Reflection

Reflection of a sound wave occurs when the wave passes between two tissues of different acoustic impedances and a fraction of the wave 'bounces' back. This forms one of the major principles of ultrasound imaging as the ultrasound probe detects these reflected waves to form the desired image.

Angle of reflection

Like light and other electromagnetic radiation, the incoming incident wave bounces off the boundary at an angle of incidence (θi), which is equal to the angle of reflection (θr).

θ_i = θ_r

This is in contrast to refraction, where the angles of incidence and refraction may not be equal but are dependent on the difference in tissue acoustic impedance.

Intensity of reflection

The intensity of the reflected wave is described by the reflection coefficient (R_I), which is defined as the intensity of the reflected sound wave (I_r) divided by the intensity of the incident sound wave (I_i).

R_I = I_r / I_i

Thus, every tissue interface has its own reflection coefficient (R_I). For example the R_{I,fat→muscle} is 0.015 meaning that if an incoming sound wave encountered a fat to muscle boundary, 1.5% of that sound wave would be reflected at that boundary. This would be compared to the R_{I,muscle→bone} which is 0.41 where 41% of the incident sound wave would be reflected.

Transmitted intensity

Due to the conservation of energy law the energy that would be transmitted through the boundary would represent all the energy from the incident sound wave which was not reflected. The transmission coefficient (T_I) is thus:

 T_I = 1 − R_I

The reflection coefficient of the typical muscle to air boundary is almost 99% making almost all the sound waves reflect off this interface. Therefore, almost no sound would make it past the air filled cavity making tissues 'beyond' this undetected by ultrasound. This is the reason gel must be used on transducers to remove any pockets of air.

Phase shift

It should also be noted that if a sound wave travels from a medium of lower acoustic impedence, (lower speed) to higher acoustic impedance (faster speed), the reflected wave undergoes a 180-degree phase shift in amplitude assuming a smooth interface between tissues. 

Recall that Z (acoustic impedance) = DC (density × speed).