# Damped wave

A damped wave is a wave whose amplitude of oscillation decreases with time, eventually going to zero, an exponentially decaying sinusoidal wave. This term also refers to an early method of radio transmission produced by the first radio transmitters, spark gap transmitters, which consisted of a series of damped radio waves. Information was carried on this signal by telegraphy, turning the transmitter on and off (on-off keying) to send messages in Morse code. Damped waves were the first practical means of radio communication, used during the wireless telegraphy era which ended around 1920. In radio engineering it is now generally referred to as "Class B" emission. However, such transmissions have a wide bandwidth and generate electrical "noise" (electromagnetic interference) which interferes with other radio transmissions.

Because of their potential to cause interference and their resulting wasteful use of radio spectrum resources, there is an international prohibition against the use of class B damped wave radio emissions, established by the International Telecommunications Union in 1938. However the definition of "damped waves" in these regulations is unclear when applied to modern technology, and recently there have been moves to amend this prohibition to exempt emerging radio technologies such as ultra-wideband transmission systems.

An ideal damped wave is an exponentially decreasing sinusoid; an oscillating sine (or cosine) wave in which the peak amplitude decreases from an initial maximum toward zero at an exponential rate

$v(t)=V_{p}e^{-\alpha t}\cos(\omega t)=V_{p}e^{-{t \over \tau }}\cos(2\pi ft)$ where

$t$ is time in seconds
$V_{p}$ is the peak amplitude of the wave.
$\omega =2\pi f$ is the angular frequency of the oscillations in radians per second
$f$ is the frequency of the oscillations in hertz
$\alpha =1/\tau$ is the damping factor of the wave
$\tau$ is the time constant of the wave in seconds; the time for the peak amplitude to decay to $1/e=0.368$ of its initial value A series of damped waves, such as would be radiated by a spark-gap transmitter. In this graph, the vertical axis is the amplitude of the wave, in units such as voltage or electric field strength; the horizontal axis is time.