Which transducer would provide the longest near-zone length?

Which transducer would provide the longest near-zone length?

• A. 10MHz, 6mm diameter aperture
• B. 10MHz, 5mm diameter aperture
• C. 10MHz, 4mm diameter aperture
• D. 10MHz, 3mm diameter aperture

Answer: (A)

Longer near-zone length comes from a larger transducer aperture at the same frequency. For a circular piston transducer, the near-field length is about L_n ≈ D^2 / (4λ), where D is the aperture diameter and λ is the wavelength in the medium. At 10 MHz in tissue, λ ≈ 1540 m/s ÷ 10,000,000 Hz ≈ 0.154 mm. Compute the near-field length for each diameter: - 6 mm: L_n ≈ 6^2 / (4×0.154) ≈ 58 mm - 5 mm: L_n ≈ 25 / 0.616 ≈ 41 mm - 4 mm: L_n ≈ 16 / 0.616 ≈ 26 mm - 3 mm: L_n ≈ 9 / 0.616 ≈ 15 mm Since L_n grows with the square of the aperture, the largest diameter provides the longest near-zone length. Therefore, the 6 mm aperture transducer yields the longest near-zone length.

Longer near-zone length comes from a larger transducer aperture at the same frequency. For a circular piston transducer, the near-field length is about L_n ≈ D^2 / (4λ), where D is the aperture diameter and λ is the wavelength in the medium.

At 10 MHz in tissue, λ ≈ 1540 m/s ÷ 10,000,000 Hz ≈ 0.154 mm.

Compute the near-field length for each diameter:

• 6 mm: L_n ≈ 6^2 / (4×0.154) ≈ 58 mm

• 5 mm: L_n ≈ 25 / 0.616 ≈ 41 mm

• 4 mm: L_n ≈ 16 / 0.616 ≈ 26 mm

• 3 mm: L_n ≈ 9 / 0.616 ≈ 15 mm

Since L_n grows with the square of the aperture, the largest diameter provides the longest near-zone length. Therefore, the 6 mm aperture transducer yields the longest near-zone length.