Total attenuation increases linearly with distance given constant attenuation coefficient. Which statement describes this relationship?

Total attenuation increases linearly with distance given constant attenuation coefficient. Which statement describes this relationship?

• A. It is inversely proportional to distance
• B. It is proportional to the square of distance
• C. It is directly proportional to distance
• D. It is independent of distance

Answer: (C)

With a constant attenuation coefficient, the attenuation collected along a path adds up evenly per unit length. Mathematically, the total attenuation along a path of length d is the integral of mu dl from 0 to d. If mu is constant, that integral becomes mu × d. So as distance increases, the total attenuation grows in direct proportion to distance. Note that transmitted intensity follows I = I0 e^{-mu d}, which is exponential in distance. The statement here refers to the cumulative attenuation along the path, which scales linearly with distance. The other options would imply wrong relationships: inverse proportionality, quadratic dependence, or no dependence on distance.

With a constant attenuation coefficient, the attenuation collected along a path adds up evenly per unit length. Mathematically, the total attenuation along a path of length d is the integral of mu dl from 0 to d. If mu is constant, that integral becomes mu × d. So as distance increases, the total attenuation grows in direct proportion to distance.

Note that transmitted intensity follows I = I0 e^{-mu d}, which is exponential in distance. The statement here refers to the cumulative attenuation along the path, which scales linearly with distance. The other options would imply wrong relationships: inverse proportionality, quadratic dependence, or no dependence on distance.