468 is the half wavelength per mega hertz assuming that the speed of light in air is about 95% of the speed in vacuum. Air is a dispersive medium, which means that the speed of an electromagnetic wave depends on the frequency. The formula is wavelength=c(f)/f where c(f)= the speed of light (an electromagnetic) wave in air is a function of the frequency. The number 468 would be different depending on humidity, for example. So Emil is right that 468/f is an approximate formula. It would be much easier to use wavelength=.95c/f where c=300 million metres per sec and f is the frequency. That gives you the length in meters. for a 3 MHz signal. You could calculate the halfwave without even using a calculator. The wave would be 100 meters and the halfwave would be 50 meters in space. Reduce it by 5% for about air, if you really want that, which would 95 for the wave and 47.5 for the halfwave. Unless distances involved are large
I have doubts that a half antenna does much to detect a fault in underground CATV cable the way described is very useful. The leaky signal will attenuate further as it transmits through the ground or conduit. You would have to know dispersive properties of the earth that can vary from point to point depending what is buried in the ground first, You would also need some kind of a pulse generator that would be fed into the cable at one end, and of course a signal meter and possibly a built in amplifier. . But then, you don't even have to go to the location of the fault with the halfwave antenna. When there is a fault in the cable, it's impedance changes, which causes a part of the pulse to be reflected back to the source where the pulse is fed, which might be considerable distance from the fault. This is what a monostatic radar does. A coax cable is an electromagnetic waveguide----signal is one dimensional--it does not spread like it would in air.
I have found thousands and thousands of underground leaks with this method. Trangulated exactly on the spot to dig up. It does work. However you do need an amplifier on the input to the signal strength meter in order to get a strong enough signal.
As far as the wireless phone's srambling system. It was the old style wireless phones before cell phones. So it used a standard hetrodine system. Interfering Signal was at 148.1Mhz
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