Physics Study Guide/Waves

=Waves= Wave is defined as the movement of any periodic motion like a spring, a pendulum, a water wave, an electric wave, a sound wave, a light wave, etc.

Any periodic wave that has amplitude varied with time, phase sinusoidally can be expressed mathematically as
 * R(t, θ) = R Sin (ωt + θ)


 * Minimum wave height (trough) at angle 0, π, 2π, ...
 * F(R,t,θ) = 0 at θ = nπ


 * Maximum wave height (peak or crest) at π/2, 3π/2, ...
 * F(R,t,θ) = R at θ = (2n+1)π/2


 * Wavelength (distance between two crests) λ = 2π.
 * λ = 2π - A circle or a wave
 * 2λ = 2(2π) - Two circles or two waves
 * kλ = k2π - Circle k or k amount of waves


 * Wave Number,
 * k


 * Velocity (or Angular Velocity),
 * ω = 2πf


 * Time Frequency,
 * f = 1 / t


 * Time
 * t = 1 / f

Wave speed is equal to the frequency times the wavelength. It can be understood as how frequently a certain distance (the wavelength in this case) is traversed.

Frequency is equal to speed divided by wavelength.

Period is equal to the inverse of frequency.

Variables

Definition of terms

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The wave’s extremes, its peaks and valleys, are called antinodes. At the middle of the wave are points that do not move, called nodes.

Examples of waves: Water waves, sound waves, light waves, seismic waves, shock waves, electromagnetic waves …

Oscillation
A wave is said to oscillate, which means to move back and forth in a regular, repeating way. This fluctuation can be between extremes of position, force, or quantity. Different types of waves have different types of oscillations.

Longitudinal waves: Oscillation is parallel to the direction of the wave. Examples: sound waves, waves in a spring.

Transverse waves: Oscillation is perpendicular to direction of the wave. Example: light

Interference
When waves overlap each other it is called interference. This is divided into constructive and destructive interference.

Constructive interference: the waves line up perfectly and add to each others’ strength.

Destructive interference: the two waves cancel each other out, resulting in no wave.This happens when angle between them is 180degrees.

Resonance
In real life, waves usually give a mishmash of constructive and destructive interference and quickly die out. However, at certain wavelengths standing waves form, resulting in resonance. These are waves that bounce back into themselves in a strengthening way, reaching maximum amplitude.

Resonance is a special case of forced vibration when the frequency of the impressed periodic force is equal to the natural frequency of the body so that it vibrates with increased amplitude, spontaneously.