# Wave

> One figure for four kinds of wave, chosen by kind:

Page: https://fframes-kit.pages.dev/docs/physics/wave/
Cargo feature: `physics` (`fframes-kit = { version = "..", features = ["physics"] }`)

One figure for four kinds of wave, chosen by `kind`:

- `WaveKind::Transverse`: the medium moves up and down;
- `WaveKind::Longitudinal`: a row of particles that bunch and spread;
- `WaveKind::Standing`: `2A sin(kx) cos(ωt)` with its nodes and dashed envelope;
- `WaveKind::Superposition`: the wave and a second one (`second_wavelength`,
  `second_amplitude`) drawn thin, with their sum drawn thick.

With `front` (the default) the medium starts at rest and the wave leaves the left end.
`marker` picks out one point of the medium, which only moves in place. `displacement(x, t)`,
`envelope(x)` and `nodes()` give the numbers. Gallery scene: `Wave` (all four).

Gallery clip of `Wave`: https://fframes-kit.pages.dev/media/scenes/Wave-1d553763.mp4

```rust
use fframes_kit::prelude::*;

fn figure<'a>(ui: &mut Ui<'a, '_, '_>) -> Svgr<'a> {
    ui.show(Wave {
        kind: WaveKind::Superposition,
        origin: (-6.0, 0.0),
        length: 12.0,
        amplitude: 0.5,
        wavelength: 3.0,
        second_wavelength: 2.2,
        speed: 3.0,
        marker: Some(6.0),
        ..ui.defaults()
    })
}
```

`harmonic(n)` turns a wave into the standing wave of a string's `n`th harmonic, fixed at
both ends (Manim-physics' `StandingWave`): `Wave { length: 9.0, ..ui.defaults() }.harmonic(3)`.
Manim-physics' `LinearWave` is `Wave { front: false, .. }` with `speed = wavelength / period`.

## API

Components are plain structs. Set the fields you need and fill the rest with `..ui.defaults()`: the defaults below come from the current theme (`theme.` values are fields of `Theme`).

### Wave

| Field | Type | Default | Description |
| --- | --- | --- | --- |
| `kind` | `WaveKind` | `WaveKind::Transverse` | What the wave shows: a transverse wave, a longitudinal one, a standing wave or two waves added. |
| `origin` | `(f64, f64)` | `(-6.0, 0.0)` | Left end of the medium, on its resting line, in units of `ui.space`. |
| `length` | `f64` | `12.0` | Length of the medium in meters. |
| `scale` | `f64` | `1.0` | Units of `ui.space` per meter. |
| `amplitude` | `f64` | `0.8` | Largest displacement in meters; a standing wave reaches twice this. |
| `wavelength` | `f64` | `4.0` | Meters between two crests. |
| `speed` | `f64` | `2.0` | Speed the wave travels right at in m/s. |
| `second_wavelength` | `f64` | `3.0` | Meters between two crests of the second wave of a `Superposition`. |
| `second_amplitude` | `f64` | `0.5` | Largest displacement in meters of the second wave of a `Superposition`. |
| `front` | `bool` | `true` | The medium is at rest at the start and the wave leaves the left end on the clock; off makes the whole length move from the start. |
| `marker` | `Option<f64>` | `None` | Meters from the left end of one point of the medium to highlight, which shows it oscillates in place; `None` for none. |
| `particles` | `usize` | `48` | Particles of a longitudinal wave. |
| `band` | `f64` | `1.2` | Meters tall, the lines that stand for the particles of a longitudinal wave. |
| `delay` | `f32` | `0.0` | Seconds after the container's start before the wave begins. |
| `time_scale` | `f32` | `1.0` | Speed of the motion over local time; 2 runs twice as fast, 1 is real time. |
| `color` | `Color` | `theme.colors.accent` | Colour of the wave, or of the first wave of a `Superposition`. |
| `second_color` | `Color` | `theme.colors.highlight` | Colour of the second wave of a `Superposition` and of the nodes of a standing wave. |
| `marker_color` | `Color` | `theme.colors.title` | Colour of the highlighted point and of the summed wave of a `Superposition`. |
| `guide_color` | `Color` | `theme.colors.muted` | Colour of the dashed axis and of a standing wave's envelope. |
| `stroke_width` | `f32` | `theme.stroke.regular` | Width of the wave line in pixels; the other lines use the theme's thin width. |
| `enter` | `Option<EnterAnim>` | `None` | How the axis draws in; `None` shows it from the start. |
| `exit` | `Option<ExitAnim>` | `None` | How the axis leaves at the end of the container; `None` stays. |
| `parts_enter` | `Option<FadeIn>` | `None` | How the medium fades in; `None` for none. |
| `parts_exit` | `Option<FadeOut>` | `None` | How the medium fades out before the end; `None` for none. |

Methods:

- `fn displacement(&self, x: f64, t: f64) -> f64`: The displacement in meters of the medium `x` meters from the left end after `t` seconds: up for the transverse kinds, to the right for the longitudinal one.
- `fn envelope(&self, x: f64) -> f64`: The largest displacement of a standing wave at `x`, `2A sin(kx)`.
- `fn harmonic(self, n: u32) -> Self`: The standing wave of the `n`th harmonic of a string `length` meters long, fixed at both ends: Manim-physics' `StandingWave(n, length)`, `n` half wavelengths along it.
- `fn nodes(&self) -> Vec<f64>`: The nodes of a standing wave, every half wavelength from the left end, in meters.

Feature `physics` · [Source](https://github.com/khanhthanhdev/fframes-kit/blob/main/fframes-kit/src/kits/physics/wave.rs#L43)