Q.How does the effective power radiated by an antenna vary with wavelength?

[!TLDR] The effective power an antenna can radiate is inversely related to wavelength -- shorter-wavelength (higher-frequency) waves are radiated far more efficiently for a given antenna size. [!ANSWER] Radiated po …

For a fixed physical antenna length, the effectiveness of radiation depends on how that length compares to the wavelength of the wave being sent -- specifically, on the ratio of antenna length to wavelength. As the operating wavelength decreases (frequency increases), this ratio grows for a given antenna, and the antenna radiates the wave's power far more efficiently; conversely, for a wave whose wavelength is very large compared to the antenna (as with a raw, unmodulated low-frequency audio signal), only a very small fraction of the power fed into the antenna actually gets radiated as an EM wave, with the rest wasted. This is exactly the reasoning behind section 13.5.2's antenna-length rule ($\lambda/4$ minimum length for efficie …

Connect the $\lambda/4$ antenna-length efficiency rule of section 13.5.2 to how radiated power scale …

Assuming radiated power is independent of wavelength/frequency, missing the direct link between the antenna-length rule and radiation efficiency th …