Question E9A08:
Which frequency band has the smallest first Fresnel zone?  

Choices:  
A: 5.8 GHz  
B: 3.4 GHz  
C: 2.4 GHz  
D: 900 MHz    

Correct Answer is  A: 5.8 GHz  

To understand Fresnel zones: the radius of the first Fresnel zone depends on wavelength (or frequency) and path geometry. For a given path, higher frequency (smaller wavelength) gives a smaller Fresnel zone.

Key formulas:
- General first Fresnel radius:
  $$r_1 = \sqrt{\frac{\lambda\, d_1 d_2}{d_1 + d_2}}$$
- At the midpoint of a path of length $d$:
  $$r_1 = \tfrac{1}{2}\sqrt{\lambda d}$$
- Practical midpoint rule of thumb (with $d$ in km and $f$ in GHz):
  $$r_1(\text{m}) \approx 8.66\,\sqrt{\frac{d_{\text{km}}}{f_{\text{GHz}}}}$$
- Clearance guideline: keep at least $60\%$ of $r_1$ clear:
  $$\text{clearance} \gtrsim 0.6\,r_1$$

Why 5.8 GHz is correct:
- Since $\lambda = \frac{c}{f}$, and $r_1 \propto \sqrt{\lambda} \propto \frac{1}{\sqrt{f}}$, the highest frequency has the smallest Fresnel zone. Among the choices, 5.8 GHz is the highest frequency.

Why the others are incorrect:
- They are lower in frequency, so their first Fresnel zones are larger for the same path:
  - 3.4 GHz: larger than 5.8 GHz
  - 2.4 GHz: larger still
  - 900 MHz: largest of the list

Order from smallest to largest Fresnel zone (same path): 5.8 GHz < 3.4 GHz < 2.4 GHz < 900 MHz.