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) ^_x cos (12^{_{$\pi$ x}} 10⁹t - ^_$\beta$z)(A/m)

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