November 26, 2021
By Kevin Cox, CSI, CDT
The Ancient Greeks and Romans are credited for inventing modern-day architectural acoustics. However, much of this occurred by mistake. Greeks and Romans were trying to solve line-of-sight issues with deeply banked seating arenas in a semi-circle configuration with broad front trumpeting performance areas. This left little to impede the line of sight from any seat in the auditorium or arena. In doing so, they created a good acoustical performance system. Later, the Romans would build large, slanted roofs above the sides of acting areas. Much by mistake again, this architectural addition resulted in reflecting sound to the rear of the auditorium and elevated acoustical performance.
The first reference to architectural acoustics is made by Vitruvius in 1st century BC in his book “De Architectura” (On Architecture). In these writings, Vitruvius describes “echeia” or sounding vases. These vases were placed on the sides of open-air stages to create a chamber that produced reverberation giving sounds a richer quality.
The Middle Ages had only an elementary knowledge of acoustics. Halls and churches are characterized by their overwhelming excessive reverberation and poor speech intelligibility. It is not until late 1900 the father of modern-day acoustics comes on the scene⸺Wallace Clement Sabine (1868-1919). Sabine used pipe organs as sound sources and seat cushions as sound absorbers in a Harvard University lab in 1898 to examine and measure the properties of sound. Sabine went on to assist in the design of the Boston Symphony Hall in 1900, considered one of the most acoustically proficient concert halls of its day. In 1888, Sabine discovered a reverberation time formula that does not appear in print until three years after his death in a collection of papers on acoustics. Today, the formula—known as Reverberation Time 60 dB—is used by acousticians all over the world in its original form. Through experimentation, Sabine was able to determine a definitive relationship between quality of acoustics, sides of the chamber, and amount of absorption, with the most important factor being reverberation time.
Sound can be described as a disturbance or turbulence passing through a physical medium in the form of longitudinal waves from a source to a receiver causing a sensation of hearing. This medium does not have to be the atmosphere but can be a solid, fluid, or gas. The speed of sound through these different media differs due to their molecular composition. The more solid a medium, the more rapidly sound is passed through it. This disturbance or turbulence is in the form of a wave that has alternating high and low pressures and moves in a longitudinal direction of propagation. This pressure creates peaks and valleys, and the distance between two pressure peaks or valleys is a wavelength. A period is the time it takes for one complete oscillation, measured in seconds, and represented with the letter ‘T.’ Frequency is the number of oscillations per second and is measured in Hertz or Hz. Amplitude is the distance between a crest (the highest point), and a valley (the lowest point), and it is measured in decibels (dB). The greater the amplitude, the louder a sound; the lower the amplitude, the quieter or less dB a sound will produce. The fewer Hz or oscillations a sound has, the deeper and lower pitched it is. The greater the number of oscillations, the higher the pitch. These variables make up all the sounds that are audible and inaudible to the human ear.
Sound wave behaviour
Once a sound is introduced into a space, it is interrupted by objects, people, and boundaries of the space itself. Materials are varying degrees of two types: those that allow sound waves to pass through, and those that do not. When encountering barriers, sound waves are likely to behave in the following ways: absorption, transmission, refraction, reflection, diffusion, and diffraction.
• Absorption occurs when a sound wave hits an obstacle and some sound energy is lost through its transfer to the molecules of the barrier; this energy is said to be absorbed. Thickness, porosity, frequency, and amplitude affect amount of absorption from a sound incident striking a surface.
• Although some sound energy is lost molecularly in the composition of the obstruction, some will make it through and be audible on the other side. This is transmission, or a sound being able to transfer through an obstruction. When specifiers and designers are looking at sound privacy of one space to another, they are trying to control transmission.
• Refraction is a variation of transmission. The difference is the soundwave bends as it passes through the obstruction.
• The sound not absorbed or transferred through an obstruction often bounces back into a space. This phenomenon is called sound reflection, and is what specifiers and designers try to control in large, untreated echoic spaces.
• A sound incident ray will often mirror off a flat hard surface, but additional rays can splay out from the incident ray. This is a process known as diffusion, the scattering of reflected sound rays.
• Diffraction is also splaying of rays, but due to indirect impact. It is a product of sound moving around an obstruction and rays splintering, or diffracting, due to this physical relationship.
• Sound produced in a space will bounce off reflective surfaces, gradually losing energy. When these reflections are mixed with each other, this is known as reverberation. Too much reverberation has a negative impact on speech intelligibility, and too little reduces the rich warm sounds like those from live music in an orchestra or concert hall setting.
Utilizing Sabine’s formula
Sabine’s formula measured the time it takes for sound energy to decrease by 60 dB after the sound incident has ceased. Measured in seconds, this is the reverberation time 60 dB (RT60). The rate of decay is going to depend on the amount of absorption in a room, its geometry, obstacles, and the properties of the sound incident itself. This will vary from space to space.
The RT60 is calculated by determining the volume of the space, and the amount of surface area (i.e. walls, floor, and ceiling). An absorption or attenuation coefficient is placed on each surface. As specifiers and designers know, most building materials are more reflective and less absorptive. The RT60 is 0.161 m (0.049 ft) times the volume of the space over the surface areas and individual coefficients. This number will reflect the time in seconds it will take a sound incident in this space to drop 60 dB.
The algebraic relationship of Sabine’s equation means any variable can be determined if the remaining components are known. Working the formula forward one can determine a modelled RT60 by knowing the volume, surface areas, and associated coefficient. Conversely, knowing the volume, the desired RT60, and the surface areas, one can determine how much treatment or absorptive coefficient material will be needed to achieve the desired effect or RT60.
