Yes, waves can be partially reflected and refracted simultaneously when they encounter a boundary between two different media. The incident wave is divided into a reflected wave that bounces back into the original medium and a refracted wave that passes into the second medium. The proportion of the wave that is reflected or refracted depends on factors like the angle of incidence, the wavelengths of the wave, and the properties of the two media including their refractive indices. This simultaneous reflection and refraction is a common phenomenon observed in various wave interactions with boundaries.

The angle of incidence plays a crucial role in determining the behaviour of waves at boundaries. It directly influences the angles of reflection and refraction. According to the law of reflection, the angle of incidence equals the angle of reflection. In refraction, a larger angle of incidence (up to the critical angle) typically results in a larger angle of refraction, though this also depends on the refractive indices of the two media involved. Beyond the critical angle, total internal reflection occurs, and all the wave energy is reflected back into the original medium, leading to no refraction.

Wave intensity is affected during both reflection and refraction. In reflection, the intensity of the reflected wave depends on the surface material and its reflectivity. A highly reflective surface, like a mirror, results in a high-intensity reflected wave. During refraction, the intensity of the refracted wave can be influenced by the absorbing characteristics of the new medium and the angle of incidence. Some wave energy is also lost as part of the wave is typically reflected at the boundary. The attenuation of wave intensity is significant in applications like fibre optics and underwater acoustics, where energy loss impacts signal quality.

The frequency of a wave doesn’t change during reflection or refraction, adhering to the principle of conservation of energy. However, the frequency influences other wave properties and, consequently, the wave’s behaviour at boundaries. Higher frequency waves, like ultraviolet light, can be reflected more than lower frequency waves under the same conditions. In refraction, although the frequency remains constant, the wave speed and wavelength change in the new medium. This is evident in optical phenomena like dispersion, where different frequencies (or colours) of light are refracted by different amounts, resulting in the separation of light into a spectrum.

The material of a boundary significantly influences how waves are reflected and refracted. Different materials have distinct refractive indices, a measure of how much a wave slows down upon entering a new medium. For instance, light entering glass from air slows down and bends towards the normal due to glass's higher refractive index. The material also affects the reflection; surfaces with higher reflectivity cause a larger portion of the incident wave to be reflected. The nature of the surface, whether it's smooth or rough, further impacts the type of reflection, leading to either specular or diffuse reflection.