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The link to your article doesn't work. Here's the current one:

http://ptonline.aip.org/journals/doc/PHTOAD-ft/vol_60/iss_12/23_1.shtml

You have very interesting site.Thanks for all.

The high concentration of ultrasonic energy within - in this case - the human body or - more generally - any matter that does not exhibit such anisotropic characteristics as to propagate ultrasound in a non-linear direction is achieved by utilisation of a principle known in the industry as "phased array" and more commonly in medicine as ecography. Assume that you have a square rigid sheet of piezoelectric crystal of such a thickness that, when excited by a voltage spike, will vibrate at its resonant frequency - in this case within the frequency range known as ultrasound. Assume you now split this sheet into a grid arrangement, and you provide each single piezoelectric part with a separate electrical connection with means of creating an individual voltage spike per part, completely independent from the others.

If you apply an equal voltage spike to all parts together, each part will produce a theoretically equivalent wavefront that, summed to the others, will produce an overall ultrasonic wavefront approximately equal to that you would have obtained if you had not split the piezoelectric crystal in the first place. The smaller the parts you divide your crystal into, the more this equality is correct.

Now assume you want to concentrate a certain amount of energy at a specific point inside a body. As the piezoelectric crystal is normally not on the surface of a probe, but embedded inside some sort of casing and coupling plastic, your ultrasound will have to travel through two different media to get to that point: the coupling plastic and the body. For the purpose of this explanation, let's assume that the body is a fully homogeneus mass. Assume that each piezoelectric part into which you have divided your original crystal is small enough to be considered an ultrasonic point source, hence producing a wave travelling away from the crystal and expanding in a spherical manner. This wave will travel through the coupling plastic and refract into the body according to Snell's law, and reach the desired point within the body in a time T. This is valid for all your piezoelectric parts since, according to our assumption that the wavefront is spherical, the wavefront will always reach the point within the body sooner or later. The only difference between the various parts into which you have divided your crystal is the time T that it will take for that front to reach the desired point.

Once all the wave trajectories have been calculated according to Snell's law, you must find which part of the crystal exhibits the shortest path to the desired point (in terms of travelling time) and compute the paths of all the other parts (always in terms of travelling time) wrt that first one, in terms of a time difference or delay Delta T, which is specific to each different part of the crystal. It follows that, if the "closest" part of the crystal is excited first (by means of a voltage peak) and all the others are excited with a time delay wrt the first one which is equal to the specific DeltaT previously calculated, all the wavefronts produced by all the parts of the crystal will reach that desired point in space at the same time.

If the system that manages the voltage peaks is precise enough (generally speaking with a time precision which is equivalent to much less than a wavelength within the matter of the body) then all the wavefronts will combine at the desired point following the principle of constructive interference, and the total energy at that point will be roughly the energy of a single wavefront at that point multiplied by the number of wavefronts, or parts of the crystal.

The energy input into the system is not sufficient for a single wavefront to interact with the matter of the body in a destructive way, but becomes sufficient once the wavefronts of all the parts of the crystal are combined together by constructive interference. The same effect can in fact be achieved by using a single-piece piezoelectric crystal coupled with an ultrasonic lens shaped according to a Fermat's surface, however in this case the point where one wants to concentrate the energy is fixed in space and determined by the geometry of the crystal and the lens. Instead, in a phased array system you create a virtual Fermat's lens by applying time delays to the parts of the crystal and gain the ability to fully control the energy distribution and the position of the point in space exhibiting the highest energy distribution.

Phased array in a nutshell.

a friend of mine drinks a lot of tequila, she also has no plaque on her teeth and doesn't floss much at all - same with her husband. she had the idea that maybe the tequila is keeping her teeth free from plaque - any truth to this?

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