Which expression correctly represents the axial resolution AR in terms of the pulse count n, the speed of sound c, and the transmit frequency f?

• A. AR ≈ (n × c) / (2f)
• B. AR ≈ (f) / (n × c)
• C. AR ≈ (2f) / (n × c)
• D. AR ≈ (n × f) / (2c)

Answer: (A)

Axial resolution is set by how long the pulse lasts along the beam, i.e., the spatial pulse length. The pulse contains n cycles, and each cycle spans a wavelength λ. So SPL = n × λ, and since λ = c/f, SPL = n × c / f. The axial resolution is about half of that length, giving AR ≈ (n × c) / (2f).

This shows why the correct expression is proportional to n and c and inversely proportional to f: more cycles or a faster sound speed lengthen the pulse, while a higher transmit frequency shortens the wavelength and improves (reduces) axial resolution. The other forms would not yield a length unit and would misplace how f and c influence AR.