 A monochromatic waveform has the phasor representation u(x 
1
​
 ,x 
2
​
 ;t)=sin(3x 
1
​
 −4x 
2
​
 −π10 
8
 t)=Im{U(x 
1
​
 ,x 
2
​
 )e 
iωt
 } in a simple nonmagnetic and lossless medium in Cartesian frame Ox 
1
​
 x 
2
​
 . Determine; a) the phasor quantity U(x 
1
​
 ,x 
2
​
 ) b) the direction of propagation  
k
^
  c) the wavenumber k[rad/m] d) the relative permittivity ε 
r
​
  of the medium.