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Localizability of bass frequencies in rooms

7794 Views 26 Replies 10 Participants Last post by darthray, Jul 20, 2021

Soulburner

Discussion Starter · Jun 20, 2021 (Edited)

Being the Audio Video Science Forum, this is an attempt to summarize the current state of understanding of our ability to determine the direction of a source of low-frequency sound. Also included are some implications for those seeking stereo bass. I have pulled information from various sources and industry experts to make this as accurate as possible, and at times, attempted to summarize it in my own words. If you have anything constructive to add to this topic, please do so. If you have links to information that contradicts anything here, please share it and I will be happy to make edits.

I hope that this reaches an interested audience here and fosters some good discussion. Let's aim to clear up any misunderstandings about this subject that have propagated in other threads. Without further ado:

AVS User said:
I will just jump in for kicks. First a question, is my understanding that our sound localization capabilities is primarily based on the brain processing small timing differences between sound arriving at different times to each of our ears (along with the construction of the outer ear acting as a filter of sorts)? If so, room or no room, the primary signal (unless it is entirely swamped by reflections, but even those arrive late enough that the brain can delineate them) arrives at our two ears at time that is different enough that we can determine direction. This true at any frequency, as the speed of propagation is the same for all sound frequencies.

The brain can use differences in time and level to determine the direction of a single sound. These are known as interaural differences. The "resolution" that we have to work with is determined by the spacing between our sensory devices, aka ears. An analogy (maybe not a perfect one, but it's apt) might be how radio telescope data gains resolution when the dishes are spaced many miles apart.

However, what works for us at higher frequencies does not work so well at low frequencies.

While the speed of sound remains the same, our perception vs frequency does not, due to the resolution we have with our natural ear spacing and how different wavelengths act when they reach us. And, it is confounded by the room. Note that there isn't a specific frequency that sets a sudden limit. We progressively lose accuracy in the ability to point to a sound source as frequency drops. So let's say we can point laterally to within 1° of a sound source at 1 kHz. Down at 200 Hz, our accuracy may drop by 10-20 degrees. Below 50-100 Hz, depending on the individual and the size of the room, it gets fuzzy and that number grows to 360°.

Starting with the basics: Sound localization - Wikipedia

Evaluation for low frequencies

"For frequencies below 800 Hz, the dimensions of the head (ear distance 21.5 cm, corresponding to an interaural time delay of 625 µs) are smaller than the half wavelength of the sound waves. So the auditory system can determine phase delays between both ears without confusion. Interaural level differences are very low in this frequency range, especially below about 200 Hz, so a precise evaluation of the input direction is nearly impossible on the basis of level differences alone. As the frequency drops below 80 Hz it becomes difficult or impossible to use either time difference or level difference to determine a sound's lateral source, because the phase difference between the ears becomes too small for a directional evaluation."

Explained further here: Introduction to Psychoacoustics - Module 07A

We know that, in a free-field environment:

For low frequency sounds (<500Hz) with wavelengths >~ 28 inches or >~0.68m (>~ 4/3 of the average head's circumference) the auditory system relies mainly on period-related interaural time differences (ITDs).
Low frequency sounds arrive at the two ears with interpretable phase differences. However, by being efficiently diffracted, they don't result in interaural level differences that are large enough to be perceptible.
The absolute highest frequency for which interaural time differences provide useful cues is 1/0.0013 = ~770Hz.
For high frequency sounds (>1500Hz) with wavelengths <~9 inches or <~0.24m (<~1/2 of the average head's circumference) the auditory system relies mainly on interaural level / intensity / amplitude differences (ILDs or IIDs) when making auditory localization judgments.
High frequency sounds cannot diffract efficiently around a listener's head, which blocks acoustic energy and produces interpretable intensity level differences.
IIDs are negligible for frequencies below 500Hz and increase gradually with increase in frequency. For high frequencies, IIDs change systematically with azimuth changes and provide reliable localization cues on the horizontal plane (except for front-to-back confusion).

Therefore while interaural time differences are used for bass sounds, the accuracy of this is reduced with frequency and fails to be accurate at subwoofer frequencies in small rooms, which confuse our perception further due to reflections.

