Final answer:
The discrepancy in wavelength relationships between the Friis transmission formula and Planck's formula arises because they describe different phenomena: the Friis formula applies to wave behavior over distance, whereas Planck's pertains to individual photon energy, which is inversely proportional to wavelength.
Step-by-step explanation:
Understanding the relationships between energy, frequency, and wavelength in electromagnetic waves is important in physics. In the context of the Friis transmission formula that you mentioned, the received power at an antenna is indeed proportional to the square of the wavelength. This relationship considers factors like antenna gains and distance between antennas in addition to the wavelength. When it comes to the energy carried by an electromagnetic wave, represented by the equation E=hc/λ, it states that the energy (E) of a photon is inversely proportional to its wavelength (λ), where 'h' is Planck's constant and 'c' is the speed of light.
The apparent discrepancy between these two relationships is because they describe two different phenomena. The Friis transmission formula describes the macroscopic behavior of electromagnetic waves over a distance, including how they are received by an antenna. The relationship of energy to wavelength for a single photon is described by Planck's formula, which applies to the microscopic quantum level, considering an individual photon's energy. It's crucial to note that in electromagnetic waves, energy transfer is proportional to amplitude squared and does not depend on frequency, which distinguishes it from mechanical waves where the energy transfer rate is proportional to both amplitude squared and frequency squared.