Auditory Time Illusions

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Richard Nyonyi

Dr. Eric Mandell

PHYS 3500

26 April 2012

AUDITORY TIME

Scientists over the years have been amazed with the human ability to perceive reality. It

has been proven that most of the time what human perceives is not fully what it is out there. Take

an example of the visual perception and how it is limited in different ways, we all see the sky to

be blue, but the sky is never blue, just because of our limited visual ability that is what we

perceive (Gibbs). This simply means we do not see everything, we only see what we are able to

see.

Similar to how our visual perception is limited in different ways, so is our auditory

perception. Sound is said to be coming from pulsating (vibrating) motion of air molecules in the

air (Hass), but why is that when someone waves a hand we dont hear any sound? Waving a

hand creates vibrations in the air so we should expect to hear something. We shall find out the

answer later. We are going to see how among others limitations, time has been playing a major

role in our auditory system. First, we shall see what time has to do with our hearing system that

causes all the illusions, and later we going to see few applications in sound processing, and see

how the time factor has helped scientists and artists to fool the human perception.

Our hearing system is such a complicated system that requires different knowledge from

physical sciences to health sciences. As we have already defined sound, the vibrations of air


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molecules reach the outer ear which is well shaped to collect useful information like detecting

direction of the incoming sound and amplifying it (Nave).

The collected and amplified air vibrations reach the ear drum and other structures inside

the ear and are converted to human neural impulses and the physics of sound marks its end. The

brain receives the impulses and translates them in a very complex mechanism that scientists are

still working on.

The good news is that we already have enough information that will help us appreciate

the role of time in this particular study. The range of human hearing is generally considered to be

20 Hz to 20,000Hz (W.Smith). In plain English, we can hear vibrations in the air that are coming

to us at the rate of 20 to 20,000 complete vibrations per second. This already answers our

question of waving a hand since there is by no means a human being will be able to wave a hand

at a rate of at least 20 complete cycles in one second, which is the just the lowest frequency we

can hear. To show that we are still talking about time, frequency is simply a count of number of

events in given unit time, in this case number of air vibrations in one second. As if this frequency


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original wave. Hope you can see straight away that this new wave wont be a good exact

representation of the original wave , the new wave seems to have the same ups and downs but we

cant ignore it`s boxed shape, and we can imagine how that will sound. Fortunately our time

factor comes to help, it can be proven mathematically that if we decrease the time interval

between snapshots, hence increasing the number of snapshots, technically equivalent of saying

increasing sampling rate we can represent the exact original waveform digitally. The question is

how much we need to increase the sampling rate to be able to do that? Now since the intended

audiences are humans, scientists agreed to take the snapshot at the rate that human hearing

system will not be able to tell the difference. Simply this means that, since our hearing range

goes to maximum of 20,000Hz they decided to take the snapshots/samples at least at the rate

twice of our maximum hearing range (Repetto). Using what is called Nyquist theorem, the

normal sampling rate of sound is never less than 40,000Hz.Usually compact discs are sampled at

a rate of 44,100Hz (Schulzrinne). So since we cannot detect differences in the sampling rate this

high, time has beaten our auditory system and if we send our sampled sound to a speaker we hear

the same sound we heard before it was processed electronically.

Let us also check on more fun side of this, let us pay attention to what musicians call

delay based effects. Of course whenever you hear a word delay, you know for sure we are

talking about time. So in simple English we are talking about time based effects. To achieve

these effects, simply they take a copy of a sound and play simultaneous with the original sound

but delaying the copy of the sound by a certain amount of time (Cousins). So the final output

contains the two equal sounds but one being delayed.

Our hearing system does detect repeated sounds that occur after 30 milliseconds

(Pattern). This is when we can unquestionably hear the two distinct sounds. Most delays that are


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above this time range is what we refer to as echo. For the repetitions of sound, below 30 ms of

course with other factors such as lowering the amplitude (volume), these repetitions of sounds

are not detected as different/distinct sounds and our brain get fooled .This addition of depth and

fullness in the sound gives our brain a sense of space. So using this technique, we can fool our

brains to assume different sizes of the surroundings. We can make the sound feel like it is being

played in the cathedral while it was just recorded outdoors. Again notice the role of time and our

ability to hear the difference.

Also, when it comes to flanging and chorusing effects no one will argue the sweet sound

the two produce. In simple English flanging is that robotic sound, while chorusing effect is the

emulation of a number of performers performing together in unison.

Basically for the chorusing effect as seen in the diagram below, not only is the copied

sound delayed between 20-30 ms but also using what is called low frequency oscillator (LFO),

the delay time is gradually shifted up and down within few milliseconds and this simulate small

variations of pitch in that small amount of time (Cousins). Simple math is that if the

pitch/frequency changes once in every 20 ms then, in one second we hear 3,000 variations of


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pitches, this simulates the idea of chorus very well and our brains are being fooled to assume that

there is a big group of performers performing the sound together.

.

For the case of flanging, the major differences with chorusing are that the delay is set

from 0 to 10 ms instead of 20 to 30, also the LFO will do its work the same way like in

chorusing but the delayed sound is simultaneously allowed to go to the output but a replication is

sent back to the delay machine (Cousins). In other words the copy of the delayed sound is sent

back to input, allowed to mix with original sound, the combination goes into the delay machine

and the loop goes on and on as the big curved arrow shows. The end result is what our brain

perceives as the metallic/robotic sound.

So it is obviously observed that our auditory system has limitations relating to time and

as a result of that what we perceive in our hearing system is not exactly what has reached in our

ears. Our brains do some very high sophisticated translations of the resulting sound. Other

information in sound that our hearing system is not capable of capturing is lost or ends up

forming a different effect as we have seen. At some point it is beneficial to have limitations. It is

a confusing just to imagine what life would be if we could hear infinitely everything. It is known

that bats make very high frequency sound above level of human hearing, and they use it to locate

their prey (Richardson), if we could hear everything, being close to bats will be truly noisy. The

same is for our visual perception, if we could see everything in the air from bacteria, pollen, and


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all microscopic particles in the air the term clear sky might not exist in a way. So obviously these

limitations are advantageous to our way of living and if we play smart enough with them, there is

still a lot more we can do to fool the human brain.


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Bibliography

Cousins, Mark. "Chorus ,Flange and phase." MusicTechmagazine (2007): 56.

Gibbs, Philips. "Why is the sky blue." 05 1997.

www.math.ucr.edu/home/baez/physics/general/bluesky/bluesky.htm. 25 04 2012.

Hass, Jeffrey. "What is sound." 2003. www.indiana.edu/~emusic/acoustics/sound.htm.25 04 2013.

Nave, Dr.Rod. HyperPhysics. 2010. web. 26 04 2012.

Pattern, John. "Diffeence Between Echo and Reverberation." 2012.www.ehow.com. 22 04 2012.

Repetto, Douglas. "Sampling theory." 2011.

music.columbia.edu/cmc/MusocandComputers/frontmatter.php. web. 22 04 2012.

Richardson, Phil. "The Secret life of Bats." 2002. www.fathom.com/course/21701775/index.html. 26 04

2012.

Schulzrinne, Henning. "Explanation of 44.1 kHz CD sampling rate." 09 01 2008.

www.cs.columbia.edu/~hgs/audio/44.1.html.25 04 2012.

W.Smith, Steven. "Human Hearing." W.Smith, Steven. The Scientist and Engineer`s Guide to Digital

Signal Processing. California Technical Publishing, 2011.

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