The propagation of high amplitude ultrasound waves is inadequate described by a linear wave equation. Non-linear propagation is to expect if the power levels are high enough to make non-linear effects significant. A non-linear propagation results in the distortion of the transmitted waveforms, resulting in the generation of harmonics of the initial frequency components transmitted by the transducer.
In the near field of ultrasound probes, the occurring diffraction and focusing effects make this process complex. The distortion of a wavefront propagating in a medium in which the compressional phase moves slightly faster than the rarefactional phase, results is the conversion of some wave energy into higher harmonics of the fundamental frequency. The effect increases strongly with increasing wave amplitude.

The elements of a rectangular array transducer (also called matrix transducer) are arranged in a rectangular pattern. Rectangular arrays with unequal rows (e.g. 3, 5, 7) of transducer elements are in real 2D (two-dimensional), but they are termed 1.5D, because the number of rows is much less than the number of columns. Their main advantage is electronic focusing even in the elevation plane (z-plane).
The transducers that are termed 2D have an equal number of rows and columns. 2D transducers have the potential to provide real-time 3D ultrasound imaging without moving the transducer.
Active matrix array transducers have several elements in the short axis and in addition multiple elements along the long axis. This allows electronic focusing in both axes, resulting in a narrower elevation axis beam width in the near field and far field.

Anatomic structures respond with characteristic features on ultrasound scanning.
There are some ultrasound terms, referring to the echo appearance, that describes tissue appearance in a uniform manner:

Tendons characteristically are hyperechoic on ultrasound because of the fibrillar pattern. Ligaments appear hyperechoic when the beam is perpendicular to the tissue. Peripheral nerves are hyperechoic relative to muscle.
Muscle appears relatively hypoechoic to tendon fibers. Close observation reveals hypoechoic muscle fibers separated by hyperechoic septae that converge on a hyperechoic aponeurosis. Articular hyaline cartilage appears hypoechoic. The presence of fluid within the joint outlining the cartilage produces a thin bright echo at this interface.
Sound beams do not penetrate the bone cortex. The very bright echo produced at the interface allows both recognition of the bone cortex but also can demonstrate fracture, spurring and bone callus bridging. Abnormal soft tissue calcification and ossification also produces bright reflective echoes.
Cysts or fluid filled areas are without internal echoes and are called echo free or anechoic and may demonstrate enhanced soft tissue echoes posterior to the fluid collection. Inflamed metatarsal bursae and calcaneal bursae clearly depict fluid swelling.

See also Beam Pattern and Zero Offset.

(short for ultrasound beam) The sound beam is the confined, directional beam of ultrasound traveling as a longitudinal wave from the transducer face into the propagation medium. The near field and the far field are two separate regions along the beam. Sound beams are either steered mechanically or electrically. Both rapidly sweep sound waves through tissues.

See also Sheer Wave, Beam Vessel Angle, Beam Steering, and Huygens Principle.

Convex transducers are today standard on every new scanner. A convex surface allows the scanning of a larger area with a smaller array. The method of focusing and beam sweeping of a convex or curvilinear / curved array is similar to a linear array transducer, except of the shape of the probe and the sector format of the created image.
The better fit to the body, caused by the curved shape with smaller convex contact surface, and the wider field of view further from the transducer face are advantages in abdominal ultrasound.
However, also a convex array is often too large to image the heart when probing between the ribs. Caused by combining a large field of view with smallest array size, phased array transducers are the best choice in cardiac ultrasound.

See also Curved Transducer.