# Fundamental Physics/Wave

 Subject classification: this is a physics resource.

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

## Sinusoidal wave source

### AC electrical sinusoidal wave generator

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

${\displaystyle v(t)=ASin\omega t}$

### Series LC

Series LC operates at equilibrium satisfy wave equation

${\displaystyle {\frac {d^{2}}{dt^{2}}}i(t)=-{\frac {1}{T}}i(t)}$

that has root of a sinusoidal wave function

${\displaystyle i(t)=ASin\omega t}$
${\displaystyle \omega ={\sqrt {\frac {1}{T}}}}$
${\displaystyle T=LC}$

### Electromagnetic sinusoidal wave generator

A coil of N turns operates at equilibrium satisfy wave equation

${\displaystyle \nabla ^{2}E(t)=-\omega E(t)}$
${\displaystyle \nabla ^{2}B(t)=-\omega B(t)}$

that has root of a sinusoidal wave function

${\displaystyle E(t)=ASin\omega t}$
${\displaystyle B(t)=ASin\omega t}$
${\displaystyle \omega ={\sqrt {\frac {1}{T}}}=C=\lambda f}$
${\displaystyle T=\mu \epsilon }$

## Summary

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