Amplitude and Intensity

There is a minimum pressure and power of matter waves below which the ear cannot detect the wave. This value is about 0.0002 dynes/cm2 , an extremely small value because the ear is very sensitive. The corresponding power or intensity limit is ~109 ergs/cm2 sec, i.e., ~10-16 w/cm2! This value places its sensitivity very close to the threshold of the power in heat motion, and thus very close to the minimum background agitation of matter in our environment. The maximum amplitude the eardrum can stand, without certain irreparable damage resulting, is ~200 dynes/cm2. Therefore, the range of sensitivity of the ear is phenomenally high, one to a million. It is the most sensitive at 1,000 cps.

The sense of touch, particularly on the fingers and tongue, is not nearly so sensitive, but responds down to much lower frequencies.

To our knowledge, man has no detection apparatus for frequencies above about 20,000 cps. However, there is some evidence that ultrasound can penetrate to the brain and cause psychological aberrations, which may or may not be a result of organic damage.

One of the most convenient ways of generating matter waves of controlled frequency is by means of the vibrating crystal. Certain crystals are piezoelectric—that is, they expand or contract if an electric voltage is applied to contacts with two different crystal faces (b). The amount of the

Piezoelectric Crystals scheme

Figure 3-2. About Piezoelectric Crystals: (a) Voltage difference is applied between two opposite faces, (b) The length changes as the applied voltage is changed, (c) Varying voltage, V, gives varying length, y. (d) Concave radiator concentrates matter waves on a target.

expansion or contraction increases with increasing applied voltage. Quartz and barium titanate are currently in wide use. If the applied voltage is varied, the crystal shape varies accordingly, or vibrates, and the matter wave so established is transmitted by contact with the medium. The amplitude of the vibration is higher the higher the vibrating voltage applied. The frequency of vibration follows that of the electrical signal, if the crystal is not too big. "The Piezoelectric Crystals scheme"  illustrates these points.

Apparatus with output which ranges from a few to a million cycles per second, and from next to nothing up to a few hundred watts per square centimeter of crystal, has been built and used.

Constructed with a concave radiating surface (d), an array of piezoelectric crystals, if properly oriented, can be made to focus an intense beam of matter waves at a point a few centimeters from the radiating surface.

For example, in recent therapeutic work beams of 1 Mc (1,000,000 cps) were focused on a small target, and delivered energy at a rate (intensity) of 8 kw/cm2 of cross-section of the target!