The acoustic properties of materials are often expressed in frequency-bands and for that reason it is reasonable to conduct the ray-tracing separately for each such frequency-band to cover the whole bandwidth of interest. If there is no frequency-dependent diffusion then all the frequency-bands can be processed simultaneously as the ray propagation paths can not diverge. In that case the energy values and material properties can be represented as vectors instead of scalar values.
The listener is typically of spherical shape in ray-tracing, although other possibilities, such as cubes or planar receivers, are possible as well. The main advantage of spherical listeners is that the associated geometric operations are typically simple. For example, computing the possible intersection of a ray with a sphere needs only computation of the shortest distance of a line from a point. After that the actual intersection detection is just a comparison of that distance and the listener radius. If an intersection is detected, then the current energy of the ray should be stored on the receiver response at the corresponding time. Another advantage is that a sphere represents an omni-directional receiver that registers rays from all directions with equal weight, and that is typically what is required of a receiver.
It is important to realize that in ray-tracing there is no need for $1/r$ or $1 / r^2$ scaling as was done with the image-source method. In the image-source method the image sources represent spherical wave-fronts with such an attenuation whereas in the ray-tracing the rays carry acoustic energy, and similar attenuation is achieved naturally. Let us consider a free field in which there are no reflections. In such an environment the number of rays passing through a listener decreases quadratically as a function of distance. Doubling the distance from the source will drop the number of rays down to one fourth of the original, and this reproduces the $1 / r^2$ energy attenuation, and that is the same as $1/r$ attenuation for sound pressure.
There are some downsides in the energy registration described above. First of those is that the specular reflections get easily smeared out in time. If the listener is relatively close to the sound source, multiple rays might pass through the listener. While this is correct in the energy-sense as discussed above, the same acoustic event may get registered at multiple time slots in the response. That would be observed as erroneous diffusion of sound, that should not happen for the direct sound or for the specular reflections. For this reason it can still be beneficial to compute the direct sound and first order specular reflections separately by use of image sources. By that means all those would retain their original nature without artifacts caused by the ray approximation. One way to fight against error caused by multiple detection of the same specular path is to use as small listeners as possible but at the cost of increasing the risk to miss some important paths.
Below you can investigate the gathered time-energy response with the same controls as in the ray-tracing example above.
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