Sinusoidal plane wave | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-06-02

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Sinusoidal_plane_wave


00:08:20 1 Alternative representations
00:15:44 1.1 Complex exponential form
00:29:23 1.2 Applications
00:33:01 2 Polarized electromagnetic plane waves
00:35:32 3 See also



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SUMMARY
=======
In physics, sinusoidal (or monochromatic) plane wave is a special case of plane wave: a field whose value varies as a sinusoidal function of time and of the distance from some fixed plane.
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
        )
        =
        A
        cos
        ⁡
        
          (
          
            2
            π
            ν
            (
            
              
                
                  x
                  →
                
              
            
            ⋅
            
              
                
                  n
                  →
                
              
            
            −
            c
            t
            )
            +
            φ
          
          )
        
        
      
    
    {\displaystyle F({\vec {x}},t)=A\cos \left(2\pi \nu ({\vec {x}}\cdot {\vec {n}}-ct)+\varphi \right)\,}
  where 
  
    
      
        
          
            
              n
              →
            
          
        
      
    
    {\displaystyle {\vec {n}}}
   is a unit-length vector, the direction of propagation of the wave, and "
  
    
      
        ⋅
      
    
    {\displaystyle \cdot }
  " denotes the dot product of two vectors.  The parameter 
  
    
      
        A
      
    
    {\displaystyle A}
  , which may be a scalar or a vector, is called the amplitude of the wave; the coefficient 
  
    
      
        ν
      
    
    {\displaystyle \nu }
  , a positive scalar, its spatial frequency; and the adimensional scalar 
  
    
      
        φ
      
    
    {\displaystyle \varphi }
  , an angle in radians, is its initial phase or phase shift.
The scalar quantity 
  
    
      
        d
        =
        
          
            
              x
              →
            
          
        
        ⋅
        
          
            
              n
              →
            
          
        
      
    
    {\displaystyle d={\vec {x}}\cdot {\vec {n}}}
   gives the (signed) displacement of the point 
  
    
      
        
          
            
              x
              →
            
          
        
      
    
    {\displaystyle {\vec {x}}}
   from the plane that is perpendicular to 
  
    
      
        
          
            
              n
              →
            
          
        
      
    
    {\displaystyle {\vec {n}}}
   and goes through the origin of the coordinate system.  This quantity is constant over each plane perpendicular to 
  
    
      
        
          
            
              n
              →
            
          
        
      
    
    {\displaystyle {\vec {n}}}
  .
At time 
  
    
      
        t
        =
        0
      
    
    {\displaystyle t=0}
  , the field 
  
    
      
        F
      
    
    {\displaystyle F}
   varies with the displacement 
  
    
      
        d
      
    
    {\displaystyle d}
   as a sinusoidal function

  
    
      
        F
        (
        
          
            
              x
              →
            
          
        
        ,
  ...