Modelling early and late sound energy relation in multi-purpose auditoria

Abstract

As established by Sabine's formula and Barron's classical theory, the sound energy model is universally and uniformly determined in the diffuse field. The measured values in the multi-purpose auditorium demonstrate how the variation in early and reverberation sound impacts the auditory perception from different seating positions. A new energy decay model is suggested through a statistical study of two auditoriums of comparable size. This model utilizes an adjustable time delay trev to accurately anticipate the energy distribution among various spatial receivers. The direct sound mainly influences the impulse response (IR) in the seats near the middle and exhibits rapid exponential buildup and decay. On the other hand, in the side seats, the smaller initial-time delay gap (ITDG) allows the early reflected sound to combine with the early reverberation sound, resulting in a noticeable reflection. By considering the geographical position, the decay rate of the individual impulse response may be determined using the local upper limit. This can help create a more precise energy model for determining energy-related parameters. This study demonstrates that the revised model includes reflected sound energy resulting in enhanced estimation. Compared to the previous Barron formula, which was based on reverberation time (RT), volume (V), and source-receiver distance (r), the revised formula now includes additional reflected energy, for instance, the time at which the first reflected sound arrives is associated with ITDG, while the average absorption coefficient (α) is determined by the reverberation time. These factors can be determined by utilizing geometric data and pre-established values. The study improved the precision of estimating energy-related factors in strength (G) at frequencies of 500Hz, 1kHz and 2kHz in two similar halls. Measured values in the multipurpose auditorium show the difference of energy distribution between early and reverberation sound affects the auditory perception between different spatial receivers. Here, a new energy decay model with an adjustable time delay trev is provided for improved prediction based on statistical analysis of two auditoriums of comparable size. The impulse response rapidly transitions into exponential decay in the seats close to the center, where direct sound predominates. The early reflected sound will mix with the initial reverberation sound in the seats next to the side to create a strong reflection. By considering the geographical position, the individual impulse response decay may be accurately estimated using the local trev related to the initial time delay gap. This can help to improve the accuracy of the energy model that is used to evaluate the parameters associated with energy ratio.