Re: [math-fun] Sonic screwdrivers for dentists?
There's several issues here. Let's deal with the narrow frequency range issue first. In order to respond to a precise tone -- e.g., B-flat -- you need a tuned resonator with a high "Q". Furthermore, since we're talking about a bulk material, you need a whole bunch of tuned resonators, all tuned to the same frequency, and relatively unaffected by the size & shape of the bulk material. In order to have a high Q, the energy dissipation per cycle has to be small relative to the energy stored per cycle. This means that it can't radiate away in the form of sound/heat/light/radio waves, etc. This is a tall order, since responding to a particular frequency (466Hz in the case of Bflat/Asharp) requires a resonator of a reasonable physical size, which might not fit into your mouth. So let's assume we're talking about an ultrasonic frequency, whose resonators could be made quite small. Let's now attack fabrication. It might be possible to 3D print a structure whose resonances are reasonably sharply tuned in such a way that you can get catastrophic failure by vibrating it at certain critical frequencies. I'm guessing, but this structure would have to have a large number of identical cells, each of whom has a high Q, and each is relatively isolated from its neighbors so that its energy doesn't dissipate too quickly. BTW, plaster-of-paris -- as used in casts for broken bones -- is NOT *cut* away, so much as *vibrated* away. When I broke my arm in the 4th grade (in the 1950's), I had a cast for 2 weeks, and then had a new cast for an additional 4 weeks. To remove the casts, the doctor used a vibrating disk that literally shook the plaster apart. It would be too dangerous to use something like a saw which could easily destroy the arm that the doctor is trying to fix! I can assure you that my cast was not tuned to a particular frequency! At 07:29 AM 8/5/2016, James Propp wrote:
Could there be a stronger adhesive that loses its adhesive virtue when you make it vibrate it just so? (Might dentists if the future say "Don't sing any loud B-flats for the next two weeks"?)
Good point about plaster-of-Paris! So let's drop the high Q constraint. All that matters is that the condition that triggers collapse of adhesion shouldn't be the kind of thing that is likely to happen accidentally as my teeth go about their business. Jim Propp On Friday, August 5, 2016, Henry Baker <hbaker1@pipeline.com> wrote:
There's several issues here.
Let's deal with the narrow frequency range issue first.
In order to respond to a precise tone -- e.g., B-flat -- you need a tuned resonator with a high "Q". Furthermore, since we're talking about a bulk material, you need a whole bunch of tuned resonators, all tuned to the same frequency, and relatively unaffected by the size & shape of the bulk material.
In order to have a high Q, the energy dissipation per cycle has to be small relative to the energy stored per cycle. This means that it can't radiate away in the form of sound/heat/light/radio waves, etc.
This is a tall order, since responding to a particular frequency (466Hz in the case of Bflat/Asharp) requires a resonator of a reasonable physical size, which might not fit into your mouth.
So let's assume we're talking about an ultrasonic frequency, whose resonators could be made quite small.
Let's now attack fabrication. It might be possible to 3D print a structure whose resonances are reasonably sharply tuned in such a way that you can get catastrophic failure by vibrating it at certain critical frequencies. I'm guessing, but this structure would have to have a large number of identical cells, each of whom has a high Q, and each is relatively isolated from its neighbors so that its energy doesn't dissipate too quickly.
BTW, plaster-of-paris -- as used in casts for broken bones -- is NOT *cut* away, so much as *vibrated* away. When I broke my arm in the 4th grade (in the 1950's), I had a cast for 2 weeks, and then had a new cast for an additional 4 weeks. To remove the casts, the doctor used a vibrating disk that literally shook the plaster apart. It would be too dangerous to use something like a saw which could easily destroy the arm that the doctor is trying to fix!
I can assure you that my cast was not tuned to a particular frequency!
At 07:29 AM 8/5/2016, James Propp wrote:
Could there be a stronger adhesive that loses its adhesive virtue when you make it vibrate it just so? (Might dentists if the future say "Don't sing any loud B-flats for the next two weeks"?)
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How about UV exposure? Dentists already use compounds that *set* under UV. On Fri, Aug 5, 2016 at 12:29 PM, James Propp <jamespropp@gmail.com> wrote:
Good point about plaster-of-Paris! So let's drop the high Q constraint. All that matters is that the condition that triggers collapse of adhesion shouldn't be the kind of thing that is likely to happen accidentally as my teeth go about their business.
Jim Propp
On Friday, August 5, 2016, Henry Baker <hbaker1@pipeline.com> wrote:
There's several issues here.
Let's deal with the narrow frequency range issue first.
