Professor
Calle
MUM
2600 – Huber and Runstein (2005) Chapter 2 Notes
E-mail:
ecalle@mdc.edu
Website:
http://www.professorcalle.com/MUM2600.htm
Angel: http://mdc.angellearning.com
Huber and Runstein (2005) - Chapter 2 Notes
1.
Nature of sound as a
brain stimulus
2.
The physiology of the
ear
3.
The psychoacoustics of
hearing (how & why brain perceives sound in a specific way.)
Sound
arrives at ear as small, periodic variations in atmospheric pressure.
Due
to their miniscule size, a barometer cannot measure variations in atmospheric
pressure created by a sound wave.
Sound-pressure
waves radiate outwardly in a 3-dimensional spherical pattern.
A
sound-pressure wave is generated when a vibrating body comes in contact with
air.
Compression
is a condition defining an area containing greater than normal atmospheric
pressure due to the squeezing of additional air molecules by a sound source
(vibrating body) into that area.
Rarefaction
defines a condition when an area with lower than normal atmospheric pressure is
created at the source of a sound-pressure wave as it moves away.
Note:
The wave and not the molecules move at the speed of sound.
Wave
propagation occurs when high-pressure compression waves push against areas of
lower pressure in the atmosphere. Sound waves move at the speed of sound (1130
feet per second at sea level and a temperature of 68¼ F). In comparison, the
speed of sound is approximately 186,000 miles per second.
Amplitude
describes the distance above or below the centerline of a waveform. Most
simply, the amplitude of a wave represents its volume. The larger the amplitude
of a sound wave, the louder its volume.
a.
Peak amplitude –
(peak value) the measurement between the maximum positive or negative signal
levels.
b.
Peak-to-peak value
– the difference between the positive and negative peak signal levels.
Frequency
– The rate at which an acoustic
generator, electrical signal or vibrating mass repeats a cycle of positive and
negative amplitude. Frequency is measured in Hertz (Hz) and is perceived by the
ear as pitch.
a.
Cycle – one
completed excursion of a wave.
b.
Hertz (Hz) – unit
of measurement used to describe/measure the number of cycles occurring in one
second.
c.
Period – the time
it takes to complete one cycle.
Velocity
– Sound travels at 1130 ft/sec.
The velocity is temperature-dependent and increases by 1.1 ft/sec with each
Fahrenheit increase of 1 degree.
Wavelength
is defined as the distance between
the beginning and the end of a cycle.
Wavelength
= Velocity/Frequency (Hz) (see Figure 1).
Seconds per cycle (T) is given as T = 1/F.
The Excel spreadsheet located in Figure 1 provides wavelength measures for
frequency multiples at temperatures of 80¼, 90¼, and 68¼. Using the formula wavelength =
temperature/frequency, we can determine the length of a sound wave. In order to
determine the variance in velocity of a wave, we simply determine the
difference between velocities of 1130 feet per second at 68¼ F and multiply the
change by 1.1 feet per second. Algebraically, we can compute this variance
using the expression (1130 + variance) where variance is computed using the
expression ((actual temperature – 68) * 1.1). Then we simply substitute
the variance expression in the original equation creating a new formula of the
form: wavelength = (1130 + ((actual temperature – 68) * 1.1))/frequency.
Figure 1- Wavelength spreadsheet
|
Temp (F) |
Freq (Hz) |
Wavelength (feet) |
|
80 |
1760 |
0.649545455 |
|
80 |
880 |
1.299090909 |
|
80 |
440 |
2.598181818 |
|
80 |
220 |
5.196363636 |
|
80 |
110 |
10.39272727 |
|
80 |
55 |
20.78545455 |
|
68 |
1760 |
0.642045455 |
|
68 |
880 |
1.284090909 |
|
68 |
440 |
2.568181818 |
|
68 |
220 |
5.136363636 |
|
68 |
110 |
10.27272727 |
|
68 |
55 |
20.54545455 |
|
90 |
1760 |
0.655795455 |
|
90 |
880 |
1.311590909 |
|
90 |
440 |
2.623181818 |
|
90 |
220 |
5.246363636 |
|
90 |
110 |
10.49272727 |
|
90 |
55 |
20.98545455 |
Wavelength measurements are particularly useful in
acoustic design applications.
Phase
– (measured in degrees) the
relative phase degree angle with another wave over 360¡ or one cycle. Like circles, acoustic waves are
described in degrees ranging from 0¼ to 360¼. Thus, one cycle or complete
excursion of a wave is defined as completing a 360¼ excursion.
