User:SunderB/Physics/3.4-Waves

= Waves =

Wave Basics
A progressive wave transfers energy in the same direction as wave travel without transferring matter.

Definitions and Parts of a wave

 * Displacement x (m) - distance of a point on a wave from the mid-point
 * Amplitude A (m) - maximum distance from the mid-point
 * Wavelength λ (m) - length of one whole oscillation
 * Period T (s) - time taken for one full oscillation
 * Frequency f (Hz) - number of full oscillations per unit time Frequency = 1 / Time period
 * Phase - how far a point is along an oscillation
 * Phase difference (radians or degrees) - how far along an oscillation one point is compared to another, either on the same wave or two different waves. 2π = 360° = one wavelength
 * Path difference - the no. of wavelengths between two points on a wave or on two different waves. Measured in terms of λ.

Wave Speed
$$\begin{alignat}{0} \text{speed of wave} = \text{wavelength} \times \text{frequency} \\ v = \lambda f \end{alignat}$$

Refraction and Refractive Index
Refractive Index:

$$n = {c \over v}$$

Snell's Law:

$$n_1 sin(\theta_1) = n_2 sin(\theta_2)$$

Critical Angle:

$$sin(\theta_c) = {n_2 \over n_1}$$

Diffraction and Two-Source Interference
$$\lambda \approx {ax \over D}$$

Stationary/Standing Waves
A standing wave, also known as a stationary wave is the superposition of two progressive waves with the same wavelength, moving in opposite directions. Features of standing waves:


 * No net energy transfer

How standing waves form:

 * The incident wave is reflected off of the closed end (of the string or tube)
 * The incident and reflected waves superpose
 * Where the two waves are in-phase (phase diff. of 0, 2π, 4π etc.), total constructive interference occurs, creating anti-nodes.
 * Where the two waves are out of phase (phase diff. of π, 3π, 5π etc.), total destructive interference occurs, creating nodes (fixed points on the wave which don't oscillate).