Which expression represents the distance from the transducer face to the beam's focus?

• A. (D^2)/(2λ)
• B. (D^2)/(4λ)
• C. D/(4λ)
• D. Dλ^2

Answer: (B)

Diffractive focusing from a circular transducer aperture sets the axial focus distance by the combination of aperture size and wavelength. For a circular aperture of diameter D radiating ultrasound with wavelength λ, the practical focus depth along the beam axis is about f ≈ D^2/(4λ). This comes from how the edge and center radiate with differing path lengths and phases; at the focus point the phase alignment across the aperture results in a strong, confined beam, and the condition leads to the D^2/λ scaling with a factor of 1/4. Since λ = c/frequency, increasing frequency (smaller λ) moves the focus quite a bit farther for the same aperture, reflecting the diffraction-based behavior. The other expressions don’t yield a length and don’t match this diffraction-based scaling, so the correct form is D^2/(4λ).