For example, in a lecture hall with a desired two-second RT60, the calculation can be used to find a measurement of sabins (a sabin is 0.09 m2 [1 sf] of perfectly absorptive material). If 2100 sabins are needed, and a 50 per cent absorptive material is being used, the amount of sabins is divided by the absorption coefficient, in this case 0.50, to come up with 390 m2 (4200 sf) of treatment needed to achieve the desired two-second RT60.
For general purposes, an RT60 of 1.5 to 2.5 seconds is considered acceptable for most spaces. Under the 1.5 second mark, there is a clearer articulation of speech, but the space starts to become acoustically dead, making it difficult to hear at the rear of the space, resulting in a loss of deeper bass tones. Above 2.5 seconds RT60, the space gains fullness and richness of sound but speech intelligibility suffers, and discerning words become difficult. Luckily, algebraic prowess is no longer a necessity for running these calculations, as several free, online acoustic reverberation calculators are readily available. These calculators can work forward to determine a space’s RT60, or backward to determine the amount of sabins or absorption needed to reach a desired RT60.
Measuring acoustic performance
For anyone who has looked at a wall assembly or opened an acoustical ceiling catalogue, they have likely come across the method for measuring and quantifying building materials. Noise Reduction Coefficient (NRC), Sound Transmission Class (STC), and Ceiling Attenuation Class (CAC) are ways to evaluate how materials will perform acoustically in each environment. NRC is a scalar representation of the amount of sound energy absorbed upon striking a surface, represented as a decimal or percentage of sound energy absorbed and rounded to the nearest 0.05. An NRC of zero indicates perfect reflection, and an NRC of one indicates perfect absorption. If half the sound energy is absorbed by a material, like in the earlier example, then it has an NRC of 0.50. This is an average sound absorption over four frequencies, 250, 500, 1000, and 2000 Hz. This is a similar measurement to the Sound Absorption Average (SAA), but the SAA is over a wider variety of frequencies, starting at 200 Hz, and going to 2500 Hz. It is rounded to the nearest 0.01. Although SAA is a more exact measurement of sound absorption, the industry standard for most acoustical products remains NRC.
STC roughly measures the decibel drop from one side of an obstruction to the other. The word decibel comes from the root deci, meaning 10, and its inventor Mr. Alexander Graham Bell. A change in 10 dB indicates a doubling or halving of a soundwave’s amplitude. STC can be between interior partitions, ceilings/floors, doors/windows, or exterior to interior. If there is a 70 dB sound incident on one side of an interior partition, and 25 dB can be heard on the opposite side, the partition has a 45 STC. CAC is a measurement that has come into existence with more open office landscapes, partitions that go under grid, and not slab to slab. CAC is like STC in that it measures a decibel drop, but STC is a two-part reduction of sound energy. If there is a sound incident on one side of a partition, one must measure in CAC the sound energy that goes through the ceiling, bounces off the structure above, and comes down into an adjacent space. The drop in decibels will be the ceiling’s CAC. Like STC, the higher the CAC, the better the performance of a ceiling (i.e. a 25 CAC is considered low performing, while a 35 CAC is considered high performing). When using a high CAC ceiling, wall construction with a minimum STC of 40 should be specified. CAC and STC are more about blocking or confining sound energy, while NRC is about absorbing it.
For years, the most common way to deploy sound absorption in a space has been using acoustical ceiling tile (ACT). The ceiling is a large, cost-effective place to create an acoustically absorbent plane, plus house electrical and HVAC components. However, continuing demands to be more sustainable and renewable have led to more resilient and recyclable materials to address these areas. Perforated aluminum is becoming a desirable means to addressing the world’s need to be better stewards of the planet. By micro-perforating aluminum panels one can create a place for sound waves to enter, and then be trapped by any number of sound absorbing materials. These materials can be both recycled and recyclable. Cellulose Fiber Acoustical Batt (CFAB) is made from recycled cotton and polyester that is treated to have a Class A fire rating, and a perfectly absorbing NRC 1.0. This material is a non-irritant and can be recycled at the end of its use. Facing this with a micro-perforated aluminum panel creates a high-performing recyclable wall or ceiling to last the life expectancy of the building.
Metals do not only provide resilience, beauty, and acoustical performance, but gains in paint technology make for an unlimited pallet for the design and viewing community. Paint coatings with 70 per cent polyvinylidene ﬂuoride (PVDF) resin formulation now mimic wood, stone, and other natural materials, offering all the natural beauty but with minimal upkeep. Further, they are suitable for indoor or outdoor use. Other finishes and coatings can be applied to metal to resist chemicals used for cleaning in critical environments that demand this process. For large expansive spaces, metal is the perfect option for wall panels and/or baffles. This gives ample opportunity to explore colour, texture, geometry, gloss, and sheen, all in a single material that is abuse resistant, resilient, and does not go into the landfill once its architectural life is over.
Kevin Cox, CSI, CDT, is the director of interior business development for ATAS International. He has more than 25 years of experience in the commercial construction industry, including positions within operations, sales, and estimating for a large commercial interior contractor. He has held positions in architectural business development and ran his own commercial contracting company for half a decade. Cox has extensive knowledge of exterior and interior wall construction, as well as interior ceilings and room acoustics. He is a member of the Construction Specifications Institute (CSI), is a director for the CSI Raleigh-Durham, NC chapter, and is a certified Construction Documents Technologist (CDT).
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