L1® vs B1 Bass Module Fall Off with Distance

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Hilmar-at-Bose wrote [1].

As many have observed, only the L1 qualifies as a Cylindrical Radiator™ loudspeaker, the B1 Bass Module certainly doesn’t as it looks a lot more like “cubical” radiator. Only a cylindrical source will display 3 dB per distance-doubling falloff. The B1 is a conventional speaker and falls off with 6 dB per distance-doubling. Does that mean that the spectrum gets unbalanced with distance, i.e. not enough bass as we move away from the source?

Not really, and here is why: The observation of so-and-so dB per distance doubling is only true in “free field”, i.e. in some imaginary space that doesn’t have any reflective surfaces. Such a thing doesn’t exist. Most places where you play generate lots and lots of reflections. At any point in the room, the sound field consists of two components:

  1. The sound that comes directly from the source aptly called “direct sound” and
  2. All the sound that comes bouncing back from the walls, called “reverberant field”.

The level of the reverberant field tends to be roughly the same everywhere in the room. When you are close to the source, the “direct sound” dominates. As you move away from the source, the direct sound drops in level and at some point called critical distance the direct sound has the same level as the reverberant field. From this point on the reverberant field dominates and the sound level remains pretty much constant no matter how much further you move away.

The level of the reverberant field, the critical distance, and the “reverb time” are all close room acoustical cousins and basically determined by the geometry and amount of absorption of the room. In nearly all rooms, there is more absorption at high frequencies and less absorption at low frequencies. Less absorption makes the reverb time longer, the reverberant field level higher, and the critical distance shorter.

Another factor that influences the critical distance is the directivity of the sound source. Let’s make a thought experiment: Imagine a sound source that radiates “normally” to the front but nothing to the back. The direct sound level doesn’t change, but the reverberant level drops by 3 dB since the total energy radiated into the room has dropped by half. That means the critical distance has increased. Of course, that’s only true if you stand in front of the source. In the rear, there is no direct sound any more and the critical distance has become zero. We see that the directionality of the sound source increases the critical distance within it’s beam, cone, pie slice (or whatever shape it radiates), but decreases the critical distance outside.

Now what has all that to do with our initial L1/B1 problem? As it turns out the L1 has a much higher critical distance than the B1 Bass Module. That has two reasons: First, there is more absorption at higher frequencies. Second, the L1 is highly directional: it doesn’t radiate up or down.

Taking all this together we see roughly the following picture: The L1 has a fairly large critical distance, i.e. it’s mostly direct sound and that falls off with ca. 3 dB per distance doubling. The B1 Bass Module has a short critical distance (not directional, low room absorption) so the behavior becomes quickly a mix of reverberant field and direct sound which tends to also look fairly similar to a 3 dB per distance-doubling fall-off over a good stretch.

To add insult to injury, this is all grossly simplified. In actual rooms, the reverberant field is never really constant, room modes get in the way, the L1 behaves not quite cylindrical in the lower mids, bass levels increase in the vicinity of wall, etc.

If it’s any consolation, we have actually measured the fall off versus distance for our combined system (L1 & B1 Bass Module) in a couple of different rooms and the 3 dB per distance-doubling describes the measured data remarkably well.