AVS User said:
In any case, In my room I can localize sound at any frequency that I can hear. I use two subs, but my main speakers are +/- a couple of DB down to 35 Hz. I can clearly identify which speaker is producing 50 Hz sound when switching back and forth between them (someone else doing the switching with my eyes closed). My neighbor and also my then partner could likewise Identify where the sound was coming from. This result was repeatable.

Not to discount your experience, but each speaker also drives modal activity differently, so that is a variable you can not eliminate from your test. But keep reading to get to the larger issues at play.

Consider that when a very long wavelength passes through you (50 Hz is 22 feet long), reaches the back wall (and the ceiling, and the floor, and the side and front walls), then comes back at you again, the end of the wave hasn't even left the transducer yet. Not only are you experiencing the "beginning" of the wave multiple times from different directions in rapid succession – with limited ear-to-ear spacing – you are also experiencing the 3-dimensional pressure environment like you are inside the wave itself. Without some spatial cue to accompany this wave, how can your brain know the original source direction? Your ears can not differentiate what is the initial sound and what is a reflection, which is all occurring within one cycle of the sound. The room is effectively steady state (the combination of direct and all reflected sounds integrated over a time interval) at low frequencies. You will see this term used many times throughout Floyd Toole's research, especially in his seminal work Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms.

This is a unique combination of factors that does not exist with higher frequencies.

With certain cues, however, we can be clued in to a sound's origin. Such cues include the initial attack of an instrument which contains high frequency sound, vibrations in the enclosure or in the floor or furniture, etc caused by the low frequency energy, or the harmonics produced by the transducers themselves. For example, playing a 50 Hz tone will get you a 2nd harmonic at 100 Hz and a 3rd harmonic at 150 Hz simultaneously.

If you use music or movie material you can definitely localize subs more easily due to the crossover being a slope and not a hard stop. In fact I have had this problem many times and it is why I have reduced my crossover to 60 Hz (70 Hz is not available with my equipment). 80 Hz can work if I use a steeper crossover slope to kill off the subs faster. I have used up to 90 Hz successfully with a steep crossover filter in a larger room with greater distances between all of the components and the seats.

A speaker without bass management won't present this problem because all of the sounds will come from the same apparent location, but pure tones will produce harmonics, the sum of which could push audibility into localizable territory, depending on frequency and level. Either way, the effect is similar: you are getting higher-frequency content from that sub/speaker whether you intended to or not, and these effects can trick you into thinking low frequency sounds are localizable.

Of course, this is my personal anecdotal experience – but if we reference Floyd Toole in Loudspeakers and Rooms for Stereophonic Sound Reproduction, and Loudspeakers and Rooms - Working Together we find the same conclusions:

Tests where bass transient signals were used support 60Hz being the limit of localizability.
Tests where 2nd order slope crossovers are used support 60Hz.
Tests where 4th-8th order slope crossovers are used support 80Hz.
The early research on woofer localization used bass transients, bass sine waves, and music for blind testing as well as for measurement. Conclusion: bass transients over 60Hz can be localized. For sine waves, it is higher.
The AES Technical Council notes in the Multichannel surround sound systems and operations document AESTD1001.1.01-10 that in small rooms, bass transients under 80Hz cannot be localized to the subs when steep crossovers are used.

And this doesn't even touch on the sighted bias of seeing the subwoofers where they are placed. Another problem altogether.

Next, I will defer to quotes from some audio industry luminaries who have something to say on this subject, in order for our readers to have access to accurate information.

From Loudspeakers and Rooms for Sound Reproduction—A Scientific Review, p. 470:

Floyd Toole said:
As with any subwoofer system, the low-pass filtering must be such that the sound output is attenuated rapidly above the crossover frequency (80 Hz). Excessive output, distortion products, or noises at higher frequencies increase the risk that listeners will localize the subwoofers. A second issue relates to the fact that in order for these systems to function fully, the bass must be monophonic below the crossover frequency. Most of the bass in common program material is highly correlated or monophonic to begin with and bass-management systems are commonplace, but some have argued that it is necessary to preserve at least two-channel playback down to some very low frequency. Experimental evidence thus far has not been encouraging to supporters of this notion (see [72] and references therein). Audible differences appear to be near or below the threshold of detection, even when experienced listeners are exposed to isolated low-frequency sounds. Another recent investigation concludes that the audible effects benefiting from channel separation relate to frequencies above about 80 Hz [73]. (In their conclusion, the authors identify a “cutoff-frequency boundary between 50 Hz and 63 Hz,” these being the center frequencies of the octave bands of noise used as signals. However, when the upper frequency limits of the bands are taken into account, the numbers change to about 71 and 89 Hz, the average of which is 80 Hz.)

