DML’s and the Inverse Square Law

In practical experience, DMLs tend to feel as though they don’t lose as much intensity over distance in an average sized room. The other noticeable characteristic is that clarity is maintained at much greater distance from the source than with a traditional loudspeaker. There’s no physical laws being broken here - it’s simply a result of how sonic energy from a DML interacts with the room itself- let’s unpack it and see why.

Let’s begin by unpacking Inverse Square Law a bit:

The Point-source loudspeaker was invented around 100 years ago - and with the passing of all of that time, we have developed a very deep understanding of their behavior. An example of this is a common audio “law” called the "Inverse Square Law” which describes the decay of a sound source’s intensity over distance. That in and of itself is rather intuitive, as most are aware that sound level diminishes the more you move away from the source of the sound. In simple terms this is because sound emanates from the source in a (theoretical) spherical pattern - and as distance increases, the same sound energy is spread across a much larger area - resulting in loss of intensity. 

The Inverse square law attempts to quantify this for us, stating that for every doubling of distance away from a sound source, audio intensity drops by 6dB (4x.) As with any scientific law, there are assumptions that have to be considered, and Inverse Square Law is no different.  

There are two main assumptions to consider - let’s start with the first:

The Inverse Square Law assumes that the sound is in a “free field” - no walls or obstructions along the path to the listener.

This gives us our first challenge to applying this law. Your average room or hall has 4- 6 main boundaries or obstructions, consisting of at least 4 walls, a ceiling, and floor, if not more - so the theoretical law cannot be directly applied and we need to consider the difference between the theoretical room and our practical application.

The second assumption that we need to consider is this:

The sound traveling from a source is in a spherical pattern originating from a single point (hence the name “Point source”)

And this brings us to our next issue - Inverse Square law applies to “Point-Source” loudspeakers yet DMLs are not point source - they are  "Distributed Mode" - meaning different frequencies emanate from different places on the surface of the transducer in a diffuse manner - creating what physicists call  “uncorrelated” sound  (for comparison, point source audio is a “correlated” sound source - where “correlated” refers to the relation between  frequency and phase. )

Let’s talk about two other terms that come into play, and then we can tie this all together and talk about how DMLs behave differently in rooms. Those terms are:

Direct Sound Field: The Direct Sound Field is the sound that originates directly from the loudspeaker - and this continues to follow an approximate 6dB loss per doubling of distance, in rooms. 

Reverberant (diffuse) Sound Field: As you move further away from the source, the reflected sound (bouncing off those hard walls and the ceiling) begins to pile up at the listener. Eventually, the level of this "reflected noise" becomes equal to or louder than the direct sound at the listener and this is referred to as the “critical distance”. Beyond the critical distance, the sound level flattens out and stops dropping significantly, and the listener ends up hearing much more of the reverberant field than direct field. Unfortunately, because all of the reflections arrive “out of time” with each other at the ear, the reflected sound field starts to just sound like “mud” and intelligibility falls off drastically. In a medium-sized room (maybe 60’ wide x 80’ deep x 10’ high ceiling,) you may experience a drop of 3dB per doubling of distance once you pass the critical distance.

How does a DML actually interact with a room, and how does this affect application of the Inverse Square Law?

DML room (boundary) interaction is significantly less “destructive” than with point source. Since a DML consists of highly diffuse “uncorrelated” sound, when the sound reflects off of a boundary, and those reflections arrive “out of time” at the listener, there are no significant summations and cancellations as you would experience with point source boundary interaction. The tendency would be to think that DMLs “throw” farther in a medium sized room than point source, but in actuality the opposite is true. With a DML being a very diffuse source, it “excites” the room much more than a directional point source - and sound dissipates very quickly - and this results in a critical distance that is significantly shorter distance than a point source loudspeaker (critical distance is where reflected audio is more dominant than direct.) However the uncorrelated nature of those reflections results in a very usable and consistent reverberant sound field. Unlike sounding like “mud” (point source) the reverberant field retains clarity and “stays together,” making it very clear and usable. As in our point source example, the reverberant space tends to lose intensity at a lesser rate than the direct sound  and since the direct field is very short with a DML, the majority of the room ends up being in the reverberant space. This results in slightly less measured audio intensity loss over distance than with point source. However - just like several other characteristics of DMLs, the perception to the listener is often a much more even sound distribution - even when deep into the reverberant sound space. DMLs continue to produce excellent clarity well into the reverberate field - where a traditional loudspeaker will have lost much of its clarity.

DML Differentiation: Overcoming the Inverse Square Law:

In this short article, we've unpacked the Inverse Square Law, discovering how it applies to Point Source loudspeakers, and how DMLs overcome some of these behaviors. Our main takeaways are:

  • DML audio intensity drops off at a lesser rate than the theoretical inverse square law once you enter the reverberant sound field, in a typical room.
  • DMLs "excite" the room, with diffuse, uncorrelated sound -  making most of the room/listening space exist in the reverberate sound field (less loss per distance.)
  • Most DML listeners in a room are in the reverberant sound field, where the positive, non-destructive room interaction produces incredible clarity, where point-source audio would have "fallen apart" in reverberant spaces.
  • Loss over distance is around 6dB in the direct field, but often 1/2 of that in the reverberant sound field. It varies by room, but we often see a 4 dB loss per doubling of distance (versus 6 with point source.)
  • DMLs retain clarity well into the reverberant sound field, adding to the perception of less loss/more evenness over distance.