Question E3B04:
What are “extraordinary” and “ordinary” waves?  

Choices:  
A: Extraordinary waves exhibit rare long-skip propagation, compared to ordinary waves, which travel shorter distances  
B: Independently propagating, elliptically polarized waves created in the ionosphere  
C: Long-path and short-path waves  
D: Refracted rays and reflected waves    

Correct Answer is  B: Independently propagating, elliptically polarized waves created in the ionosphere  

To understand “ordinary” (O) and “extraordinary” (X) waves, remember magneto-ionic theory: the ionosphere is a magnetized plasma. An HF wave entering it splits into two independent characteristic modes with different propagation properties.

Why the correct answer is correct (B)
- The Earth’s magnetic field makes the ionosphere birefringent, so an incoming wave splits into two independently propagating, elliptically polarized modes: the ordinary (O) and extraordinary (X) waves.
- They have different refractive indices, absorption, and critical frequencies, and usually different takeoff/return behavior.

Why the other choices are incorrect
- A: “Long-skip vs short-skip” is not the definition. Both O and X modes can support long paths; skip distance depends on layer height, frequency, and angle, not the O/X label alone.
- C: “Long-path and short-path” refer to going the long way around Earth vs the short way, unrelated to O/X magneto-ionic modes.
- D: “Refracted rays and reflected waves” describes mechanisms of bending/return, not the two polarization modes created by the ionized, magnetized medium.

Useful formulas and rules of thumb
- Plasma (electron) frequency:
  $$f_p \text{ (Hz)} \approx 8{,}980 \,\sqrt{N_e \text{ (cm}^{-3}\text{)}}$$
  or
  $$f_p \text{ (MHz)} \approx 9\,\sqrt{N_e \text{ (10}^{12}\text{ m}^{-3}\text{)}}$$
- Electron gyrofrequency (cyclotron frequency):
  $$f_H \text{ (MHz)} \approx 2.8\,B \text{ (gauss)}$$
  For Earth’s field near mid-latitudes, $f_H$ is roughly 1–1.5 MHz.
- Approximate vertical-incidence critical frequencies:
  - Ordinary mode: $$f_{c,O} \approx f_p$$
  - Extraordinary mode: $$f_{c,X} \approx \sqrt{f_p^2 + f_H^2}$$
  Thus, the X-mode usually supports a slightly higher usable frequency than the O-mode.
- Polarization note: the O and X waves are generally elliptically polarized; for special angles relative to the geomagnetic field, they can approach circular (parallel) or linear (perpendicular) polarization.