What is the free-space path loss formula and how does it scale with distance and wavelength?

• A. PL(d) = (4πd/λ)^2; path loss grows with distance and decreases with wavelength; expressed in dB as 20 log10(4πd/λ)
• B. PL(d) = (2πd/λ)^2; path loss decreases with distance
• C. PL(d) = (4πd/λ)^2; decreases with distance
• D. PL(d) = (4πd/λ)^-2; grows with distance

Answer: (A)

In free-space propagation, power fans out in all directions as it travels, so the loss grows with distance and decreases with wavelength. The standard free-space path loss in linear terms is PL(d) = (4πd/λ)^2. This shows a squared increase with distance: if you double the distance, the loss goes up by a factor of four, which shows up as a 6 dB increase in decibels. Because λ is in the denominator, longer wavelengths (larger λ) reduce the loss, since the (4πd/λ) term gets smaller. When you convert to decibels, it becomes FSPL(dB) = 20 log10(4πd/λ), which cleanly reflects both dependencies: distance increases the loss, wavelength decreases it. The correct option matches this form and the stated behavior. The other choices either swap constants (2π instead of 4π), imply the loss decreases with distance, or use an inverted exponent, which don’t align with the physics or the standard FSPL expression.