If
two waveforms are in phase (have same frequency, shape and peak amplitude) and
are added together, their amplitude doubles and the resulting waveform will
have the same frequency, shape and phase. If two waveforms differ by 180¡, they will cancel each other out. They will create
zero amplitude. When two waveforms are partially out of phase, the will
constructively interfere (gain) at points were both are positive or both are
negative. Waveforms will destructively interfere at points where the signs
(+/-) of the two waveforms are opposing.
Phase-shift
– describes one waveforms lead or lag time in respect to another. Caused
by time delay usually due to distance. In order to avoid hearing the
interferences by keeping them above 20k Hz, the path-length difference must be
less than 0.34 inches or 0.03 ms.
Fundamental
– a specific pitch that is being generated or played. A note.
Partials
– various frequencies that exist in addition to the fundamental pitch
being played.
Overtones
– partials higher in pitch than the fundamental.
Harmonics
– overtone frequencies that are whole-number multiples of the
fundamental.
Simple
Waves such as square, triangle, and saw tooth waves are continuous and
repeating in nature.
Complex
Waves are naturally occurring in sound and speech and typically do not repeat.
Timbre
is synonymous with harmonic balance.
Sound
waves reflect off a surface at an angle equal to and in the exact opposite
direction of the initial angle of impact.
Solid,
smooth surfaces produce a straight bounce of sound waves.
A
convex surface (bubble) radiates outward in a wide dispersion pattern.
Concave
surfaces focus sound waves to a single point.
A
corner with an angle of 90¡ reflects the pattern back in its original incident
direction. This is why corners often provide a magnification of sound.
Frequency
response – The charted output of a sound-producing device over a
range of frequencies. Usually charted in the range of human hearing from 20
– 20,000 Hz.
Flat-frequency
response is when a device passes all frequencies (in a range) evenly.
1.
Attack – level at
note start
2.
Sustain – volume
changes during duration
3.
Decay – fade or
reduction over time once note has stopped sounding.
Unit
of measurement used for measuring sound pressure level.
DB
is a logarithmic value that expresses differences in intensities between two
levels.
It
stands for 1/10th of one bell after Alexander Graham Bell
(telephone).
Measured
in logarithmic numbers.
Logarithm
is a mathematical function that reduces large number values into smaller more
manageable ones.
Log
numbers increase exponentially instead of linearly. We hear exponentially.
Log
basics:
Log
2 = 0.3
Log
10 = 1
Log
100 = 2
If
number is a power of 10, log is equal to number of zeros.
Numbers
> 1 have a positive (+) log value.
Numbers
< 1 have a negative (-) log value.
Sound-pressure
level
SPL
is the acoustic pressure built up within a defined atmospheric area usually a
square centimeter or cm2.
Voltage
You
can measure acoustic energy by comparing one voltage level to another.
Voltage
is defined as: A unit of measure of the "push" of electric current.
The higher the voltage, the more force there is to push the current through the
wire.
Power
A
measure of wattage or current associated with signals carried through the audio
signal path. Power units are called watts. Watts are defined as a measure of
electrical power that is determined by multiplying the voltage by the amperage.
Ohms
are the units representing load impedance. Lower impedances are harder for
amplifiers to drive. For example, 2 8 ohm rated speakers connected in parallel
will result in a 4 ohm amplifier load.
Load
impedance is defined as:
The
impedance seen by one channel of a power amplifier; it is determined by the
number of speakers wired to the channel, the impedance characteristics of each
channel, and how they are wired to one another.
The
opposition to output current flow caused by the input that it feeds.
www.recordingeq.com/glossary/glosko.htm
The
ear
A
sound produces waves that compress and rarefy (thin out) the air between the
source and listener.
Waves
are captured by the ear canal and then directed to the eardrum.
The
eardrum transforms the wave into mechanical vibrations that are transferred
into the inner ear by three bones: hammer, anvil and stirrup. These bones act
as an amplifier and a limiter.
The
vibrations are then applied to the cochlea or inner-ear. The cochlea is a
snail-like, tubular organ with two fluid filled chambers. In the chamber are
small hair recept
ors
lined in a row along the length of the inner-ear. The hairs respond to different frequencies. Permanent
hearing loss occurs when these are damaged or due to aging.
THRESHOLD
OF HEARING IN DIFFERENT MEASUREMENTS
SPL
= 0.0002 microbar
One
microbar is = one-millionth normal atmospheric pressure.
Usually
denoted as 0 dB SPL or the level the average person hears a specific frequency
only 50% of the time.
The
threshold of feeling is defined as
acoustic levels causing discomfort 50% of the time typically around 118 dB SPL
between 200Hz and 10kHz.
