There is an inverse relation between the rate of decay ( the time constant ) of a damped wave and its bandwidth; the longer the damped waves take to decay toward zero, the narrower the frequency band the radio signal occupies, so the less it interferes with other transmissions.
22.
Further, as can be seen from the phase changes " ? t " ? z " in the solution " u " 1, the velocity oscillations propagate as a damped wave away from the wall, with wavelength " ? " and phase speed " ? / ? ".
23.
Early transmitters were spark gap transmitters : a mechanical device would make sparks at a fixed but audible rate; the sparks would put energy into a resonant circuit that would then ring at the desired transmission frequency ( which might be 100 kHz ); this ringing would quickly decay, so the output of the transmitter would be a succession of damped waves.
24.
Because the " damped waves " are a train of regularly spaced radio frequency triangle waves that occur at an audio rate, early crystal, magnetic and Fleming valve detectors heard them as a musical note, rich in harmonics, making it easy for the human ear to " copy " messages and identify stations by their unique sound, even under adverse conditions.
