I was going to get right to blowing up Patient Zero’s head. But then I remembered that there might be someone in the audience whose sole purpose in life is to make the presenter miserable, by asking a show-stopper question. Richard Feynman, known for his kindness in all other ways, was famous for this. Some blame him for the death of Werner Heisenberg, who made the mistake of showing up at Caltech with a half-baked theory. Shattered, Heisenberg died the following year.  So I came prepared.

Full of hubris, the troublemaker says, just loud enough to make everybody stop, “What about window glass? How are you going to make it penetrate a window? I consulted eDiplomat to see if, maybe, people in Havana sleep with the windows open. This must be the way for most people, because Cuba does not have the massive power grid required to support an air conditioned existence. But I came across this:

All leased homes are furnished with a basic set of U.S. Government furniture, draperies, and major appliances, including a washer, dryer, gas range, water cooler, freezer, refrigerator, air-conditioners, dehumidifiers, ceiling fans, and residential alarm system. All houses also have generators due to occasional power outages. USINT handles all preventive maintenance and minor repairs in leased houses. Cubalse handles major repairs.

So it may be necessary to penetrate glass. And if I say no, the troublemaker in the audience will say (loudly), “Are you trying to tell me that the Russkies have made a weapon that only works in tropical countries? Gimme a break.” If you’re a techie, please be patient as I now try to clue everybody in. The actual solution is not what you would expect.

Glass actually conducts sound very well. It is used in ultrasonic inspection systems. But recall: a wave likes to stick to whatever it’s in. To an ultrasound wave in air, this is what doesn’t happen:

• The air wave hits the glass.
• The wave converts to a sound wave in glass.
• The sound exits the glass on the other side.

The above does not happen to any significant degree. The difference in springiness of air and glass is too great. The sound that would do this bounces off instead. But there are more ways to skin a cat.

Why do we hear anything at all from the outside? Much of it comes from leaks around the windows. But some sound comes through the glass itself. This is because a pane of window glass bends back and forth in response to sound pressure. Instead of having waves inside the glass, the whole pane moves. It moves because glass is slightly flexible. When you’re just missing the postman, and you bang frantically on the glass, your knock produces a faintly musical tone. Could we make a pane of glass resonate like a drum?

A pane of glass is a little similar to a drum head, but the differences are major. A drum head is made of an elastic material held under tension. When the drum is struck, the drum head vibrates with what are called standing waves. These waves have fixed frequencies that are characteristic of the drum and the tension. You could make the drum head resonate with a sound beam, but the drum would respond in its own way, which is probably not what you want.

NASA studied the resonances of residential plate glass, and found very low frequency resonances, what we would call bass notes. They are of no help in blowing up human heads. So how is glass different from a drum head?

• Glass is not supple, and it is not held under tension. However glass vibrates, it is entirely different from a drum.
• Glass has spring properties. It has a “bending moment”. This means that if you apply force to a pane of glass, it will deform slightly. Under pressure, the nearest side compresses slightly. The far side stretches slightly. When you release the pressure, it will spring back.
• That glass conducts sound well tells us that a vibration based on the above will be efficient. It will not waste a lot of sound by turning it into heat.
• In sum, glass can be made to vibrate in modes based on the bending moment.

But what good is it if we are stuck with the standing waves that vary with every pane of glass and aren’t helpful to our evil purpose? The answer is to ignore them. In return, they will ignore you.

We use (Youtube) traveling waves instead, not passing through the glass, but along the pane, from one end to the other, rippling the surface as they go. Normally, we would think of grabbing one end of the pane and shaking it somehow. Just as in the Youtube video, the shake would propagate (move) along the pane until it reaches the other side, where it would bounce back or be absorbed. This isn’t available to us.

We can do it with the ultrasound beam that is lingering outside the window, hungry for its victim. If the beam impacts the glass straight on, nothing much happens. But if the beam hits the glass at an inclined angle, much can happen. The trick is to get the angle just right.

Sound moves in air at about 1100 feet per second. Call this C_air. The bending-moment wave has a velocity also. Call it C_m. It is not a bulk property. Besides the glass itself, it depends upon the thickness. Suppose it’s 3300 feet per second. Then by inclining the beam to the glass at 19 degrees from vertical, the phases of the wave in the beam and the glass wave will match up. The formula is just:

sin( angle from perpendicular) = C_air / C_m.

Notice that it is independent of frequency. The clandestine operator may choose a position that gives access to a line of windows that are known from previous measurement. The angle can also be adjusted by elevation.

What happens at the glass edges? At ultrasound frequencies, a pane of window glass is very large. The edges are far, far away, so they don’t count much.

Now the glass has become our friend. Perhaps 10% of the ultrasound beam will make it through. But it is now a secondary radiator that can illuminate the sleeper’s head even if it’s not visible to the beam outside. If this is not beneficial to the situation, the glass can be shattered by the beam instead.

Yuck! But it’s all for the motherland.

To be continued shortly – the payload.