In order to respond to a precise tone -- e.g., B-flat -- you need a tuned resonator with a high "Q". Furthermore, since we're talking about a bulk material, you need a whole bunch of tuned resonators, all tuned to the same frequency, and relatively unaffected by the size & shape of the bulk material.
In order to have a high Q, the energy dissipation per cycle has to be small relative to the energy stored per cycle. This means that it can't radiate away in the form of sound/heat/light/radio waves, etc.
This is a tall order, since responding to a particular frequency (466Hz in the case of Bflat/Asharp) requires a resonator of a reasonable physical size, which might not fit into your mouth.
So let's assume we're talking about an ultrasonic frequency, whose resonators could be made quite small.
Let's now attack fabrication. It might be possible to 3D print a structure whose resonances are reasonably sharply tuned in such a way that you can get catastrophic failure by vibrating it at certain critical frequencies. I'm guessing, but this structure would have to have a large number of identical cells, each of whom has a high Q, and each is relatively isolated from its neighbors so that its energy doesn't dissipate too quickly.
BTW, plaster-of-paris -- as used in casts for broken bones -- is NOT *cut* away, so much as *vibrated* away. When I broke my arm in the 4th grade (in the 1950's), I had a cast for 2 weeks, and then had a new cast for an additional 4 weeks. To remove the casts, the doctor used a vibrating disk that literally shook the plaster apart. It would be too dangerous to use something like a saw which could easily destroy the arm that the doctor is trying to fix!
I can assure you that my cast was not tuned to a particular frequency!
At 07:29 AM 8/5/2016, James Propp wrote:
Could there be a stronger adhesive that loses its adhesive virtue when you make it vibrate it just so? (Might dentists if the future say "Don't sing any loud B-flats for the next two weeks"?)
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How about UV exposure? Dentists already use compounds that *set* under UV.
Sure, why not? But in this specific application, isn’t most of the material shadowed by the crown? This suggests we want some kind of “unset” wavefront that will propagate through the bulk from a localized origin. That’d actually be a pretty fun material, whether or not it was also an adhesive in one of its states. Flipping between the set/unset states also preferrably needs to require relatively low-power. You do want to avoid setting it off accidentally. Sonic’s maybe not so good (because harmonics, which all non-linearities produce). Could you make a trigger/initiator nano-widget that requires a very specific “key”? (Perhaps some kind of DNA or other macromolecular sequence?) That would have all kinds of interesting applications (for various values of “interesting”!)
UV hardening is an exothermic reaction, so you'd have to add heat as well as UV light to make the reaction go the other way. On Fri, Aug 5, 2016 at 12:22 PM, Marc LeBrun <mlb@well.com> wrote:
How about UV exposure? Dentists already use compounds that *set* under UV.
Sure, why not? But in this specific application, isn’t most of the material shadowed by the crown?
This suggests we want some kind of “unset” wavefront that will propagate through the bulk from a localized origin.
That’d actually be a pretty fun material, whether or not it was also an adhesive in one of its states.
Flipping between the set/unset states also preferrably needs to require relatively low-power.
You do want to avoid setting it off accidentally. Sonic’s maybe not so good (because harmonics, which all non-linearities produce).
Could you make a trigger/initiator nano-widget that requires a very specific “key”? (Perhaps some kind of DNA or other macromolecular sequence?)
That would have all kinds of interesting applications (for various values of “interesting”!)
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
This is true of the UV-activated epoxies used in dentistry today. I don't think it's a necessary property of any imaginable material. On Fri, Aug 5, 2016 at 2:34 PM, Mike Stay <metaweta@gmail.com> wrote:
UV hardening is an exothermic reaction, so you'd have to add heat as well as UV light to make the reaction go the other way.
On Fri, Aug 5, 2016 at 12:22 PM, Marc LeBrun <mlb@well.com> wrote:
How about UV exposure? Dentists already use compounds that *set* under UV.
Sure, why not? But in this specific application, isn’t most of the material shadowed by the crown?
This suggests we want some kind of “unset” wavefront that will propagate through the bulk from a localized origin.
That’d actually be a pretty fun material, whether or not it was also an adhesive in one of its states.
Flipping between the set/unset states also preferrably needs to require relatively low-power.
You do want to avoid setting it off accidentally. Sonic’s maybe not so good (because harmonics, which all non-linearities produce).
Could you make a trigger/initiator nano-widget that requires a very specific “key”? (Perhaps some kind of DNA or other macromolecular sequence?)
That would have all kinds of interesting applications (for various values of “interesting”!)
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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participants (5)
-
Allan Wechsler -
Henry Baker -
James Propp -
Marc LeBrun -
Mike Stay