#
nLab

amplitude

### Context

#### Harmonic analysis

# Contents

## Idea

The *amplitude* of a wave is a measure for its maximal change with space and time.

## Definition

For $n \in \mathbb{N}$ and $\mathbb{R}^n$ the corresponding Cartesian space, a plane wave is a function $\mathbb{R}^n \to \mathbb{C}$ of the form

$\vec x \mapsto A e^{-2 \pi i \vec k \cdot \vec x}
\,.$

Here $a \in \mathbb{C}$ is the *amplitude* of the plane wave (while $\vec k$ s its wave vector).