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The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expression $$H_z (x,y,z,t) = 0.1 \: cos(25 \pi x) \: \: \cos(30.3 \: \pi y) \: \: \cos(12 \pi \times 10^9 t- \beta z) \: \: (A/m)$$

The cross-sectional dimensions of the waveguide are give as $a=0.08 \: m$ and $b=0.033 \: m$. The mode of propagation inside the waveguide is

  1. $TM_{12}$
  2. $TM_{21}$
  3. $TE_{21}$
  4. $TE_{12}$
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