If an ultrasonic wave is transmitted through an interface where the first material has a higher acoustic impedance but the same velocity as the second material, the angle of refraction will be

• A. Greater than the angle of incidence
• B. Less than the angle of incidence
• C. The same as the angle of incidence
• D. Beyond the critical angle

Answer: (C)

When an ultrasonic wave crosses into another medium, the bend of its path is set by how fast the wave travels in each material, not by the impedance alone. The boundary condition requires the tangential component of the wavevector to be continuous, which gives sin(incident angle) divided by the wave speed in the first medium equals sin(refracted angle) divided by the wave speed in the second. If the speeds are the same, those sines are equal, so the refracted angle equals the incident angle. Impedance differences change how much of the wave is transmitted versus reflected, but they do not change the direction when the speeds are equal. The idea of a critical angle or a refracted angle becoming larger or smaller arises from a speed difference, which isn’t the case here. Therefore, the angle of refraction is the same as the angle of incidence.