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

 * [[Image:Wave_characteristics.svg|350px|]]


 * 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
 * $$A(t,\theta) = A Sin (\omega t + \theta)$$

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,
 * &omega; Angular Velocity
 * k Wave's Number
 * &phi; Angle.

If Amplitude does not depend on time is called Standing Wave
 * $$A(x,t) = A(x)$$

Wave's Examples

 * {| class="wikitable" width=100% align=center

! 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 ||λ = v / f λ = C / fo λ = C / nfo || E = m v2 E = h fo  E = h nfo
 * }
 * 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 ||λ = v / f λ = C / fo λ = C / nfo || E = m v2 E = h fo  E = h nfo
 * }
 * Black Body Radiation Light Wave || V C C || 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
 * $$F(t,\theta) = A Sin (\omega t + \theta)$$


 * {| class="wikitable" width=100% align=center

! Wave !! Amplitude !! Wave Length !! Speed !! Period !! Phase Angle
 * [[Image:Wave characteristics.svg|center|300px|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.


 * {| class="wikitable" width=100% align=center

! Wave Phenomenons !! Definition!! Examples !! Picture
 * Reflection || Wave is reflected back into the medium it comes from at an angle of reflection || ||[[File:Ray_Diagram_2.PNG]]
 * Refraction|| Wave travels through a medium at an angle of fraction || Ánh Sáng truyền từ Không khí qua Nước || [[File:Ray_Diagram.PNG]]
 * 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 || || Two-Slit_Diffraction.png
 * Dispersion || Wave is being reflected and refracted  || Ánh Sáng đi qua Lăng Kín || Prism-rainbow.svg
 * }
 * 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 || || Two-Slit_Diffraction.png
 * Dispersion || Wave is being reflected and refracted  || Ánh Sáng đi qua Lăng Kín || Prism-rainbow.svg
 * }
 * }
 * }