Final answer:
The divergence of sound waves in the far field depends on the sound wave's frequency and the diameter of the crystal. Larger crystal diameters lead to less divergence, directing the sound beam more narrowly as it moves away from the source.
Step-by-step explanation:
The amount of divergence that occurs in the far field is determined by the sound wave's frequency and the diameter of the crystal. In the context of ultrasound physics, the element of the transducer responsible for producing the sound waves is the piezoelectric crystal, which vibrates at set frequencies. The size of this crystal plays a crucial role in determining the divergence of the wave, as well as the directivity pattern. Larger diameter transducers at a fixed frequency produce a sound beam with less divergence than those with smaller diameters. The divergence is inversely related to the diameter of the transducer's crystal and the frequency used.
For example, a larger crystal diameter at a given frequency results in a sound beam with a narrower spread as it propagates, creating a more focused beam. Conversely, a smaller diameter results in a beam that diverges more quickly. This principle is similar to how light beams diverge depending on the aperture size of a lens or opening.