Professor Calle

MUM 2600 – Huber and Runstein (2005) Chapter 2 Notes

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Huber and Runstein (2005) - Chapter 2 Notes

Examination of sound

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-Pressure Waves

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.

 

Waveform Characteristics

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.

 

VelocitySound 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.

 

Harmonic Content

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.

 

Reflection of sound

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.

 

Diffraction - The ability of sound waves to bend around an obstacle and reconstruct.

 

Frequency responseThe 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.

 

Envelope – Characteristic variations in sound level over the duration of a note.

1.   Attack – level at note start

2.   Sustain – volume changes during duration

3.   Decay – fade or reduction over time once note has stopped sounding.

 

Decibels

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