# Short Version

Is there is an element of sound theory that quantifies how "far away" a sound seems to be coming from?

And is there a way to maximize that value in a sythisized stereo signal?

# Long Version

I was reading about the THX sound, and came across a YouTube video that visualizes the sound:

not just in a spectogram

but also using a Lissajous curve

If you listen to the sound, you will notice it starts mono; both channels are in-phase with each other, and so the line is nearly verticle:

but the mono channel begins to rotate, meaning you are hearing the mono sound move around you:

and then the two channels begin to separate, and you hear different content in each ear, which shows the rotating line beginning to separate:

until finally the channels are fully separate:

the higher frequencies are progressively added in:

And throughout all this, as higher and higher frequencies are added, the sound becomes "more expansive"

• rather than sounding like it is created close within me
• it sounds like it is progressively coming from further and further away from me
• all around me; like an expanding shell

# Sound Theory Question

But even at it's height of harmonizing, the sound still doesn't sound like it's from more then 25 meters away.

Is there a theoretical concept to the term I am asking about?

• can headphones reproduce it?
• can a sound signal be synthisized that has the theoritical "most" of it?

Is it simply adding higher and higher frequencies?

• and if so, doesn't that mean that the young can perceive sounds from further and further away
• because they have better hearing response

Note: Which seems to imply that "hearing loss" is actually "distance loss".

And the only way for something to sound "infinitely far away", would be if the listener had "infinite frequency response"?

tl;dr: How to make a tone that theoretically sounds like it's coming from infinitely far away?

• A sound infinitely far away would have zero intensity, so it's easy: silence is what a sound infinitely far away would sound like. Also, air absorbs high frequencies more than low, so farther away sounds have less high frequency content, not more. Commented Jan 21 at 4:59
• The question uses the phrase "sounds like", which, to be honest, takes the answer out of the realm of theory and puts it into the realm of human perception. Now the question is "How do I modify and/or embellish the sound to make a person feel like it came from far away?" The usual suspects are some EQ coloration (mentioned in stillsleep's answer) and reverberation/echo effects. Commented Jan 21 at 11:26
• Don't vandalise your question just because you are not getting the answers you hoped for. Your research shows some serious theory/comprehension holes, which the answers have attempted to fill. Aside from matters of manners, you no longer own any content posted on SE. By posting you have licensed your content under Creative Commons licensing terms CC BY-SA 4.0 Commented Jan 23 at 18:13

How to make a tone that theoretically sounds like it's coming from infinitely far away?

In a word: don't.

To simulate a physical phenomenon at some infinite distance, it's useful to evaluate how it would behave at a really large distance. There's probably someone slammimg a door somewhere 100 mile from you now. How does it sound like to you?

Every metric that we use to gauge the distance of a sound tends towards silence in proportion to the sound's distance from the listener.

A faraway sound has to travel way more to reach your ear than the same sound happening right next to you. It's going to sound more diffuse, have less higher frequencies, and be quieter than the same sound happening at a shorter distance.

A sound that's infinitely far away is going to be infinitely diffuse, infinitely darker, and infinitely quieter. What does that leave you with?

You're confusing several issues here - not least of which is that there is no true directionality in headphones other than an artificial left & right.

There is no 3D positioning information at all, because each ear can only hear one speaker; no haas effect, no true directionality. You're then confusing 'phase-ness' with directionality. Headphones can makes sounds appear impossibly right inside your head or far away, by simply adjusting phase, because of the first point.

You've then totally missed that distance removes high frequencies, it doesn't add them. It also adds ambience.

Take the closest thing we have reasonable access to that could approach 'infinite' anything.
Thunder & lightning.
It's not infinitely loud, but it's almost enough to rupture your eardrms should you happen to be within a few yards of it. From this distance thunder is, in effect, white noise; it has a rapid onset but basically consists of all frequencies at once.

By the time you're a mile away - count 5 seconds between flash & bang - then you can hear the start of the peal still retains some higher frequencies, but you hear it pitch down [as if someone was closing down a LPF] and end in lower frequencies. This is because higher frequencies travel faster than lower, but also are subject to more chaotic absorption & dissipation in reflections, so arrive first, weakened. This is known as dispersion - see PhysicsSE - Sound frequencies travel at the same speed?.

At only a mile you're already starting to lose the high frequencies to absorption. By the time your lightning is 5 miles away you will have lost the high frequencies altogether - they will simply be absorbed into the atmosphere. The low frequencies will still arrive, but they will be reflected off every surface between there & you & arrive in a confused jumble of bass rumble that may go on for several seconds - compared to the initial strike which would have been over in milliseconds.

So, you see your infinite distance would really just peter out in only a handful of miles, basically absorbed into the general background noise.
They do reckon they can still hear the Big Bang if they look in the right place. Let's imagine it's all in the bass ;)

In an audio mix [on speakers not headphones] you push a sound into the far field by dulling then slightly overpowering the original signal with early reflections - these can be heading towards out of phase as might happen in a natural room - haas effect gives your directionality based on the relationship between the original signal & the reflections.

• I don't think thunder pitches down. That would require a stretching of the soundwave. I don't hear much thunder, but from memory, it just loses energy top to bottom over distance as the higher energy component waves dissipate, as you describe later. Maybe that's what you meant anyway. I find high energy sounds like far artillery with smearing transients and powerful reflections fascinating. I hate to say, but this uniquely horrific moment of terror brought with it a sound that's ... just something else.
– n00dles
Commented Jan 24 at 17:52
• @n00dles - It's not that they pitch-bend, it's that they start out as white noise, but the highs get lost faster, so the lows then follow through & start to reverberate. Many [but not all] of these demonstrate the principal - samplefocus.com/tag/thunder You can't truly compare explosions because they don't start with the same frequency spectrum, they're really a very low frequency pulse. Commented Jan 24 at 18:03
• Yeah, it's fascinating isn't it, all that sound comes from a rapid pressure change, basically a single pulse or small group of pulses. It reminds me of the balloon in the anechoic chamber. Amazing. I suppose, in isolation, thunder would just sound like a large electrical "snap" close up. (btw, you said "but you hear it pitch down", that's why I said that lol. You must mean like the cutoff frequency going down on an LPF).
– n00dles
Commented Jan 24 at 19:00