Given Russian strengths in physics and weakness  in electronics, the Russian solution is likely to be what is called “simple and elegant”, more like the carburetor of an old-fashioned car than fancy electronic fuel injection.

Our gadget needs parts that actually make noise. Loudspeakers make sounds like human voices, music, bells, chimes, whistles, anything you want. But  every loudspeaker has a natural frequency, like the tone of a bell, that it likes to sing louder than anything else. Music players are designed to avoid this. Wasteful of energy, but more pleasingly, a speaker is made to talk like a parrot.

So the simplest approach to our nefarious gadget is to make a speaker that sings at the frequency we want, which is somewhere around 30kHz. This is how ultrasonic cleaners work, with a specialized speaker —  called a transducer, that makes that frequency and no other.

But sticking to a single frequency is very limiting and it doesn’t concentrate energy like the cymbal clash. Each Patient Zero is different. The room, windows, shape of the skull, all vary. The dimensions of the person’s head vary depending upon the angle with respect to the ultrasound beam. We want to hit all the possibilities. A single frequency won’t do.

In the last article, we worked backwards from the head to deduce a range of attack frequencies. Some  victims report audible sounds of much less than ultrasonic frequencies. These could be produced by:

• Mixing of ultrasound of different frequencies on room surfaces.
• Sub-harmonics created by room surfaces.
• Sub harmonics and mixing in the gadget itself. But this would make it very noisy on the street late at night.

The design that follows attempts to account for the audible sounds.

There are two kinds of transducers. Our interest is in the “piezo”, which changes shape when energized by an electric field. Here are some you can bolt to  an ultrasound cleaner tank. Piezos are found in stove and grill igniters,  because they work both ways. If you squeeze them, they make electricity for the spark. If you excite them with electricity, they make sound. A piezo is actually a kind of capacitor, where the polarization comes with mechanical strain.

A piezo is like a bell, with a preferred tone, but since it is a capacitor, it can be connected with an inductor, which is some wire wound around a ferromagnetic core, to make a tank circuit. The combination is a bell of a different, lower frequency. A tank circuit stores energy. We can fill it up with energy, and it will “ring”, resonate, for a while. It can release energy suddenly, like the ignition circuit in a car, or gradually.

This tank circuit is a harmonic oscillator (animation). In the universe of small, the harmonic oscillator is the most fundamental block we know. Each of these has a natural resonant frequency.  Two or more  can be coupled together and trade energy. Watch these two oscillators trade energy (animation.)

Inside one of these piezos is a thin flat disk of ceramic. It looks like a little piece of pottery. For our gadget, we can make it any shape we want, although the electricity is applied across the thinner dimension. Each crystal expands and contracts.

Attach each crystal to its own inductor. This changes the above frequencies, slowing them down a bit. Each of these combinations is a tank circuit,  can be made to vibrate with an electrical signal, and can store energy for a pulse. Each can be driven by a source of electrical power with a choice of frequency. So now the frequencies can be independent, and varied within a narrow range.

Now arrange the crystals in a stack. How they touch is extremely important.  A layer in between  acts as a spring, a third element. So we have four things to play with:

• Resonant frequency of the crystal.
• Size of the inductor.
• Springiness of the separator.
• Frequencies of the electric power for each crystal.

Let’s try this with just two crystals to start. Arrange the above so that one of the crystals vibrates at 25kHz (25,000 cycles/second), and the other at 30kHz (30,000 cycles/second). So the 30kHz crystal is moving 6/5 times faster than the 25kHz crystal. If we start each crystal vibrating at the same time, the 25 kHz crystal will catch up when the 30kHz crystal has gone 6 cycles, and the 25 kHz crystal has gone 5 cycles. This repeats over and over.

By themselves, the crystals store most of this energy. To make it go out as a beam in air, we need a radiator. An old-fashioned spring-wound Victrola has a needle that follows the groove in a record. By itself, the sound of the needle is faint. It is coupled into the air by a horn. Our radiator will probably  not be a horn, but you get the idea.

When the two crystals match up, they have maximum length at the same time.  When they are opposed, their length changes cancel out. When they are pushing together, combining to maximum length, this is the time to take some energy out and send it to the radiator. This can be done by attaching the radiator to the crystal stack with an elastic material that becomes progressively more rigid under pressure.

Homework: Suppose you have a stack of 4 piezo crystals, each tuned to  different frequencies: 20, 25  30 and 40kHz. Start them off at the same time. How many cycles of the 40kHz crystal occur before they are all back in sync, pushing in the same direction? Hint: Divide them all by 5. The least common multiple of 4,5, 6, and 8 is 120.

What do the above numbers mean? We are concentrating power, getting close to a pulse.

Next:  Bells and Whistles.

To be continued shortly.