The Red Rocks Effect: Low Frequency Behavior in Raked Venues
Prediction software has become an indispensable component of the modern sound system design process. System designers can create a 3D mockup of the audience geometry and then experiment with loudspeaker choice, quantity, placement and aiming until the predicted coverage meets the design goals. The software can calculate rigging weights, centers of gravity, safety factors, and other information needed to deploy the system as designed. Then the proper gear can be put on the truck and taken to the gig, and the system can be deployed properly the first time.
There’s an important distinction to be made here: the prediction tools used by system designers for live events - tools like MAPP 3D, ArrayCalc, Soundvision, and so forth - typically focus on the coverage of the direct sound onto the audience geometry, with either no or limited ability to consider reflections off venue boundaries. Acoustics and venue designers have access to more complex and advanced tools such as Odeon, CATT-Acoustic, and EASE (not EASE Focus) that can model absorption coefficients, materials properties and ray-traced reflections to create a full simulation of the actual room acoustics, not just the direct sound from the system.
Given how strongly the acoustic environments influence the listening experience of our live events, it might seem that paying attention to just the direct sound in the prediction stage is quite myopic. Consider, though, that those of us tasked with temporarily deploying systems into these spaces can’t do anything about it either way, and regardless of how hostile the acoustic environment is, the strategy is always the same - maximize energy onto the listening area, and minimize energy onto walls, ceilings, and everywhere else unoccupied by listeners. How much would having an accurate prediction of RT60 (reverberation decay times) in each octave band change that approach? The architects and acousticians who design and shape the acoustical behavior of these spaces can benefit greatly from this information, but the live event techs who are in the space for a day? Probably not so much.
Prediction Works…
Although the direct-sound-only approach may seem like a tremendous limitation, I submit that the reason we’ve made it this far with these tools is that, by and large, they work. For example: Figure 1 below is a slide from my educational presentations, showing a comparison between the predicted system response and actual measured response at four locations in a medium-sized theater.
Figure 1: Predicted response from four locations in a theater (top) compared with the measured response from those same locations (bottom).
The system is doing what the prediction said it would. By any reasonable interpretation, that predicted data can be considered accurate enough to inform our design process.
Except…
If you’re expecting a “but…” at this point, you’re correct. Here it comes:
Regular readers will recall the discussion of design efforts to increase low frequency uniformity at Red Rocks Amphitheater over the last few summers. The unexpected thing was that, in both of the designs mentioned in that post, the subwoofer design worked too well. In both cases I ended up with an excess of LF in the rear of the venue, to my ear approximately 6 dB, and had to dial back the beamsteering a bit to get back to the expected - and desired - results.
Returning to the venue this year afforded the opportunity to gather some data with the hopes of further investigation. My 2023 and 2024 prediction data are visible in Figure 1 of the article linked above so I won’t rehash it here. FIGURE 2 below shows the 2025 prediction, of one side of the flown sub array, at 40 Hz:
FIGURE 2: Flown sub array, one side, 40 Hz, 1/3 oct, 3 dB isobars
As usual, we’re viewing the prediction in 3 dB isobars, which means that from mix position (about fifty feet from the stage) to the rear of the venue, the array goes through four color transitions, a loss of 12 dB.
Now let’s compare the predicted 40 Hz behavior against the actual measured behavior. Measuring subwoofers in real-world conditions is somewhat of an inexact science, but the trend line in FIGURE 3 tells the tale:
FIGURE 3: Predicted vs Measured front to back sub loss @ 40 Hz, normalized
At first blush, the difference might seem to be attributable to a boundary effect, but this is normalized data, not absolute SPL. That means any absolute change in level is removed from consideration. (The boundary-related behaviors of flown vs ground-stacked subwoofers are widely misunderstood, as demonstrated in this paper and this paper.) What we are seeing here is different - not just an increase in level due to the surface plane, but an actual reduction in the loss rate over distance.
In other words, something is going on with the inverse square law. As acoustic energy radiates outwards from a source, conceptualized as an expanding sphere, a doubling of the radius equates to the energy being spread over four times the surface area. In the live sound industry, we often word this as “a loss of 6 dB per distance double.”
FIGURE 4: A graphical illustration of the Inverse Square Law by Borb, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=3816716
Returning again to Figure 3, note the increase in level at the last data point in the rear of the venue - this is a boundary effect, caused by coupling off the large vertical wall directly behind these seats that supports the venue’s ADA seating area and visitors center. You can hear this effect for yourself by leaning against the rear wall of a venue and listening to the increase in bass response.
But how do we explain the decreased loss rate up the hill?
It’s The Rake
My hypothesis was that flown subwoofer arrays at Red Rocks are not radiating spherically (or hemi-spherically) into free space, but instead the raked audience geometry acts as a sort of acoustic “ramp” or “funnel,” effectively cramming the radiated energy into less than four times the surface area for every distance double. The expanding wavefront has less space to radiate into as it moves forward than it would if it were in free space or in a venue with a flat floor, so the loss rate is decreased compared to what the inverse squared law states, and therefore what our direct-sound-only prediction software predicts.
