The subject of acoustics encompasses elements of both physical science and cognitive perception. Our ears deliver complex information that the brain interprets, such as level, pitch, and location; our brain also deciphers language from the acoustical information that it gathers. The problem is that often the features making a room excellent for music are the very same features that make the room a poor choice for speech intelligibility.

The house of worship is rarely a perfect acoustical model when it comes to understanding speech or listening to music, especially in large spaces where the reverberant sound level is most often the culprit. Other issues, such as early reflections, refraction, and absorption, all contribute in a complex way to the “acoustic signature” of the space, and can also contribute to problems with intelligibility. Surprisingly, it can often be the untreated, highly focused reflections that cause the biggest problems with intelligibility. In any case, it is usually a compromise between music and speech that must be struck when designing houses of worship, and if you are lucky enough to be involved with such a project from its inception, when the architect can be influenced, then there will at least be some control over the outcome.

More often than not, when a sound system must be adapted to an existing house of worship, a combination of subjectivity and empirical measurement is used to affect the outcome. Let's look at some of the ways acoustical attributes of a space are defined as it pertains to the application of sound in houses of worship.

Live- and Dead-Sounding Rooms

People both in and out of the audio industry use the term “live” and “dead” to describe the way a room sounds. Actually, it is a mixture of the direct sound level and the early reflected sound level that defines how live or dead a room sounds, and neither of these is reverberation. Here are some definitions for better understanding.

Direct field sound contains no reflections. This is the first sound that hits your ears, and is separated from any reflected sound or reverberation effects due to the room you happen to be listening in. Imagine a room that is so acoustically absorbent that you hear only the sound emanating from the source (such as in an anechoic chamber). Early reflected field sounds, however, are reflected back into the room from flat surfaces and objects in the room. There is an initial time delay gap (ITDG) between the direct sound and the early reflected sounds, and it is this time delay that gives our brains the psycho-acoustical cues that allow perception of room size. ITDG is what provides a sense of realism in artificially generated reverb effects in the studio. Reverb time (RT60) is defined as the time it takes for the sound in a room to decay by 60dB. As you can see from these relationships, reverb time is the final phase in what happens acoustically in a room.

Reverberation of the spoken word begins to affect intelligibility after only a few milliseconds. The brain will combine signals arriving within the first 40ms with the direct field sound and serve to enhance the level (volume) of this sound. Reflections arriving after 40ms degrade the perception of the sound of syllables. Beyond that, as arrival times increase, words run together and eventually sound like distinct echoes because of the longest reflection times. These late reflections pose serious problems to intelligibility, depending upon intensity and arrival time. Interestingly, too short a reverberation time can also be detrimental, especially in rooms where music is important. The optimum reverberation time for houses of worship is between 1.4 and 2.2 seconds.

The Sabine Equation

Now that we have some of the definitions, let's try some math. This equation (developed by Sabine in 1898) will determine the reverberation time (RT60) of a given space. It is quite useful in various derivations for calculating the reverberation time of a room prior to its construction.

RT60 is reverberation time in seconds

V is the volume of the room in cubic feet

S is the total surface area of the room in square feet

a is the average absorption coefficient of room surfaces

Sa is total absorption in sabins

To use this equation, it is important to note that the total absorption in a room involves the absorption coefficients multiplied by the total square feet. Surface area applies to every surface in the room. All building materials have absorption and reflection characteristics that result in a coefficient number known as a. These values can be found in acoustical reference books, measured at different frequencies. The resultant of the expression S × a gives the absorption in units known as sabins. Once the calculations for the floor materials, wall materials, ceiling materials, and other surfaces have been made, it is simple to use the equation to solve for the reverberation time of the room.

The Fitzroy Equation

Due to an editing error, the Fitzroy Equation printed in this article was incorrect. The correct Fitzroy Equation is as follows:

In the 1950s, Dariel Fitzroy modified the theoretical Sabine equation to allow for more of a real-world application. It reads as follows:

In this equation, XY is the area of the side wall in square feet; XZ is the area of the end walls in square feet; YZ is the area of the floor and ceiling in square feet; S is the total boundary surface area; ayz is the average absorption coefficient of the floors and ceiling; V is the total volume of the room in cubic feet, and K is 0.049, a constant. This means that there are three axes for the reverberant field — walls end to end, walls side to side, and floor to ceiling. Because materials on these surfaces are almost never the same, we can get a more accurate real-world number with this equation.

The Big Picture

It is important to note that the aforementioned measurements are empirical. They assume complete mixing of all sound, which in real life does not always happen. Also, there are changing aspects of any room — temperature, humidity, and the number of people filling the seats, which all affect the resulting room sound. People are generally absorptive, but more people in a room will usually increase the temperature, which will decrease the velocity of sound in air. Add to this an air conditioner to counteract the rise in heat, and we get a temperature gradient in the room causing the sound to become refracted in a certain direction. It quickly becomes apparent that we are attempting to model a fairly complex interaction of aspects that can be difficult to accurately predict without direct measurement.

Another complexity in houses of worship is unique room shapes. Curved surfaces and convex or concave room sections can be beautiful, but they can also create their own unique set of acoustic problems. Concave surfaces tend to focus energy, while convex surfaces can cause troublesome reflections that enhance certain frequencies. It is clearly difficult to predict the ways in which a sound wave will reflect from a curved surface, and they are better avoided in the design process if possible. The closer a listener sits to a curved surface, the more difficulty the listener will have in discerning certain frequencies and directional cues from the sound they hear. In order to combat this nemesis, a designer will have to employ the principles of diffraction and absorption creatively.

Reflections, Diffraction, and More

All sounds have a certain wavelength, and when one of these waves hits an object larger than one-quarter of the wavelength, it results in reflections. The intensity of these reflections is directly proportional to the absorption coefficient of the material they hit. Just as light bends when it passes through a prism, sound waves also bend when the object in question is ¼ — wavelength or smaller in size. When the sound diffracts around an object, it loses some of its intensity. Refraction happens when the sound passes from one medium to another, such as the temperature gradient mentioned in an earlier example, or when sound propagating through air encounters glass. Glass re-radiates the sound diaphragmatically both into the listening space and into the air space on the other side of the glass. Glass is a unique case in that it can combine reflection, diffraction, and diffusion in one material, depending upon thickness and how extensively braced the glass is to the support structure. Technically, diffraction occurs when sound encounters material that moves with the impact of the acoustical energy. This motion, or “give,” of the material causes the sound to be partially absorbed and partially reflected back into the listening space, resulting in a net loss or diffusion of energy reflected back into the room. Hanging textile materials in a free space can provide diffraction of unwanted sound in houses of worship and is an excellent way to combine aesthetics with good acoustical design.

Creative use of absorptive material is usually the best way to handle wayward sound energy in a large room. Wall hangings, absorptive ceiling materials, cushioned seats, thick carpeting, and structures designed using the properties of the Helmholtz resonator (especially good for curved surfaces) are used creatively in houses of worship to stop these reflections. There will always be the aesthetic issues, and there are many building materials available today that will blend into the architecture. Although aesthetics are very important, an adequate balance between sound treatment design and visual beauty must be reached for successful sound in houses of worship.

S&VC editor Nat Hecht can be reached at: