# 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.

!A wave with constant
amplitude.{width="400"}
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**.

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Variables

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\

+-------------------------------+
| **λ:** wavelength (m)\        |
| **v:** wave speed (m/s)\      |
| **f:** frequency (1/s), (Hz)\ |
| **T:** period (s)             |
+-------------------------------+

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Definition of terms

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+----------------------------------------------------------------------+
| **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.\                              |
| \                                                                    |
| **Wave speed (v)**: the speed at which the wave pattern moves.       |
| Units: meters per second, (m/s)\                                     |
| \                                                                    |
| **Frequency of oscillation (*f*)** (or just **frequency**): the      |
| number of times the wave pattern repeats itself in one second.       |
| Units: seconds^-1^ = (1/s) = hertz (Hz) In sound, *f* tells us the   |
| pitch. The inverse of frequecy is the period of oscillation.\        |
| \                                                                    |
| **Period of oscillation (*T*)** (or just **period**): duration of    |
| time between one wave and the next one passing the same spot. Units: |
| seconds (s). The inverse of the period is frequency. Use a capital,  |
| italic *T* and not a lowercase one, which is used for time.\         |
| \                                                                    |
| **Amplitude (*A*)**: the maximum height of the wave measured from    |
| the average height of the wave (the wave's center). Unit: meters (m) |
+----------------------------------------------------------------------+

Image here

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.*

