The AR formula AR ≈ (n × c) / (2f) shows AR is directly proportional to which variables?

• A. It shows AR is inversely proportional to f
• B. It shows AR is independent of c
• C. It shows AR is proportional to f^2
• D. It shows AR is directly proportional to c and inversely proportional to f

Answer: (D)

Axial resolution is tied to the spatial pulse length, which equals the number of cycles times the wavelength. Since wavelength equals c divided by f, the axial resolution formula becomes AR ≈ (n × c) / (2f). This shows AR increases with higher sound speed c and with more cycles n, and it decreases as frequency f increases. So AR is directly proportional to c (and to n) and inversely proportional to f. The option that states AR grows with c and shrinks with f captures these key relationships from the formula, making it the best description. It also aligns with the understanding that more cycles and higher c worsen axial resolution, while higher frequency improves it.