Which transducer will produce a longer focal length, assuming crystal diameter remains constant?

The transducer associated with a longer focal length, while maintaining a constant crystal diameter, is the unfocused transducer. The focal length is influenced by the properties of the transducer design.

In general, unfocused transducers have longer focal lengths compared to their focused counterparts when other design aspects like frequency are constant. This is because the beam divergence is less in unfocused designs, promoting a longer distance over which the beam remains tight before it diverges significantly.

While both focused and unfocused transducers can be used for various imaging applications, focused transducers concentrate energy into a smaller area, resulting in a shorter focal length due to the design that enhances resolution in the near field but may limit depth of penetration and overall imaging range.

The frequencies of the transducers (5 MHz versus 10 MHz) do affect the axial resolution and penetration depth, but in terms of focusing characteristics with a constant diameter crystal, the unfocused transducers yield a longer focal length. Hence, among the provided options, the unfocused transducer, regardless of the frequency mentioned, is the one that achieves a longer focal length under these conditions.