If a traveling wave encounters a change in the physical properties of the medium through which it propagates, the wave will be perturbed where the change occurs. This perturbation generally involves some level of reflection, absorption and transmission at the boundary.
For example, if a wavefront impinges on an ideally rigid surface, all of the wave energy will be reflected from the surface. However, if the surface is instead covered with a layer of absorbing material, only a portion of the wave energy will be reflected, with the remainder being trapped and damped within the material.
The extent of such reflection can be characterized by a reflection coefficient (), which specifies the ratio of reflected to incident wave energy. Materials that are very reflective will have a value of close to 1, while will be close to zero for materials that are very absorptive. In general, the reflection coefficient will be frequency dependent.
Wave reflection from surfaces will also depend on the shape of the surface. If an acoustic wave encounters a rigid wall that is flat over at least several wavelengths in all directions, the wavefront will be reflected from that surface at an angle equal to its angle of incidence (referred to as “specular” reflection). On the other hand, a wall that is very uneven will reflect a wavefront in many directions (referred to as “diffuse” scattering).
Figure 18 illustrates a source-listener arrangement with “multipath” wave propagation. If the time delay between the arrival of the direct and reflected waves is greater than about 50 milliseconds, the reflected sound will be perceived as an echo.
Figure 18:
A source-listener arrangement with an “echo” or “floor bounce” propagation delay.
The system of Fig. 19 (top) provides a signal processing block diagram to simulate the sound wave propagation of Fig. 18 using digital delay lines. The scale factors and account for losses over the respective direct and reflected paths due to air absorption and spherical spreading. If the floor had a reflection coefficient less than one, this could also be included in the factor.
Figure 19:
Floor reflection block diagrams.
The delay common to the two paths can be pulled out and implemented separately, as illustrated in the lower part of Fig. 19. In this case, the length of the delay line for the reflected path must be adjusted by subtracting from it the common delay length and its attenuation factor appropriately scaled.
is found as:
If the gain factors were only used to simulate spherical propagation scaling, the scaling for the reflected path in the lower plot of Fig. 19 would be calculated relative to as: