If the frequency of a phased array probe is doubled, what happens to the near-field length?

The relationship between the frequency of a phased array probe and its near-field length is rooted in the principles of acoustics and wave propagation. The near-field length is influenced by the frequency of the sound waves; specifically, it is inversely related to the frequency.

When the frequency of a probe is doubled, the wavelength of the sound waves is halved (since wavelength is inversely proportional to frequency). The near-field length can be calculated using the formula:

[ \text{Near-field length} = \frac{D^2}{\lambda} ]

Where (D) is the diameter of the transducer and (\lambda) is the wavelength. Since the wavelength decreases as frequency increases, doubling the frequency means that the wavelength is halved. Thus, the near-field length decreases by a factor of two with respect to the wavelength. However, because of the squared relationship in the formula (specifically, the (D^2) term), the near-field length actually decreases by a factor of four when the frequency is doubled.

Therefore, the correct understanding is that increasing the frequency leads to a shortening of the near-field length due to the halving of the wavelength while also considering the effect of the squared transducer diameter in