section_path: Special waves/Plane waves
section_name: Plane waves
paragraph_text: Plane waves
  
  A plane wave is a kind of wave whose value varies only in one spatial direction. That is, its value is constant on a plane that is perpendicular to that direction. Plane waves can be specified by a vector of unit length n ^ {\displaystyle {\hat {n}}} indicating the direction that the wave varies in, and a wave profile describing how the wave varies as a function of the displacement along that direction (n ^ ⋅ x → {\displaystyle {\hat {n}}\cdot {\vec {x}}}) and time (t {\displaystyle t}). Since the wave profile only depends on the position x → {\displaystyle {\vec {x}}} in the combination n ^ ⋅ x → {\displaystyle {\hat {n}}\cdot {\vec {x}}}, any displacement in directions perpendicular to n ^ {\displaystyle {\hat {n}}} cannot affect the value of the field.
  
  Plane waves are often used to model electromagnetic waves far from a source. For electromagnetic plane waves, the electric and magnetic fields themselves are transverse to the direction of propagation, and also perpendicular to each other.