Analysis of Sabine and Eyring equations and their application to concert hall audience and chair absorption

Historically, two equations have been used for predicting reverberation times, Sabine and Eyring. A precise means is presented for determining Eyring absorption coefficients alpha(eyring) when the Sabine coefficients alpha(sabine) are known, and vice versa. Thus, either formula can be used provided the absorption coefficients for the Sabine formula are allowed to exceed 1.0. The Sabine formula is not an approximation to the Eyring equation and is not a shortcoming. Given low reverberation times, the ratio of alpha(sabine) to alpha(eyring) may become greater than 2.0. It is vital that, for correct prediction of reverberation times, the absorption coefficients used in either formula must have been determined in spaces similar in size and shape, with similar locations of high absorption (audience) areas, and with similar reverberation times. For concert halls, it is found that, when the audience area (fully occupied) and midfrequency reverberation time are postulated, the hall volume is directly proportional to the audience absorption coefficient. Approximately 6% greater room volumes are needed when choosing nonrectangular versus classical-rectangular shaped halls and approximately 10% greater volumes when choosing heavily upholstered versus medium upholstered chairs. Determinations of audience sound absorption coefficients are presented, based on published acoustical and architectural data for 20 halls.     

The sound strength parameter G and its importance in evaluating and planning the acoustics of halls for music

The parameter, "Strength of Sound G" is closely related to loudness. Its magnitude is dependent, inversely, on the total sound absorption in a room. By comparison, the reverberation time (RT) is both inversely related to the total sound absorption in a hall and directly related to its cubic volume. Hence, G and RT in combination are vital in planning the acoustics of a concert hall. A newly proposed "Bass Index" is related to the loudness of the bass sound and equals the value of G at 125 Hz in decibels minus its value at mid-frequencies. Listener envelopment (LEV) is shown for most halls to be directly related to the mid-frequency value of G. The broadening of sound, i.e., apparent source width (ASW) is given by degree of source broadening (DSB) which is determined from the combined effect of early lateral reflections as measured by binaural quality index (BQI) and strength G. The optimum values and limits of these parameters are discussed.     

A Comparison of Two Variational Methods

A discussion is given of the relation between the maximum functionaltheorem and Schwinger's variational principle, and it is shownthat the bound given by Schwinger's principle is better thanor the same as that given by the maximum functional theorem.     

Water-Soluble Polymeric Carbon Nitride Colloidal Nanoparticles for Highly Selective Quasi-Homogeneous Photocatalysis

Heptazine-based polymeric carbon nitrides (PCN) are promising photocatalysts for light-driven redox transformations. However, their activity is hampered by low surface area resulting in low concentration of accessible active sites. Herein, we report a bottom-up preparation of PCN nanoparticles with a narrow size distribution (ca. 10±3 nm), which are fully soluble in water showing no gelation or precipitation over several months. They allow photocatalysis to be carried out under quasi-homogeneous conditions. The superior performance of water-soluble PCN, compared to conventional solid PCN, is shown in photocatalytic H₂O₂ production via reduction of oxygen accompanied by highly selective photooxidation of 4-methoxybenzyl alcohol and benzyl alcohol or lignocellulose-derived feedstock (ethanol, glycerol, glucose). The dissolved photocatalyst can be easily recovered and re-dissolved by simple modulation of the ionic strength of the medium, without any loss of activity and selectivity.     

Acoustical design of the opera house of the New National Theatre, Tokyo, Japan

Architect Takahiko Yanagisawa's preface explains his approach to the design. The NNT opera house seats 1810, its volume is 14500 m3, and its reverberation time, with audience, is 1.5 s (proscenium curtain open). Measurements on CAD computer and 1:10 wooden models and full-sized materials samples were conducted over a 7-yr. period. The main floor is almost rectangular, the three balconies have modest fan shape in plan, although the balcony facia at each level create a rectangular shape. The unique design has a large curved reflector in front of and above the proscenium and six curved reflecting surfaces at the front ends of the three side balconies to form, in combination, an "acoustic trumpet." These surfaces, along with the balcony faces and the shaped ceiling, distribute the singers' voices uniformly over the seating areas from a large portion of the large stage at sound levels that easily override the orchestra in the pit.