Correct Answer - Option 2 : 16 cm
Concept:
The cut-off frequency for a rectangular waveguide with dimension ‘a (length)’ and ‘b (width)’ is given as:
\({{f}_{c\left( mn \right)}}=\frac{c}{2}\sqrt{{{\left( \frac{m}{a} \right)}^{2}}+{{\left( \frac{n}{b} \right)}^{2}}}\)
'm' and 'n' represents the possible modes.
The cut-off/critical wavelength is given as:
\({{\rm{λ }}_{\rm{C}}} = \frac{2}{{\sqrt {{{\left( {\frac{{\rm{m}}}{{\rm{a}}}} \right)}^2} + {{\left( {\frac{{\rm{n}}}{{\rm{b}}}} \right)}^2}} }}\)
Calculation:
Given: a = 8 cm, b = 4 cm
For H10 mode
i.e. m = 1 and n = 0, we get
\({{\rm{λ }}_{\rm{C}}} = \frac{2}{{\sqrt {{{\left( {\frac{{\rm{1}}}{{\rm{8}}}} \right)}^2} + {{\left( {\frac{{\rm{0}}}{{\rm{4}}}} \right)}^2}} }}\)
λC = 2 × 8 cm = 16 cm