David Griesinger, who advocated for stereo bass while working at Harman, wrote:

David Griesinger said:
I believe this model is of high importance for both the study of hearing and speech, and for the practical problem of designing better concert halls and opera houses. The model - assuming it is correct - shows that the human auditory mechanism has evolved over millions of years for the purpose of extracting the maxumum amount of information from a sound field in the presence of non-vital interference of many kinds. The information most needed is the identification of the pitch, timber, localization, and distance of a possibly life threatening source of sound. It makes sense that most of this information is encoded in the sound waves that reach the ear in the harmonics of complex tones - not in the fundamentals. Most background noise is inversely proportional to frequency in its spectrum, and thus is much stronger at low frequencies than at high frequencies. But in addition, the harmonics - being at higher frequencies - contain more information about the pitch of the fundamentals than the fundamentals themselves, and are also easier to localize, since the interaural level differences at high frequencies are much higher than at low frequencies.

He also acknowledges:

David Griesinger said:
The statement that low frequencies cannot be localized is easily shown to be true when a sine tone as used as a signal.

He goes on to propose some "tricks" and conditions in which a system can be created to localize low bass frequencies, however these are specialized conditions and usually do not exist in home rooms. If you are interested you can read about that in his paper here: http://www.davidgriesinger.com/asa05.pdf

Earl Geddes is one of the leading authorities in loudspeaker design and small room acoustics:

Earl Geddes said:
It is only reasonable that as the frequency falls the differences in level and timing at the two ears must vanish. This is simple physics. As such the spatial resolving power of our two ear system must also vanish. What is not so clear is the speed that this happens. I think that WithTarragon has it correct in that the resolution is pretty well gone at 50 Hz and pretty well apparent at 300 Hz. My question would be "is this in a free field?" where I would certainly assume that it has to be (otherwise what are the conditions?) That means that adding in the effect a small room has - the fact that the sound is now arriving at all kinds of different angles within even a ms. - and the resolution cannot possibly go up - it has to go down. Hence for me, I would find that LF localization in a small room would be pretty poor up to about 100 Hz. It will improve up until the spatial resolution is dominated by the rooms early reflections (which limit the spatial resolution at higher frequencies, aka imaging.)

Now the LF resolution I have stated above assumes a reverberant field. If one is close to the source then there are near-field and direct-field effects that could be more audible than the reverberant field effects. For example, there could be differences in level at the two ears from the 6 dB falloff with distance, or near-field phase effects that differ at the two ears.

Nevertheless, all of this is academic. Even if we could perfectly localize bass down to 20 Hz no matter what, practically all source material would not support this configuration, being encoded with mono bass to avoid phase issues between speakers and complaints from headphone users who do not tolerate bass in one ear. Therefore instead of pursuing stereo bass, Harman developed Soundfield Management – because the research is clear that minimizing modal activity gives an immediate and positive effect that translates across all material. In the rare event where a recording is found to have significant bass in only one channel (I have heard some, and with headphones it is not pleasant), is it worth the tradeoff of living with unoptimized room modes and phase interactions between your components, in order to maximize this effect?

All of this follows the same theme: it's not the source of low frequencies themselves that we are locating from a subwoofer in a room, but the higher frequency content on the crossover slope, the harmonics, the mechanical or enclosure noises your subwoofer may be making, and/or sympathetic vibrations that accompany the waves that tip us off to their apparent source. Speakers can not create pure tones, and the localization of instruments is determined mostly by their overtones and higher-frequency transient attacks, not their fundamentals. Music contains complex sounds that inevitably have plenty of localizable content in their spectrum. If they didn't, localization would be exceedingly difficult due to the way our hearing works at low frequencies and how rooms confound the situation further.

No one can dictate how an enthusiast should set up a system, including as to attempt to enjoy certain kinds of spatial cues that accompany their bass. However, they should understand the underlying physics of what they are actually hearing, including any potential shortcomings of setting up a system to do so. They should also understand the best practices for achieving good bass in a room and make decisions accordingly.

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