Physics Course/Waves

Waves

Waves are disturbances travelling in a medium. Wave is a periodic oscillation travels through medium at Speed v and carries an energy E

$v=\lambda f$

Waves are divided in two types of waves. Waves that have the direction of oscillation the same as the direction of travel are called Transverse Waves. Waves that have the direction of oscillation perpendicular to the direction of the travel are called Longitudinal Waves.

Wave Characteristics

• Wavelength

Wavelength is defined as distance between two peaks of the wave

λ = 2π

• Speed

$v={\frac {2\pi }{t}}=\lambda f$

• Angular of Speed

$\omega =2\pi f$

• Frequency of Time

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

• Amplitude

$F(t,\theta )=0$ at $\theta =n\pi$. Amplitude of the wave equals to zero at angle of nπ

$F(t,\theta )=R$ at $\theta =(2n+1){\frac {\pi }{2}}$. Amplitude of the wave equals to the peak value at angle of (2n+1)π/2

• Wave's Function

$A(t,\theta )=ASin(\omega t+\theta )$

Wave's Equation

Every wave can be expressed by a derivative equation. The simplest form of a wave's oscillation travels in direction x in time t

${\frac {1}{v^{2}}}{\frac {\partial ^{2}y}{\partial t^{2}}}={\frac {\partial ^{2}y}{\partial x^{2}}}.$

v is the speed of wave travelling. Root of the wave's equation is solved by Jean le Rond d'Alembert:

$y(x,t)=F(x-vt)+E(x+vt)$

Can be described as the sum of periodic waves

$y(x,t)=A(x,t)\cos(\omega t-kx+\varphi ),\,$

A(x, t) is the amplitude of the wave,

ω Angular Velocity

k Wave's Number

φ Angle.

If Amplitude does not depend on time is called Standing Wave

$A(x,t)=A(x)$

Wave's Examples

Wave	Speed	Frequency	Wave Length	Energy
Light Wave	C = 3 x 1018 m/s
Sound Wave	V = λ f = 300 m/s
Electric Wave		60Hz
ElectroMagnetic Wave	C = 3 x 1018 m/s	MHz - THz	λ = C / f	E = h f = h nfo
Black Body Radiation Light Wave	V C C	f < fo f = fo f > fo	λ = v / f λ = C / fo λ = C / nfo	E = m v2 E = h fo E = h nfo

Summary

Wave is used to describe a motion of an oscillation through space. There are two types of waves.

1. Transverse Wave has the oscillation's direction the same direction of oscillation. For instance, Electric Wave.
2. Longitudianl Wave has the oscillation's direction perpendicular to the direction of oscillation. For example, Sound Wave

Every Wave has a Wave's Equation in the form

$F(t,\theta )=ASin(\omega t+\theta )$

Wave	Amplitude	Wave Length	Speed	Period	Phase Angle
A wave with constant amplitude.	$F(t,\theta )=0$ at angle $\theta =n\pi$ $F(t,\theta )=A$ at angle $\theta =(2n+1){\frac {\pi }{2}}$	$k\lambda$	$v=\lambda f$	$2\pi$	$\theta$

Wave could carry Energy, Information. Wave's speed can be changed by Reflection, Refraction, Diffraction even undergo Frequency change by Energy Absorption or Radiation.

Wave Phenomenons	Definition	Examples	Picture
Reflection	Wave is reflected back into the medium it comes from at an angle of reflection
Refraction	Wave travels through a medium at an angle of fraction	Ánh Sáng truyền từ Không khí qua Nước
Diffraction and Interference	Two waves of same direction or of opposite direction travel toward each other interfere constructively or Destructively to produce Constructive Interferences or Destructive Interferences
Dispersion	Wave is being reflected and refracted	Ánh Sáng đi qua Lăng Kín