According to Snell's law, the angle of transmission is related to the incident beam angle and

• A. The amount of acoustic impedance mismatch at an interface.
• B. The change in frequency that occurs at an interface.
• C. One-half of the angle of incidence.
• D. The relative speeds of sound in the two media.

Answer: (D)

Snell's law for sound shows the bend of the transmitted wave depends on how fast sound travels in each medium. When a wave hits a boundary at an angle, the relationship between the incident angle and the transmitted angle is set by the speeds of sound in the two media. Mathematically, sin(theta_transmitted) relates to sin(theta_incident) through the ratio of speeds: sin(theta_transmitted) = (c2/c1) sin(theta_incident), or equivalently sin(theta_incident)/c1 = sin(theta_transmitted)/c2. So the angle of transmission is determined by the relative speeds of sound in the two media.

The frequency, on the other hand, doesn’t change across the boundary for a harmonic source; what changes is the wavelength to accommodate the new speed. Impedance mismatch affects how much energy is reflected versus transmitted, not the direction of the transmitted ray. The idea that the transmission angle is half the incidence angle doesn’t fit Snell’s law.