Steven Marks secret

[stprue]

@all

Some good info on standing waves!!!

Opposing waves
Standing waves
Standing wave in stationary medium. The red dots represent the wave nodes.
A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue).


Electric force vector (E) and magnetic force vector (H) of a standing wave.
Standing waves in a string â€" the fundamental mode and the first 6 overtones.


A two-dimensional standing wave on a disk; this is the fundamental mode
A higher harmonic standing wave on a disk with a node at the center of the drum.



As an example of the second type, a standing wave in a transmission line is a wave in which the distribution of current, voltage, or field strength is formed by the superposition of two waves of the same frequency propagating in opposite directions. The effect is a series of nodes (zero displacement) and anti-nodes (maximum displacement) at fixed points along the transmission line. Such a standing wave may be formed when a wave is transmitted into one end of a transmission line and is reflected from the other end by an impedance mismatch, i.e., discontinuity, such as an open circuit or a short.[1] The failure of the line to transfer power at the standing wave frequency will usually result in attenuation distortion.

Another example is standing waves in the open ocean formed by waves with the same wave period moving in opposite directions. These may form near storm centres, or from reflection of a swell at the shore, and are the source of microbaroms and microseisms.

In practice, losses in the transmission line and other components mean that a perfect reflection and a pure standing wave are never achieved. The result is a partial standing wave, which is a superposition of a standing wave and a traveling wave. The degree to which the wave resembles either a pure standing wave or a pure traveling wave is measured by the standing wave ratio (SWR).[2]

[edit] Mathematical description
In one dimension, two waves with the same frequency, wavelength and amplitude traveling in opposite directions will interfere and produce a standing wave or stationary wave. For example: a harmonic wave traveling to the right and hitting the end of the string produces a standing wave. The reflective wave has to have the same amplitude and frequency as the incoming wave.

If the string is held at both ends, forcing zero movement at the ends, the ends become zeroes or nodes of the wave. The length of the string then becomes a measure of which waves the string will entertain: the longest wavelength is called the fundamental. Half a wavelength of the fundamental fits on the string. Shorter wavelengths also can be supported as long as multiples of half a wavelength fit on the string. The frequencies of these waves all are multiples of the fundamental, and are called harmonics or overtones. For example, a guitar player can select an overtone by putting a finger on a string to force a node at the proper position between the ends of the string, suppressing all harmonics that do not share this node.

Let the harmonic waves be represented by the equations below:


and


where:

y0 is the amplitude of the wave,
ω (called angular frequency, measured in radians per second) is 2π times the frequency (in hertz),
k (called the wave number and measured in radians per metre) is 2π divided by the wavelength λ (in metres), and
x and t are variables for longitudinal position and time, respectively.
So the resultant wave y equation will be the sum of y1 and y2:


Using a trigonometric identity to simplify, the standing wave is described by:


This describes a wave that oscillates in time, but has a spatial dependence that is stationary: sin(kx). At locations x = 0, λ/2, λ, 3λ/2, ... called the nodes the amplitude is always zero, whereas at locations x = λ/4, 3λ/4, 5λ/4, ... called the anti-nodes, the amplitude is maximum. The distance between two conjugative nodes or anti-nodes is λ/2.

Standing waves can also occur in more than one dimension, such as in a resonator. The illustration on the right shows a standing wave on a disk.

[giantkiller]

No see picture?

[stprue]

Yes I know and I'm sorry.  It didn't copy!  It is clearer if you Wiki it that's where it is from.

[stprue]

Doesn't the mathematical description sound like SM?

[tishatang]

@Otto and All

Do you suppose SM could have used something like one of these self-powered radio circuits shown here:  You could put one of these in front of each of the two coils.

http://www.crystalradio.net/crystalplans/

Scroll down to #153 Free Power Radios.  Here is page two of three showing the circuits.  File too big to attach.  You will have to download.

http://www.crystalradio.net/crystalplans/xximages/Free2.JPG

If one coil is tuned to around 200Khz and the other coil is turned to 60 hertz, they might gain in power like you would pushing a swing?  One circuit is designed to capture 60 Hz and the last one good for all stray frequencies.

Tishatang