
His slides are here.
https://apps.dtic.mil/sti/pdfs/ADA371867.pdf

 

[berkeman]

Thread paused for a bit to check copyright violations...

 

[berkeman]

After further review, it looks like this thread is okay for Fair Use copyright laws. Please be sure to only quote/post short parts of copyrighted works and post attribution. Thank you.

 

[Frabjous]

After further review, it looks like this thread is okay for Fair Use copyright laws. Please be sure to only quote/post short parts of copyrighted works and post attribution. Thank you.

I guess I beat the rap.

 

[Squizzie]

It will depend on the circumstances, and the interpretation of your question.

Yes, it is possible for an ideal gas to be non-linear, after all, it can support a shock wave, or fluid cavitation. But then no, ideal gasses are assumed to be linear for small amplitude sound waves.

@Baluncore, @Frabjous, @renormalize, @nasu:
Are you happy with that answer?
In the pressure continuum between a loud sound, with an overpressure of ~100 Pa , and the event that occurred on the Beirut Rooftop , with an overpressure of 1-2 psi: or around 10,000 Pa, where does the acoustics become nonlinear?
Where does the ratio of ω/k (frequency/wavelength) change from a value that remains constant for 0<overpressure < 100 Pa to something different for 10,000 < overpressure?

 

[Frabjous]

@Baluncore, @Frabjous, @renormalize, @nasu:
Are you happy with that answer?
In the pressure continuum between a loud sound, with an overpressure of ~100 Pa , and the event that occurred on the Beirut Rooftop , with an overpressure of 1-2 psi: or around 10,000 Pa, where does the acoustics become nonlinear?
Where does the ratio of ω/k (frequency/wavelength) change from a value that remains constant for 0<overpressure < 100 Pa to something different for 10,000 < overpressure?

It’s complicated and many times it depends on what question you are focusing on. Here is an exerpt from the Hamilton transcript mentioned earlier.

 

[Squizzie]

It’s complicated and many times it depends on what question you are focusing on.

OK, but in terms of the specific question I asked :

In the pressure continuum between a loud sound, with an overpressure of ~100 Pa , and the event that occurred on the Beirut Rooftop , with an overpressure of 1-2 psi: or around 10,000 Pa, where does the acoustics become nonlinear?
Where does the ratio of ω/k (frequency/wavelength) change from a value that remains constant for 0<overpressure < 100 Pa to something different for 10,000 < overpressure?

what is the answer?

 

[Frabjous]

OK, but in terms of the specific question I asked :

what is the answer?

For an ideal gas, the sound speed changes for overpressures greater than zero.
The proper question is when does it begin to change the answer. For Hamilton’s example, you see effects at ~630 Pa.

 

[Squizzie]

For an ideal gas, the sound speed changes for overpressures greater than zero.

Does that mean that if recorded two sounds from, a (loud) gunshot and a much quieter bell, created simultaneously (say within 2 ms) at NTP, from a distance of say 3.4 km, that the gunshot would be observed before the bell, or after the bell?

 

[renormalize]

The proper question is when does it begin to change the answer. For Hamilton’s example, you see effects at ~630 Pa.

Hamilton's example pressure is roughly similar to that from an answer I gave to Squizzy three weeks ago in a private conversation. I quote below a portion of my message to him:

"What constitutes a "small amplitude" acoustic wave in air depends, not just on overpressure, but also on wave frequency and propagation distance. Take a look at the following graph for single-frequency, plane-parallel sound waves from https://apps.dtic.mil/sti/tr/pdf/ADA035694.pdf:

Evidently, nonlinear propagation of finite-amplitude sound becomes more pronounced for higher frequencies and longer distances. But note that among all the measured cases, linear (small-amplitude) behavior persists for source SPLs of less than about 135 dB. So one very particular answer to your question is:
In the frequency band 0.5−3.57 kHz over distances between 14.8−25.8 m, a maximum source SPL/overpressure of ∼135 dB=112 Pa=0.016 psi can be propagated by a small-amplitude sound wave. Beyond that the wave enters into the regime of finite-amplitude nonlinear acoustics."

But since Squizzy is still asking about this, I guess he rejected my answer. Maybe your Hamilton quote will be more convincing to him!

 

[Baluncore]

... where does the acoustics become nonlinear?

Where the spectrum of the waveform develops higher frequency energy content, or harmonic energy, due to waveform distortion.

We must deal with real-world complexity, by using whatever works under the circumstances.
There is not always a black or white answer, sometimes it is black and white at the same time.

