Which property determines how much of an incident sound wave is reflected at the boundary and how much enters the second medium?

Which property determines how much of an incident sound wave is reflected at the boundary and how much enters the second medium?

• A. Impedance
• B. Attenuation
• C. Velocity
• D. Phase

Answer: (A)

The key idea is impedance mismatch between the two media. Acoustic impedance, Z, is the product of a medium’s density and the speed of sound in it (Z = ρc). When a sound wave hits a boundary, the boundary conditions require pressure and particle velocity to be continuous, and the fraction of energy reflected versus transmitted depends on how different the impedances are on either side. The pressure reflection coefficient is (Z2 − Z1) / (Z2 + Z1), so a large difference in impedance means more energy is reflected and less enters the second medium; a small difference means more energy transmits. For example, a boundary between air and water has a huge impedance mismatch, so most of the incident energy reflects and only a small portion enters the second medium. In contrast, if the two media have similar impedances, most energy passes through. Attenuation describes energy loss as the wave travels within a medium, not the split at the boundary. Velocity affects impedance but does not by itself determine how much reflects at a boundary. Phase describes the shift in the wave’s phase upon reflection, which is another consequence of impedance contrast but not the amount that is reflected or transmitted.

The key idea is impedance mismatch between the two media. Acoustic impedance, Z, is the product of a medium’s density and the speed of sound in it (Z = ρc). When a sound wave hits a boundary, the boundary conditions require pressure and particle velocity to be continuous, and the fraction of energy reflected versus transmitted depends on how different the impedances are on either side. The pressure reflection coefficient is (Z2 − Z1) / (Z2 + Z1), so a large difference in impedance means more energy is reflected and less enters the second medium; a small difference means more energy transmits.

For example, a boundary between air and water has a huge impedance mismatch, so most of the incident energy reflects and only a small portion enters the second medium. In contrast, if the two media have similar impedances, most energy passes through.

Attenuation describes energy loss as the wave travels within a medium, not the split at the boundary. Velocity affects impedance but does not by itself determine how much reflects at a boundary. Phase describes the shift in the wave’s phase upon reflection, which is another consequence of impedance contrast but not the amount that is reflected or transmitted.