# 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

$f(t)=A\sin \omega t$ Wave equation

$f^{''}(t)=-\omega f(t)$ ## Sinusoidal wave in motion

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

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