Which formula correctly expresses focal depth in cm using diameter in millimeters and frequency in MHz?

Which formula correctly expresses focal depth in cm using diameter in millimeters and frequency in MHz?

• A. focal depth (cm) = diameter (mm)^2 x frequency (MHz) / 61.6
• B. focal depth (cm) = diameter (mm)^2 x frequency (MHz) * 61.6
• C. focal depth (cm) = diameter (mm)^2 / frequency (MHz) * 61.6
• D. focal depth (cm) = diameter (mm) x frequency (MHz) / 61.6

Answer: (A)

Focal depth is determined by how diffraction through the transducer’s aperture focuses the ultrasound beam. A larger aperture (diameter) and a higher frequency (which means a shorter wavelength) push the focal point deeper. A simple diffraction estimate gives F ≈ D^2/(4λ), where D is the aperture diameter and λ is the wavelength. Using λ = c/f, with c about 1,540 m/s, and converting to the given units (D in millimeters, f in megahertz, and F in centimeters) leads to F(cm) = D^2 × f(MHz) / 61.6. That constant 61.6 comes from 4 times the speed of sound in tissue (about 1.54 mm/µs) and the unit conversions. So the expression that matches this relationship is focal depth in centimeters equal to diameter squared (in millimeters) times frequency (in megahertz) divided by 61.6. The other forms either omit the squared diameter, move the constant incorrectly, or place the division/multiplication in the wrong position, which would not reflect how focal depth scales with aperture and frequency.

Focal depth is determined by how diffraction through the transducer’s aperture focuses the ultrasound beam. A larger aperture (diameter) and a higher frequency (which means a shorter wavelength) push the focal point deeper. A simple diffraction estimate gives F ≈ D^2/(4λ), where D is the aperture diameter and λ is the wavelength.

Using λ = c/f, with c about 1,540 m/s, and converting to the given units (D in millimeters, f in megahertz, and F in centimeters) leads to F(cm) = D^2 × f(MHz) / 61.6. That constant 61.6 comes from 4 times the speed of sound in tissue (about 1.54 mm/µs) and the unit conversions.

So the expression that matches this relationship is focal depth in centimeters equal to diameter squared (in millimeters) times frequency (in megahertz) divided by 61.6. The other forms either omit the squared diameter, move the constant incorrectly, or place the division/multiplication in the wrong position, which would not reflect how focal depth scales with aperture and frequency.