The
threshold of pain is defined as an
acoustic level causing pain 50% of the time typically around 140 dB SPL between
200Hz and 10kHz.
Harmonic
distortion occurs naturally in the ear whenever it is saturated with audio
waves above a safe level. Harmonic distortion is not part of original signal.
The
input and output amplitude of linear devices have the same input/output ratio
at all signal levels. The ear is non-linear. Because of the non-linearity of
the ear, tones often interact with each other as opposed to being heard
separately. As a result, three types of interaction occur:
1.
Beats – 2 tones
differing slightly in frequency and having approximately the same amplitude
will produce beats. Occurs when two instruments play the same note. Beats slow
down and stop as two tones reach the same pitch. The beat is a third tone that
is the sum of the two tones when they are in phase and the difference when they
are out of phase.
2.
Combination tones
– produced when 2 loud tones differ by more than 50Hz. The ear produces
an additional set of tones thatÕs equal to both the sum and difference between
the 2 original tones and is also equal to the sum and difference in their
harmonics. Sum tone = Freq1 +
Freq2, Difference tone = Freq1 – Freq2. Difference tones can easily be
heard when theyÕre below the frequency of both toneÕs fundamentals.
3.
Masking – a
phenomenon where by loud signals prevent the ear from hearing softer signals.
This is exaggerated when the frequencies of the sounds are close to each other.
Important in mixing because similar frequencies will mask softer similar
frequencies. For example, a fluglelhorn will mask another flugelhorn easier
than it will mask a soprano saxophone.
Direction
One
ear cannot perceive direction of a sound while two ears are designed to do so.
Location or identification of aural positioning is called spatial or binaural
localization.
Ear
receives 3 cues:
1.
Interaural intensity
differences – middle to high frequencies originating on a particular
side, will reach that same side at a higher intensity level.
2.
Interaural arrival time
differences – used by ear for lower, slower frequencies.
3.
The effects of the outer
ear (pinnae) – the two ridges of the ear tell us if sound originates from
the front, rear or below.
1
&2 give direction or panning. Changing direction or intensity of frequency
from left to right.
Spatial
perception
Ears
and brain give us distance as well as a sense of the space in which sound
occurs. Only a percentage of sound reaches ear directly. A larger amount
reflects off of surfaces or is absorbed by surfaces creating more or less
signal respectively.
Sound
travels through air at 1130 feet pre second. Direct waves travel shortest path.
Early
reflections are the ones that reach after bouncing off surfaces. Sometimes
these waves are heard after the original source stops and are called
reverberation. Direct sound determines perception of source location. Size
conveys true timbre of sound source.
Early
reflections, those bouncing off of the largest or most prominent boundaries in
room, arrive less than 50msc after the brain perceives the original sound
source. As a rule, the farther the boundaries are located from the source and
listener, the longer the delay.
Temporal
fusion – early reflections arriving earlier than 30msc of direct sound
are suppressed and fused with the source sound. The 30msc limit is not fixed
and depends on the sounds envelope. Fusion breaks down a 4msc for transient
clicks and as long as 80msc for slowly evolving sounds such as an organ note or
long notes on a violin.
Reverb - sounds reaching after more than 50msc reflect off
of so many surfaces that they reach listener as a continuous stream from all
directions. Characterized by a gradual decrease in amplitude and a sense of
warmth and body added to the sound. Timbre is very different from original
sound due to the number of bounces.
Decay
time or reverb time is the time for persisting sound to decrease to 60 dB below
itÕs original level. As one gets closer to source, the source sound gets louder
while the reverb stays the same. The ratio between the source sound loudness
and the reverb allows listener to judge distance from the sound source,
Repeating
a signal with a short delay of 4-20msc, makes part seem doubled. Using short
delays offers an electronically enhanced method of doubling audio tracks. From
a production standpoint, if you want tracks to sound doubled, physically
doubling the musical performances offers a more natural effect though the
process is more time-consuming and expensive.
Slap
echo or slap back describes longer delays of more than 35msc cause a discreet
echo. Slap echo is often used to thicken up the sound of guitar tracks and many
other tracks.
References
Calle,
E. J. (2006). Music as a branch of mathematics. Retrieved September
15, 2007,
from: http://www.professorcalle.com/assests/MDCC/Math%20conference/Math_conference_draft_1_7_07.pdf
Huber, D. M., M., &
Runstein, R. E. (2005). Modern recording techniques (6th ed.).
Burlington,
MA: Focal Press.
Recording Institute of
Detroit. (2004). Audio recording terms glossary and index.
Retrieved
September 16, 2007, from: http://www.recordingeq.com/glossary/glosae.htm