Final answer:
The question pertains to acoustic analogs to the Fresnel equations for sound waves at arbitrary angles of incidence and is seeking the expressions for pressure and density continuity at the boundaries. Snell's law in acoustics, similar to optics, can describe the relationship between angles and refraction based on the ratio of the speeds of sound in different media.
Step-by-step explanation:
The student is inquiring about acoustical analogs to the Fresnel equations, which describe the reflection and transmission (refraction) of light at an interface between two media and the related intensities and phases for different angles of incidence.
Specifically, the question is asking for the formulas that describe the continuity of pressure and density for sound waves as they reflect and refract at arbitrary angles when encountering a boundary between two different acoustic media.
For sound waves, similar to light, the boundary conditions that must be satisfied at an interface include the continuity of pressure and the particle velocity component normal to the surface. The analogous acoustic equations involve ratios of the acoustic impedances of the media and the angles of incidence and refraction, similar to Snell's law.
Snell's law for acoustics, which relates the angles of incidence and transmission to the ratio of the speeds of sound in each medium, is given as n₁ sin θ₁ = n₂ sin θ₂, where n₁ and n₂ are the refractive indices and θ₁ and θ₂ are the angles with respect to the normal of the interface.
While the namesake and discovery of Snell's law are often attributed to Willebrord Snell, it is important to recognize the earlier contributions of the Arabian physicist Ibn Sahl to the law of refraction.