The world of live sound reinforcement is somewhat of a “wild west” when compared to the more rigorous academic tradition of acoustics, so I reached out to several acoustician friends of mine to ask about this acoustic ramping effect, if it had a proper name (for lack of a better term, I’ve been referring to it in my notes as the Red Rocks Effect) and if it had a body of research attached to it. They all agreed this “acoustic ramp” hypothesis was a sound explanation for the decreased loss rate up the hill, but didn’t recall any research or an official term for the concept. A search through the Journal of the Acoustical Society of America archives didn’t turn up anything fruitful, but we plan to keep digging, and if anything surfaces, I will update this post accordingly.
Isolating the Variable
A proper (wave-based) acoustic simulation should help us put the “acoustic ramp” hypothesis to the test by isolating the effect of the rigid raked geometry. I used ConverTool to convert the audience geometry from ArrayCalc to .DXF format, and imported that geometry into Treble, a web-based acoustic simulation tool. I added four receiver probes along the rake, one approximately at mix position and three further up the hill. For sources I used both a single omnidirectional point source and a single SL-SUB.
FIGURE 5: A screenshot from the Treble simulation project
The simulation included no other geometry other than the audience rake, and allowed me to adjust the properties of the rake to be either acoustically transparent at 95% absorption (virtually no effect on the sound waves, like a free-field, direct-sound prediction) or acoustically rigid (5% absorption, akin to a solid rock surface that sound waves can’t pass through). If the rigid (non-absorptive) rake geometry is slowing the loss rate, we’ll see it in the simulation.
FIGURE 6 shows the results for a single SL-SUB subwoofer flown about 35 feet off the ground:
FIGURE 6: Simulated front to back sub loss @ 40 Hz for rigid vs acoustically transparent audience rake.
The simulation did show a 6 dB level increase when taking into account the boundary effect of the rigid audience area as opposed to the free field data, but this shows the level-normalized to isolate the difference in loss rate. We also see slight bends in the lines because my probes were not perfectly spaced apart going up the hill, but the trend is clear.
The “acoustic ramp” behavior is clearly visible once the simulation is programmed to consider the rigidity of the audience rake, effectively “funneling” the acoustic energy up the hill and slowing the loss rate, and the 7 dB disparity in the rear of the venue agrees surprisingly well with the empirical measurement data and my subjective perception of the effect.
Expanded Scope
For all its cultural and industry allure, Red Rocks isn’t magical, which means this behavior should be visible in other venues with rigid, raked floor architecture.
A sports arena with a flat, concrete floor and a raked, concrete 100 level should also exhibit this effect towards the rear, once the floor transitions from flat to raked. I would expect the effect to be less pronounced, as voms and hallways act as pressure “outlets”, but we should still observe a decrease in LF loss rate towards the rear as compared to the direct-sound-only prediction.
And, in fact, we do, as seen in this arena data from my Step by Step design series (Part 1, Part 2), where the prediction predicts 3 dB of loss at 50 Hz in the rear of the venue, and the actual data reveals…. basically none at all:
FIGURE 7: 50 Hz prediction shows 3 dB of level variance between mix position and the upper rake, while the real-world data shows none.
Note here that the discrepancy in the pink and green traces is due to the 30 Hz HPF response in the wireless units used, whereas the Orange trace is a wired microphone at FOH. But throughout the entire sub range we see basically no level loss at all from front to back. The pink position is “under” the flown sub array, so the attenuation there makes sense (the design includes small ground subs in the pit for this reason) but we don’t see the expected loss up in the raked area of the venue, on the lip of the 200 level.
Conclusion
Given all this, it seems quite reasonable to expect to observe this behavior to various degrees whenever we’re confronted with a raked, rigid audience geometry: be more pronounced when the geometry is solid concrete, earth or stone with no “pressure outlets” - in fact, Red Rocks may be an archetypal example - and less so when the audience area has porting, hallways voms, or is “acoustically porous” like open-frame metal bleachers.
The behavior will be missed by our standard direct-field prediction tools, but perhaps as prediction technology advances, we may see some “trickle down” from the more advanced acoustical simulation platforms into our day to day industry software tools. Of course, this opens up a Pandora’s box of giving the prediction enough data to be accurate - and in this case, vom locations and the absorption coefficients of arena seating are probably not parameters most live event systems designers want to add to their plate of considerations. If nothing else, perhaps this is empirical support for a “gut feeling” experienced designers may have about sub behavior in such spaces. There’s always value in discovering that there’s some scientific underpinning to justify your hunches.
The author wishes to thank Cheyenne Mendoza, Davis Darrington, Ethan Winer, Michael Fay and Dr. Adam Hill for their assistance with this project.