# Maximum gain possible by sound wave focusing

Jonathan212
Just like a concave mirror concentrates light, it can also concentrate sound waves. Ray diagrams like the following look as if all waves converge to a single point of INFINITE power density which of course is not true, probably because of the wave nature of light or sound. What is the correct power density at the focus point, relative to the incoming sound power density?

Is there a way to use multiple concave mirrors to focus all the sound from a source into a single very sharp point, with enough power density to sculpt granite?

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Mentor
Sound is a pressure wave, so the maximum amplitude is dictated by atmospheric pressure:

A sound of 194 dB has a pressuredeviation of 101.325 kPa, which is ambient pressure at sea level and 0 degrees C. Thus, the sound waves are creating vacuums between themselves, and no higher amplitudeis possible.
A dirty calc says if you focus a sound wave to that intensity at 1 square centimeter, that's a power of 3 kW. Probably need the rms of that, so call it 2.1 kW.

Of course, that assumes you can generate a sound with that power level in the first place.

So I'll say that compares quite unfavorably to a pneumatic drill.

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anorlunda
Staff Emeritus
They sell commercial equipment for stone laser engraving. I would guess that the same principle could be used for sculpting, depending on the scale you are thinking of.

What is your scale of interest? A knicknack or Mount Rushmore?

russ_watters
Jonathan212
Just checking a claim that sound (not light) wave focusing was used to shape and move large stones in ancient times. If we were to start with a large bell ringing, large enough that a human can barely stand it, can the sound be focused into any arbitrarily small area or are we limited to a quarter wavelength or something?

Gold Member
move large stones
You can lookup acoustic levitation. which for current technology works on small objects.
If you like Physics Girl, she has a go at assembling a kit, with some sparse explanation,
https://makezine.com/2017/12/18/physics-girl-builds-an-acoustic-levitator/
Other levitators do use a sound source and a reflective surface.

Note that to move the levitating object, one has to move the machine, which supports the object, so you are no farther ahead than before.
Extending current tech to large objects ... some hurdles to overcome before that would be possible.

Normally, trying to focus sound waves into an area less than one wavelength results in a defraction that causes a loss of energy. According to Phys.org, some guys at Paris tech have focused sound waves down to an area less than 1/25 of a wavelength, using only one exotic material; empty Coke cans.

Also: pretty clear that the total energy being applied cannot be greater than the energy input. A focusing reflective surface might be useful for concentrating the energy to a narrow point for cutting or cracking a rock, but the over all push that the rock receives is no more than the energy used to ring the bell. If we have a big burly guy swing a mallet and strike the bell, then we could have the same guy swing the same mallet and hit the rock, and it would move just about the same distance. I suppose that sound waves in the ground could reduce friction, allowing the rocks to be slid around more easily. Pretty unlikely, though.

Jonathan212
What about accumulating energy over time? Into a constrained standing wave? The shape of a trumpet comes to mind. Operating in reverse.

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Staff Emeritus
A trumpet doesn't concentrate sound energy - just the reverse. Only ~1% of the energy "leaks" out the bell - there is an enormous impedance mismatch between the inside and outside of the horn.

Gold Member
What about accumulating energy over time? Into a constrained standing wave? The shape of a trumpet comes to mind. Operating in reverse.

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The energy stored in a standing wave, for instance in a resonator, is dependent on a factor called Q, which is the energy stored divided by the energy lost per cycle. We cannot make a store build up indefinitely because it will be full when the energy source is fully committed supplying the energy lost per cycle. But of course, resonance is a technique for obtaining a store of energy that can suddenly be released. For instance, an electric spark gap connected across an LC circuit.
As far as focusing is concerned, there are the diffraction issues to consider, as with microwaves. The example illustrated shows a parallel beam arriving at the reflector, so that is immediately unrealistic because all beams diverge due to diffraction. So where will a parallel beam come from? If we assume a point source, and then collect the energy with a reflector and focus it on to another point, the second point will be larger than the first due to diffraction, so what have we achieved? Maybe a spark located at the focus of a reflector could deliver a compact patch of sound to a nearby surface, assuming the focussing was correct.

Jonathan212
So what do you guys think would happen if you took this bass tuba, put a drum at the large end, hit the drum, and put a finger on the mouthpiece? Or put another object?

Or, instead of a drum, place a loud church bell next to the large end?

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Jonathan212
I reckon the following path of sound is plausible. To create strong standing waves. Maybe with a little reshaping - nice math problem: what is the equation of the optimal curve that does this? Could try an exponential curve and see what happens. Or a piece of a parabola.

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Just checking a claim that sound (not light) wave focusing was used to shape and move large stones in ancient times.
Could you please give us some more details about that claim? Is it stricthly about sound, or some mechanical tweaking allowed?

can the sound be focused into any arbitrarily small area
Sound - no. But the energy and force - well, yes. Cylinder phonographs (the ones which could record too) did exactly that, for example.

