Sinusoidal wave

Fundamental sinusoidal wave

All sinusoidal wave has a trigonometry function called Wave function which satisfies a differential equation called Wave equation

• Wave function

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

• Wave equation

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

For all sinusoidal wave that has a wavelength ${\displaystyle \lambda }$

• Wave length

${\displaystyle \lambda }$

• Time

${\displaystyle t}$

• Speed

${\displaystyle v=frac{\lambda }{t}=\lambda f=\omega }$

• Angular speed

${\displaystyle \omega =\lambda f}$

• Frequency

${\displaystyle f={\frac {1}{t}}}$

Harmonic sinusoidal wave

• Wave function

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

• Wave equation

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

For all sinusoidal wave that has a wavelength ${\displaystyle k\lambda }$

• Wave length

${\displaystyle k\lambda }$

• Time

${\displaystyle t}$

• Speed

${\displaystyle v={\frac {k\lambda }{t}}=k\lambda f=k\omega }$

• Angular speed

${\displaystyle \omega =k\lambda f={\frac {v}{k}}}$

• Frequency

${\displaystyle f={\frac {1}{t}}}$