Plane wave

In <a href="/facts/Physics/a7aH2y08">physics</a>, a plane wave is a special case of a <a href="/facts/Wave_(physics)/I3EeyInV">wave</a> or <a href="/facts/Field_(physics)/FJdAKeRA">field</a>: a physical quantity whose value, at any given moment, is constant through any plane that is perpendicular to a fixed direction in space.
For any position 
 
 
 
 
 
 
 x
 →
 
 
 
 
 
 {\displaystyle {\vec {x}}}
 
 in space and any time 
 
 
 
 t
 
 
 {\displaystyle t}
 
, the value of such a field can be written as

F
        (
        
          
            
              x
              →
            
          
        
        ,
        t
        )
        =
        G
        (
        
          
            
              x
              →
            
          
        
        ⋅
        
          
            
              n
              →
            
          
        
        ,
        t
        )
        ,
      
    
    {\displaystyle F({\vec {x}},t)=G({\vec {x}}\cdot {\vec {n}},t),}

where 
 
 
 
 
 
 
 n
 →
 
 
 
 
 
 {\displaystyle {\vec {n}}}
 
 is a <a href="/facts/Unit_vector/GyaXneDn">unit-length vector</a>, and 
 
 
 
 G
 (
 d
 ,
 t
 )
 
 
 {\displaystyle G(d,t)}
 
 is a function that gives the field's value as dependent on only two <a href="/facts/Real_number/R02gw5Pb">real</a> parameters: the time 
 
 
 
 t
 
 
 {\displaystyle t}
 
, and the scalar-valued <a href="/facts/Displacement_(geometry)/jkmEfS3C">displacement</a> 
 
 
 
 d
 =
 
 
 
 x
 →
 
 
 
 ⋅
 
 
 
 n
 →
 
 
 
 
 
 {\displaystyle d={\vec {x}}\cdot {\vec {n}}}
 
 of the point 
 
 
 
 
 
 
 x
 →
 
 
 
 
 
 {\displaystyle {\vec {x}}}
 
 along the direction 
 
 
 
 
 
 
 n
 →
 
 
 
 
 
 {\displaystyle {\vec {n}}}
 
. The displacement is constant over each plane perpendicular to 
 
 
 
 
 
 
 n
 →
 
 
 
 
 
 {\displaystyle {\vec {n}}}
 
.
The values of the field 
 
 
 
 F
 
 
 {\displaystyle F}
 
 may be scalars, vectors, or any other physical or mathematical quantity. They can be <a href="/facts/Complex_numbers/2w7mqI7e">complex numbers</a>, as in a <a href="/facts/Sinusoidal_plane_wave/BGMWIa0Q">complex exponential plane wave</a>. 
When the values of 
 
 
 
 F
 
 
 {\displaystyle F}
 
 are vectors, the wave is said to be a <a href="/facts/Longitudinal_wave/KoysWuIN">longitudinal wave</a> if the vectors are always collinear with the vector 
 
 
 
 
 
 
 n
 →
 
 
 
 
 
 {\displaystyle {\vec {n}}}
 
, and a <a href="/facts/Transverse_wave/WVLe5XKX">transverse wave</a> if they are always orthogonal (perpendicular) to it.

Plane wave open-in-new

Plane wave