Physics Study Guide/Waves
Waves[edit]
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
λ: wavelength (m) |
Definition of terms
Wavelength (λ): The length of one wave, or the distance from a point on one wave to the same point on the next wave. Units: meters (m). In light, λ tells us the color. |
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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[edit]
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[edit]
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.
Resonance[edit]
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.