(a) A rectangular waveguide has width a = 3.0 cm. Find its cutoff frequency for the TE₁₀ mode. Can a 6 GHz signal propagate? (b) A 50 Ω coaxial cable feeds an antenna of 75 Ω. What fraction of power is reflected? Step 1: f_c = c/(2a) = 3.00×10⁸/(2 × 0.03) = 5.0×10⁹ Hz = 5.0 GHz. A 6 GHz signal is above cutoff → it propagates (as TE₁₀). A 4 GHz signal would decay exponentially and not propagate. Step 2: Reflection coefficient Γ = (Z_L − Z₀)/(Z_L + Z₀) = (75 − 50)/(75 + 50) = 25/125 = 0.2. Reflected power fraction = |Γ|² = 0.04 = 4%; 96% reaches the antenna. If the load were a short (0 Ω), Γ = −1 and 100% reflects — standing waves form, which is why RF engineers obsess over matching.