Which factor causes near-field length to scale with the square of the transducer diameter, assuming wavelength is constant?

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Multiple Choice

Which factor causes near-field length to scale with the square of the transducer diameter, assuming wavelength is constant?

Explanation:
The near-field length grows with the square of the transducer diameter when the wavelength is fixed because the distance marking the transition from the near to the far field for a circular aperture scales with D^2/λ. With λ constant, that becomes proportional to D^2. So if you double the diameter, the near-field length increases by a factor of 2^2, which is four. That’s why the correct factor is four times. The other options reflect linear or inverse relationships that don’t capture the D^2 dependence.

The near-field length grows with the square of the transducer diameter when the wavelength is fixed because the distance marking the transition from the near to the far field for a circular aperture scales with D^2/λ. With λ constant, that becomes proportional to D^2. So if you double the diameter, the near-field length increases by a factor of 2^2, which is four. That’s why the correct factor is four times. The other options reflect linear or inverse relationships that don’t capture the D^2 dependence.

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