# Fundamental Physics/Wave

Wave is defined as periodic oscillation carries energy travels in space. When talking about wave, we talk about wavelength, speed, angular speed, frequency

## Sinusoidal wave

For any sinusoidal wave Its characteristics are list in the table below

 Wave oscillation equation ${\frac {d^{2}}{dt^{2}}}f(t)=-\omega f(t)$ Wave function $f(t)=ASin\omega t$ Wavelength $s=\lambda$ Wave's speed $v={\frac {s}{t}}={\frac {\lambda }{t}}$ Wave's angular speed $\omega =\lambda f$ Wave's frequency $f={\frac {1}{t}}$ ## Sinusoidal wave source

### AC electrical sinusoidal wave generator

An interaction of 2 electromagnets creates an AC electricity that has amplitude varies sinusoidally

$v(t)=ASin\omega t$  ### Series LC Series LC operates at equilibrium satisfy wave equation

${\frac {d^{2}}{dt^{2}}}i(t)=-{\frac {1}{T}}i(t)$ that has root of a sinusoidal wave function $i(t)=ASin\omega t$ $\omega ={\sqrt {\frac {1}{T}}}$ $T=LC$ ### Electromagnetic sinusoidal wave generator A coil of N turns operates at equilibrium satisfy wave equation

$\nabla ^{2}E(t)=-\omega E(t)$ $\nabla ^{2}B(t)=-\omega B(t)$ that has root of a sinusoidal wave function $E(t)=ASin\omega t$ $B(t)=ASin\omega t$ $\omega ={\sqrt {\frac {1}{T}}}=C=\lambda f$ $T=\mu \epsilon$ ## Summary

 Wave Sinusoidal wave Sinusoidal Plane wave  Wave equation ${\frac {d^{2}}{dt^{2}}}f(t)=-\omega f(t)$ $\nabla ^{2}E(t)=-\omega E(t)$ $\nabla ^{2}B(t)=-\omega B(t)$ Wave function $f(t)=ASin\omega t$ $\omega ={\sqrt {\frac {1}{T}}}$ $T=LC$ $E(t)=ASin\omega t$ $B(t)=ASin\omega t$ $\omega ={\sqrt {\frac {1}{T}}}=C=\lambda f$ $T=\mu \epsilon$ 