Energy distribution at an interface with impedance mismatch results in which of the following?

• A. All energy reflected
• B. No energy transmitted
• C. Division of sound energy into transmitted and reflected modes
• D. Energy is absorbed completely

Answer: (C)

When a ultrasonic wave encounters an interface between two materials with different acoustic impedances, part of the energy is reflected back into the first medium and part is transmitted into the second. The impedance mismatch causes this split because the boundary conditions require the pressure and particle velocity to satisfy continuity across the boundary, so the wave must partly reflect and partly continue forward. Energy conservation (ignoring losses) means the incident energy equals the sum of the reflected and transmitted energies. At normal incidence, the fraction reflected is R = ((Z2 − Z1)/(Z2 + Z1))^2 and the transmitted fraction is T = 1 − R (or T = 4Z1Z2/(Z1 + Z2)^2). If the impedances match, all energy transmits; with mismatch, some energy is reflected in addition to what is transmitted. In real materials, a small portion can also be absorbed at the boundary, but the fundamental outcome is that energy divides into transmitted and reflected waves.