¶Wave Kinematics and Electromagnetism

A wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. For electromagnetic (EM) waves like light and radio signals, the disturbance is a self-propagating oscillation of coupled electric and magnetic fields.

The fundamental relationship governing periodic waves connects the wave speed $v$, the frequency $f$, and the spatial wavelength $\lambda$: $v = f \cdot \lambda$

¶Wave Parameters

• $\lambda$ (Wavelength): The spatial period of the wave—the distance over which the wave's shape repeats. In the SI system, it is measured in metres (m).
• $f$ (Frequency): The number of occurrences of a repeating event per unit of time, measured in Hertz (Hz), where 1 Hz = 1 cycle per second.
• $v$ (Phase Velocity): The rate at which the phase of the wave propagates in space. For EM waves in a perfect vacuum, $v = c$ (the speed of light, $\approx 3 \times 10^8$ m/s).

¶Implications for Antenna Design

In radio astronomy and spacecraft communications, antenna design is strictly dictated by the wavelength of the carrier signal. For optimal resonance and maximum power transmission/reception, the physical length of a dipole antenna is typically constructed to be exactly one half-wavelength ($\lambda/2$).

For parabolic reflector antennas (like those used in the NASA Deep Space Network), the diameter of the dish determines the diffraction limit and gain of the antenna. The gain $G$ is proportional to $(D/\lambda)^2$, meaning higher frequencies (shorter wavelengths) allow for much more tightly focused communication beams using the same physical hardware size.

Reference: Griffiths, D. J. (2017). Introduction to Electrodynamics (4th ed.). Cambridge University Press.

¶References

• Vibrations and Waves (MIT Introductory Physics Series) (A.P. French)
• Fundamentals of Physics (David Halliday, Robert Resnick, Jearl Walker)
• The Physics Classroom: Properties of Waves