Wave Motion & EM Waves (II)
Chih-Chieh Kang Electrooptical Eng.Dept. STUT Sinusoidal Traveling Waves Sinusoidal Waves Snapshot of a traveling sinusoidal wave (at a fixed time, t = 0), and 0=0 Vertical displacement of the traveling wave: Wavelength the distance between two successive crests or troughs. Amplitude Aone half the wave height or the distance from either the crest or the trough to the equilibrium points Phase = 2z/ Sinusoidal Traveling Waves
A wave does not change its shape as it travels through space. For a traveling sinusoidal wave moving at a speed v, the wave function at some later time t : Phase Lead & Phase Lag (Ulaby) Sinusoidal Traveling Waves
For the time a wave traveling a distance of one wavelength is called period T The frequency of a sinusoidal wave f Sinusoidal Traveling Waves
The angular wave number (or propagation number) of a sinusoidal wavek Wave function Harmonic Traveling Waves
For a traveling sinusoidal wave (at a fixed point z = 0) angular frequency=2/T=2f wave function Speed of a Wave For a traveling wave, its waveform retains the same phase Phase velocity v : the velocity of the waveform as it moves across the medium Mathematical Description of a Wave
Waves are solutions to the wave equation 1-D waves wave function, vphase velocity -Where does wave equation come from? -What do solutions look like? -How much energy do they carry? Wave Equation for a String
Each small piece of string obeys Newtons Law Small displacement, so Net force is proportional to curvature Wave Equation for a String
Newtons 2nd Law >>(mass density leads to the wave equation with - wave function=transversedisplacement - phase velocity