A room mode by any other name...

A certain percentage of my life has been and still is devoted to small room acoustics. I consider myself somewhat of an expert on this subject, though others may disagree. (Don't worry—I'm well aware of who you are.) In recent years, confusion has arisen over the exact definitions of certain small room acoustics technical terms that have long been taken for granted.

Specifically, I am talking about standing waves, room resonances, room modes, normal modes, eigentones, et al. In the long history of architectural acoustics and its subset of small room acoustics, these terms have been widely accepted as synonymous. In the context of small room acoustics, a standing wave is a resonance is a (room or normal) mode is an eigentone is a(n)...

This assumption of synonymity was largely without question for a long time. Recently, however, it has been called into question and, after several years, it would appear that the issue is still unresolved. Specifically, the correctness of grouping standing wave in with the other terms describing what is, to avoid confusion throughout the rest of this blog, a room mode has been hotly debated on numerous acoustics forums.

For those of you not familiar, a room mode is defined by the Rayleigh solution to the wave equation for rooms with infintely rigid boundaries. In the case of rectangular rooms, this solution is conveniently simplified to this equation:

For small rectangular rooms, this equation is incredibly useful for figuring out ahead of time what will happen when a sound source, such as a loudspeaker, is placed in the room. In the cases of existing rooms with a fixed sound source already in place, the equation can be used to determine what type of problems (i.e., which room modes) are being experienced, thus dictating where in the room acoustical treatments might be placed to counter the unwanted effects. Convenient online calculators are available, like this one.

The confusion about the term standing wave arises when one considers the exact definition. According to the American National Standard for Acoustical Terminology, ANSI S1.1-1994 (reaffirmed in 2004):

"6.20 standing wave. Periodic wave having a fixed distribution in space which is the result of interference of progressive waves of the same frequency and kind. Such waves are characterized by the existence of nodes or partial nodes and antinodes that are fixed in space."

Resonance is not implicit when one uses the term "standing wave." There are wave interferences that can occur in small rooms that do not come about as a result of resonant behavior.

Room modes are fixed and defined by the properties of a room. In the case of a small rectangular room, the length, width, and height of the room are all that are needed to solve the above equation. A sound source placed in the room will excite the room modes to greater or lesser degrees depending on its exact position. But, regardless of source position, the frequencies of the room modes are fixed and cannot be changed unless the room is changed. Quod erat demonstrandum.

Standing waves that do not correspond to room modes can occur in small rooms if circumstances are just right. This is sometimes the case when a low frequency wave from a loudspeaker at one end of a room bounces off the opposite wall and interferes with the wave coming from the loudspeaker. No resonance need be present for wave interference to take place, thus creating a standing wave pattern in the room. Or is this a standing wave? That is the question!

Philip Newell, in his magnificent text, Recording Studio Design, is careful to differentiate resonant standing waves (room modes) from the more broadly defined standing waves. The following is excerpted from the definition of Standing waves and resonances in Newell's Glossary of terms:

"It should be stressed that standing waves always exist when like waves interfere, whether a resonance situation occurs or not, and that the common usage of the term 'standing wave' to describe only resonant conditions is both erroneous and misleading."

This perspective is debatable. Some respected thinkers in the field of acoustics would argue that the sort of non-resonant behavior being described does not conform to the definition of a standing wave. I cannot say I agree. I cannot say I disagree. What would be best, IMHO, is if those of us who consider ourselves "experts" could better delineate the exact type of behavior they are referring to when using the term standing wave.

As a parting thought, a fair amount of heated discussion has taken place on the Internet concerning this (seemingly minor) subject. I grow increasingly convinced that it may never be resolved. (It certainly would be nice to resolve the whole thing right here and now...but I am not unrealistic.) What is unfortunate is that some of the discussions, I feel, have irritated people in the myriad acoustics forums; people who are mostly novices, who only seek simple advice for making their room(s) sound better, and who do not wish to bear witness to what amounts to a debate of semantics between a few members of the acoustical literati. IMHO, acoustics forums are not the best place for this debate. I feel the issue can be resolved easily and then left alone. I hope the above will help us "experts" work towards that goal.