The ratio of the effective surface area to

The ratio of the effective surface area to the effective volume for the three prayer halls is plotted in Fig. 4. The effect of the large hemispherical domes in reducing the surface area is represented by the solid square plots. The upper curves in Fig. 4 clearly show the low surface area/volume (SA/V) ratio of the sphere compared with the other geometrical shapes. The SA/V ratio for a unit volume of a sphere is 4.836. By contrast, the SA/V ratio of a cube is 6 (Schmidt-Nielsen, 1984; Vogel, 1988). Thus, using geometrical shapes that are similar to the curved surface of a sphere, such as icosahedrons and dodecahedrons, reduces the SA/V ratio.
Characteristics of the architectural finishing materials of mosques In most contemporary mosques, the walls and ceilings are probably constructed of hard reflective materials because of the ease of maintenance and hygienic issues. A common material used in walls because of its luxurious and rich visual characteristics is marble. The hand-crafted ornaments in marble have been replaced in present-day mosques with GRC because of its mass production potential and ease of construction. In most cases, the materials selected for walls and ceilings are made of hard reflective materials. The floor is commonly laid with carpet. The high acoustic aa utp characteristics of the carpet regulate the effect of creating a highly reverberant space, if installed above the underlay. A list of common finishing materials used in contemporary mosques and the three halls examined in this work is shown in Table 2. The analysis of the relative relationship of the geometrical parameters and selected material characteristics is shown in Fig. 5 for each octave band frequency. The equal trends shown by curves a and b also reflect the linear increase in volume with increasing surface area. The curves reflect an increase of 2.5 times of an order in the main and daily prayer halls of the Dewela Mosque and 2 times in the Damascus City Centre Mosque (Fig. 3). The SA/V ratio effect is also shown in Fig. 5c, with the presence of curved surfaces, such as the hemispherical domes, in the main and daily prayer halls of the Dewela Mosque and the rectangular shaped abstract form of the Damascus City Centre Mosque. Plotting the absorption characteristics relative to volume, resulted in lower values for the Damascus City Centre Mosque prayer hall because of its low SA/V ratio.
The computer model simulation Given the nature and complexity of the interior geometry of the three prayer halls examined, implementing a feasible computer model theory is important to obtain good quality data. The examined halls are large architectural spaces. Thus, aside from the near field effect, the far field contribution is important to model in the three-dimensional space. Simplified and two-dimensional approaches (Clayden et al., 1975; Holmes and Lyon, 1974) are not suitable. Thus, in this work, the ray tracing model was implemented during the computer predictions. The ray tracing technique (Heutschi, 1995) is based on following the reflections on the surface areas of each ray emitted from the source location (Fig. 6) as it undergoes reflections and diffraction at building surfaces until the order of the reflection of the rays exceeds a specified amount. The intensity at a point due to direct sound is calculated using the inverse square law. The numbers of rays generated in each run must be large enough to acquire quality data. The generation is repeated several times and usually more than 100,000 rays are used. The ray tracing approach (Heutschi, 1995) has proven to be very accurate and reliable, as long as a sufficient number of rays are used. The number of rays is easily verified for each space and volume individually by increasing the number of rays in packets of 500 until a convergence criterion is reached.
RT evaluation Once the source position was determined, the software generated the number of rays required, which interacted with the modeled surface reflections, to obtain an estimated RT. The rays continued to lose energy with increasing reflection order until it attenuated to a certain quantity (e.g., 40–60dB). At this point, the rays were considered completely absorbed and contributed no more energy to the resultant sound field. The collective behavior was resumed in the estimation of the RT for each frequency. The resultant decay curves for the three examined prayer halls are shown in Fig. 7, which presents the geometrical features of the three prayer halls and the absorption coefficients of materials.