Jonathan212

Maybe it is not about sound traveling through air but hard objects therefore wavelengths are much smaller.

Maybe it is not about sound traveling through air but hard objects therefore wavelengths are much smaller.
For waves of the same period, faster waves in a metal would travel further than in air so would have longer wavelengths, not shorter.

I reckon the following path of sound is plausible. To create strong standing waves.
At low frequencies the horn generates a spherical wave, axial with the horn. The spherical wave front is guided by and remains perpendicular with the surface of the horn as it expands. Reversing the process; where will you get an inside-out spherical wave to concentrate in the horn? Maybe you could use a lens made from a slow wave material such as a spherical balloon full of a heavy gas such as CO2.
If you have a plane wave things will be easier as you can use a parabolic reflector for both the transmit and the receive.

Maybe you should read more about the subject before you risk confusing yourself by leaping to wrong conclusions.

Jonathan212
Thanks for correcting me about the wavelength. Not sure mimicking the spherical wave is needed, or even a round shape of the wave at all, but even then, we could always put a round bell at the entrance and hit it.

I think the sound comes from the vibrating metal of the entire instrument, not something at the mouth of the musician. Maybe another shape is optimal for accumulating energy over time. Just like you can hit a lever and break something much stronger than your hand, same seems feasible with sound waves. This is exactly the principle of Edison's phonograph. But how do you scale it up to break stones?

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But how do you scale it up to break stones?
You study the art of lithotripsy using a lithotripter.

Ultrasonic welding uses tapered transformers to concentrate energy. It also uses a shaped anvil as a mirror behind the target to prevent losses.

That makes this a bit hard.

If it is just air, then I would say there is no way to break up granite by focused sonic waves. Possible workarounds exists:
- mechanical amplification/focusing. The already mentioned cylinder phonographs are doing just this: through a membrane and a needle they can focus the power of the incoming sound waves to a very small area (tip of the needle). Usually, sound waves has very little energy, barely enough to make some marks on the wax cylinder. But maybe some big drum-like thing, with a chisel on one side and with some really heavy drumstick on the other...
- if it is not air but some fluid, then cavitation (caused by focused sound waves) sure can do the job. It is used to drill metals (Sorry, my google search about 'ultrasonic cavitation' ended with tons of 'fat management', so I won't link anything )
- Ultrasonic drilling has 'sonic' in them, so maybe that's also counts, even if it is really more about drilling
- If it is not strictly 'sonic' but 'blast' is also allowed, then even in air, focused blast waves can do serious damage, even on rocks.

Jonathan212
Remember we need something more productive than a chisel and a hammer or it would be pointless.

I think the sound comes from the vibrating metal of the entire instrument, not something at the mouth of the musician.
The energy comes from the mouth of the musician. The air in the instrument is resonant and so selects the note keyed. The instrument material is held by the musician, it has high losses so is not a significant resonant metal component.
You have no idea of what you are trying to do.

You defined this little brainstorming before as:
Just checking a claim that sound (not light) wave focusing was used to shape and move large stones in ancient times.
Without adding more sources to that original claim I think this topic IS pointless.
Just give us something to work with, because right now we have nothing.

russ_watters
If it is just air, then I would say there is no way to break up granite by focused sonic waves.
You need to consider cavitation. When a partial vacuum bubble collapses it generates very high temperatures capable of shattering rock.

Just checking a claim that sound (not light) wave focusing was used to shape and move large stones in ancient times.
Knapping rocks involves generating a sound wave that fractures the rock along a predetermined line.

There is no claim that light waves have been used to shape rocks. It is important that you be able to separate reality from fiction.

You need to consider cavitation.
You mean, cavitation in air
I wrote "If it is just air"...

Remember we need something more productive than a chisel and a hammer or it would be pointless.
The idea that a concentrated point of energy must be used denies the fact that when two irregular surfaces rest against each other there will be very few, probably only three points of contact. That will concentrate contact energy to the proudest points that can then be reduced by rubbing the surfaces together with water to flush the rock dust, and or a cutting compound. Any two rocks can be quickly mated in place that way, to less than a 1mm gap. They can then be left assembled without any need for mortar.
Depending on the generating motion, spherical and elliptical mating surfaces are typical. Parabolic and spherical mirrors are generated by lapping in a similar way. Precision surface plates are made from granite slabs by opposing surfaces in sets of three in a way that cancels all curvature.

There is no need for focused light or sound energy to work rocks, you just need good organisation and some time, and you get a better result.
A waterwheel or engine driven crank to slide the rocks back and forth would make the work physically easier.

Mentor