# Fundamental Physics/Motion/Wave

## Wave

Wave is a Periodic motion of a periodic oscillation carries energy travels in space. For example, Light wave, Sound wave, Electric wave, Electromagnetic wave . When talking about wave, we talk about wavelength, speed, angular speed, frequency

## Sinusoidal wave

It can be shoen that all sinusoidal wave has a mathematical Wave function which is a root of a Wave equation as shown below

Wave function

${\displaystyle f(t)=A\sin \omega t}$

Wave equation

${\displaystyle f^{''}(t)=-\omega f(t)}$

## Sinusoidal wave in motion

${\displaystyle s=f(t)=A\sin \omega t=\lambda }$
${\displaystyle a=f^{''}(t)=-\omega f(t)}$
${\displaystyle v={\frac {\lambda }{t}}=\lambda f=\omega }$

## Oscillation wave

 Oscillation wave Wave equation Wave function Angulat speed Spring's vertical oscillation wave ${\displaystyle y^{''}(t)=-\omega y(t)}$ ${\displaystyle y(t)=A\sin \omega t}$ ${\displaystyle \omega ={\sqrt {\frac {k}{m}}}}$ Spring's horizontal oscillation wave ${\displaystyle x^{''}(t)=-\omega x(t)}$ ${\displaystyle x(t)=A\sin \omega t}$ ${\displaystyle \omega ={\sqrt {\frac {k}{m}}}}$ Pendulum's vertical oscillation wave ${\displaystyle y^{''}(t)=-\omega y(t)}$ ${\displaystyle y(t)=A\sin \omega t}$ ${\displaystyle \omega ={\sqrt {\frac {l}{g}}}}$ Electric current oscillation wave ${\displaystyle i^{''}(t)=-\omega i(t)}$ ${\displaystyle i(t)=A\sin \omega t}$ ${\displaystyle \omega ={\sqrt {\frac {1}{T}}}}$${\displaystyle T=LC}$ Electric current of decay amplitude oscillation wave ${\displaystyle i^{''}(t)=-2\alpha i^{'}(t)-\beta i(t)}$ ${\displaystyle i(t)=A(\alpha )\sin \omega t}$ ${\displaystyle \omega ={\sqrt {\beta -\alpha }}}$${\displaystyle T=LC}$ Electromagnetic oscillation wave ${\displaystyle E^{''}(t)=-\omega E(t)}$${\displaystyle B^{''}(t)=-\omega B(t)}$ ${\displaystyle B(t)=A\sin \omega t}$${\displaystyle B(t)=A\sin \omega t}$ ${\displaystyle \omega ={\sqrt {\frac {1}{T}}}}$${\displaystyle T=\mu \epsilon }$

Wave