 

[Frabjous]

Does that mean that if recorded two sounds from, a (loud) gunshot and a much quieter bell, created simultaneously (say within 2 ms) at NTP, from a distance of say 3.4 km, that the gunshot would be observed before the bell, or after the bell?

Not necessarily. Things have to take time to catch up. Here’s a plot from Pierce.

 

[Squizzie]

We must deal with real-world complexity, by using whatever works under the circumstances.

Check my post #8: I asked the question in the context of an ideal gas. No "real-world" complexities!

 

[Squizzie]

Not necessarily.

I provided a very clear experiment. What do Hamilton's equations yield? Would the gunshot be observed before the bell, or after the bell?

 

[Frabjous]

I provided a very clear experiment. What do Hamilton's equations yield? Would the gunshot be observed before the bell, or after the bell?

Your “very clear experiment” is actually poorly defined and filled with real world complexities.

So under your policy of

No "real-world" complexities!

I decline to answer.

 

[Vanadium 50]

I asked the question in the context of an ideal gas. No "real-world" complexities!

That's just silly.

Is your ideal gas monatomic? Diatomic? Do its molecules take up space? Maybe it's not made up of atoms at all. Does it have a heat capacity at constant volume? Constany pressure? Are they the same or different?

You can't say "ideal" without specifying which idealizations you are using. (And which ones you are not)

Anticipating your objection, PV = nRT is a static equation. There are no sound waves in this gas, since P is the same everywehre.

 

[Baluncore]

I asked the question in the context of an ideal gas. No "real-world" complexities!

Do you include non-linearity as a "real-world" complexity ?

 

[russ_watters]

...and the event that occurred on the Beirut Rooftop , with an overpressure of 1-2 psi: or around 10,000 Pa, where does the acoustics become nonlinear?

Check my post #8: I asked the question in the context of an ideal gas. No "real-world" complexities!

C'mon. You ask about a real world event and then try to apply non real-world constraints? What are you doing here? What is your goal? What is the real question? You're getting truly spectacular instruction but you seem intent to play games with it instead of learning what they are trying to tell you. Please make your line of questioning make sense. Rapidly.

 

[Squizzie]

C'mon. You ask about a real world event and then try to apply non real-world constraints? What are you doing here? What is your goal? What is the real question? You're getting truly spectacular instruction but you seem intent to play games with it instead of learning what they are trying to tell you. Please make your line of questioning make sense. Rapidly.

OK, but give me overnight to frame my answer carefully. I sense a sword of Damocles hanging over my answer.

 

[renormalize]

Where does the ratio of ω/k (frequency/wavelength) change from a value that remains constant for 0<overpressure < 100 Pa to something different for 10,000 < overpressure?

Your question is unanswerable as asked: the onset of nonlinear acoustic propagation is a function of both the sound frequency and the distance to the source. Here's a graph from a study of the onset of nonlinearity in noise from a jet engine: https://physics.byu.edu/docs/publication/646:

Evidently, at a distance of ##305\text{ m}##, nonlinear effects begin to be seen at a surprisingly modest SPL of ##\sim100\text{ dB}=2\text{ Pa}=0.0003\text{ psi}## for frequencies from ##\sim2-20\text{ kHz}##. Can you sharpen your question by citing the specific frequency and distance you're asking about?

 

[Baluncore]

OK, but give me a overnight to frame my answer carefully. I sense a sword of Damocles hanging over my answer.

I agree, it will take time to manipulate scientists into saying something that agrees with your false belief. You already know the answer you want, and you are probably the most dogmatic member I know still here on PF. All you have to do now, is restrict the question to where your belief is acceptable. You will never accept that scientific terminology can have an actual meaning.

Participating in your threads is like playing musical chairs, you will win, because you are prepared to argue against the accepted science. That is Brandolini's law at play.
https://en.wikipedia.org/wiki/Brandolini's_law

 

[Vanadium 50]

I sense a sword of Damocles hanging over my answer.

Indeed. And who do you think put it there?

This thread probably is one of the best from the point of view of information provided, and one of the worst for the impact of this information. There is a great deal of information on how sound waves behave, and that's countered by, so far as I can tell, the statement that if you ignore non-linearities, what you are left with is linear.

 

[nasu]

Whereas standard acoustic textbooks may dedicate a limited space to nonlinear waves, there are whole books treating only nonlinear effects. This is an example I remember from my university years. I liked the sound of this word, "soliton".
They had conferences on these topics. So definitely not an ignored topic. This was 1978.
https://www.cambridge.org/core/jour...8-300-pp-975/5F487793DADDA3A82EAA4C1849AA3D88