Sound in a medium propagates in the form of a wave. A fraction of these sound waves are reflected off the surfaces in a closed environment while the rest of the sound waves are absorbed by the surface medium. Due to this, the intensity of the sound wave initially propagated from the source differs with the position of the audience in the room. Several parameters affect the intensity of sound waves in a room. Acoustic parameters like Clarity (C50) [1] that are key to the auditory comfort of the audience need to be studied in detail to determine a strategy to maintain conditions of acoustic ideality in a room. The audience, being the most important part of the room, need to be in a state of auditory satisfaction, irrespective of their position in the closed room. The surface absorption coefficients, commercially known as the Sound Transmission Class (STC), also affect the clarity and intensity of the sound in a walled room. Various simulations using I-SIMPA, an open source software are performed to determine the conditions of acoustic ideality in the closed environment. These simulations have been performed by varying the surface absorption percentages of the floor, ceiling and walls of the acoustic model, keeping in mind the effect of the external environment.

The simple chamber for testing is designed with a single source and two receivers as shown in Fig. 1. The dimension and positions of the source and receivers are as follows:

Chamber Dimensions: 9.3 m × 7.7 m × 2.8 m (width × length × height) [2].

The various parameters considered prior to performing the simulation are listed in Table 1. The calculation method preferred is Simulation de la Propagation de Particules Sonores (abbreviated as SPPS) method owing to the advantages offered by the sound particle concept over the sound ray concept in calculation and modelling [3]. Energetic type of calculation is preferred for modelling over the ‘random modelling’ calculation type due to the fact that the energy of the particle depends on the atmospheric absorption and the absorption coefficients of the material [4].

The environmental parameters that need to be considered can be defined in the properties and the various environmental properties considered for this analysis are shown in Fig. 2. Atmospheric absorption is negligible at standard temperature and pressure conditions [5].

The work carried in this paper is represented as two parts. In the first part, the theoretical analysis of the chamber with its performance analysis is presented and the second part concentrates on the simulation analysis of the same and variation with wall absorption percentages and chamber dimensions. The schematic of workflow is shown in Fig. 3.

The theoretical analysis Clarity C50 was carried out and verified by using the standard equation pertaining to its mathematical calculations.

In definitive terms, C50 is the ratio between the early sound energy (between 0 and 50 ms) and late sound energy (50 ms onwards) [6]. The C-50 values in dB, generally decreases as the distance from the source increases. Being a measure of intelligibility of speech in an environment, Clarity (C50) is defined in terms of the time limit after which the intelligibility becomes detrimental. The critical time limit is 50 ms. The anticipated value C_50,E for the definition measure C50 was theoretically calculated by means of the formula used in the EASERA Appendix [7] as given below:

(1) C50,E=10log10γs(rHrx)2+1−e−13.8.0.05Te−13.8.0.05TdB

where,

r_x-distance from sound source to listener in m

r_H-Half room diffuse-field distance

(2) rH=0.057VTm

V-Volume in m³

T-reverberation time in s

γ _s–Front-to-random factor of a normal speaker characteristic

Reverberation Time was calculated using the standard Sabine’s formula [8]. According to Sabine

(3) RT=0.161×VSas

where

V is the volume of the room/system under consideration (in m³).

For a source transmitting frequency of 500 Hz, the reverberation time (RT60) is calculated for different values of absorption coefficients of walls, ceiling and floor. The total Sabine absorption [6] and Reverberation time (RT60) obtained using (3) for various coefficients are shown in Table 2.

The theoretically calculated RT60 for various coefficients in Table 2 are modelled below. The verification of the above table for RT60 using I-SIMPA is shown in Fig. 4.

Figs. 4a–4g depict the simulation output for RT60 with different values of surface absorption coefficients according to Table 2. A comparison of the values obtained by simulation and theoretical analysis is shown in Table 3.

It is clear from Table 3 that the values of RT60 from the simulation and using the theoretical calculations carried out for the same simulation settings are nearly equal. This implies that I-SIMPA is an efficient tool that can be used for analysis of reverberation times. Although the I-Simpa simulations indicate the values of RT15, it can be assumed that the values of RT60 and RT15 are approximately equal due to the “Sabine-like” nature of the room [9]. The varying sound intensities at different points in a chamber can cause great discomfort to the audience present in the area of sound reception [10].

Clarity (C50) is calculated by using the formula (1) obtained from the EASARA appendix, for different values of absorption coefficients of walls, ceiling, and floor as per Table 2. The theoretical values calculated for Clarity (C50) are shown in Table 4.

Figs. 5a–5g depicts the simulation output for C50 with different values of surface absorption coefficients according to Table 2. A comparison of the values obtained by simulation and theoretical analysis is shown in Table 5.

It is clear from Table 5 that the values of C50 in the simulation and the theoretical calculations carried out for the same simulation settings are very close to each other in value. This implies that I-SIMPA simulations produce results corresponding to the actual theoretical values obtained using standard mathematical equations.

The simulations analysis C50 were carried for the following two major circumstances:

Single Source

By primarily varying the distribution and number of sources in the chamber, the conditions required to maintain a constant value of C50 in the majority of the chamber were obtained by altering the wall absorption coefficients and chamber dimensions.

The following conclusions can be drawn from the various simulations conducted by means of changing the absorption percentages of the different surfaces in the chamber:

Clarity (C50) pattern is the same for all parameter changes but the value differs with each change of parameter.

The varying sound intensities at different points in a chamber can cause great discomfort to the audience present in the area of sound reception. This paper provides an insight into how the Clarity (C50) can be made constant in the greater part of the chamber by merely varying the surface absorption coefficients of the surfaces and by varying the number and arrangement of the sources in the designed chamber. A combined study of other important acoustic parameters along with C50 can provide a deeper understanding into how the condition of acoustic ideality can be effected in any closed chamber. It has been seen that these ideal conditions can be maintained by varying the values of absorption percentages of the surfaces involved. Commercially, ‘Sound Transmission Class’ (STC) gives an objective measure of the absorption percentages of the surfaces constituting the chamber. The STC rating is a measure of the reduction in decibel noise that a material can provide.