Module 01 - Analog and Digital Audio

In a longitudinal wave, such as sound, the direction of particle motion is parallel to the direction of wave motion.. If the speaker is small in comparison with the wavelength being emi

Module 01

Analog and Digital Audio

In this module you will learn about the nature of sound, soundproofing, acoustics and acoustic treatment, analog audio electronics and digital audio

Learning outcomes

To understand the way in which sound behaves in air, how sound interacts with hard and soft

•

materials; flat and irregular surfaces

To possess the basic background knowledge of recording studio acoustic design

Real world components 32

Resistors in series and parallel 33

Digital versus analog 34

Analog to digital conversion 36

Problems in digital systems 38

The Nature of Sound

We all know the experience of sound, and we all

learned in school that it is a vibration of air molecules

that stimulates our eardrums People who work with

sound every day tend not to think about the science

of sound and take it for granted But unless you have

assimilated a good understanding of the nature of the

medium in which you work, how are you ever going to

make it really work for you?

Sound starts with a vibrating source, commonly the

vocal folds (formerly known as the ‘vocal cords’ or

sometimes ‘vocal chords’), musical instruments and

loudspeaker diaphragms, as far as we are concerned

Let us think of a loudspeaker diaphragm It vibrates

forwards and backwards and pushes against air

molecules On a forward push, it squeezes air molecules

together causing a ‘compression’, or region of high

pressure On pulling back it separates air molecules

causing a ‘rarefaction’, or region of low pressure The

compressions and rarefactions travel away from the

diaphragm in the form of a wave motion

Wave motions are all around us, from the water

waves we see in the sea (best viewed from a ship -

the breaking effect near the shore disguises their true

nature), to all forms of electromagnetic radiation such

as x-rays, light, microwaves and radio waves

The child’s toy commonly known as the ‘slinky spring’

can display a wave very much like a sound wave The

slinky is a spring – the metal versions work best –

of around 15 cm in diameter and perhaps 4 m long

when lightly stretched If two people pull it out and

one gives a sharp forward and backward impulse, the

compression produced will travel to the end of the

spring and – if the other person holds his or her end

firmly – reflect back

This demonstrates a longitudinal wave where the

direction of wave motion is in the same direction of

the motion of the actual material (we can call the

motion of the material the ‘particle motion’) A sound

wave is a longitudinal wave

Vocal folds - illustration courtesy University

of California, Berkley

‘Slinky’ spring - photo by Roger McLassus

(GFDL)

Contrast this with a water wave where the wave

moves parallel to the surface of the sea, but water

molecules move up and down This is a transverse

wave Electromagnetic waves are transverse waves

too

One feature that the water wave demonstrates

perfectly is that if you look out from the side of a

ship at a piece of flotsam riding the wave, the wave

appears to travel from place to place, carrying energy

as it does so, but the flotsam simply bobs up and

down Other than wind or tide acting directly on the

flotsam itself, it will bob up and down all day without

going anywhere

This is true of sound too A sound wave leaves a

loudspeaker cabinet, but this doesn’t mean that air

travels away from the cabinet The air molecules

simply vibrate forwards and backwards, never going

anywhere (When air molecules travel from one place

to another that is called, in purely technical terms, a

wind!)

If this were not so then either a vacuum would

develop inside or around the cabinet and there would

be a danger of asphyxiation Obviously this doesn’t

happen Oddly enough, if you put your hand in front

of a bass loudspeaker you will feel a breeze, if not a

full-on wind, on your hand This is an illusion since

you feel the air molecules when they press on your

hand, but not when they pull back

In a transverse wave, such as a water wave,

the direction of particle motion is at right angles

(‘perpendicular’) to the direction of wave motion In

a longitudinal wave, such as sound, the direction of

particle motion is parallel to the direction of wave

motion

Although the longitudinal wave in the slinky spring

is similar to a sound wave, it doesn’t quite tell the

whole story The slinky wave is confined within the

spring whereas a sound wave spreads out readily

It is possible to think of each air molecule (actually

oxygen, nitrogen and an increasing amount of carbon

dioxide) that vibrates under the influence of a sound

wave as a sound source in its own right

Transverse wave created on a string Photo

courtesy Union College

Molecules are of course very small, and it is a feature of

small sound sources – or point sources – that they emit

sound equally in all directions, or ‘omnidirectionally’

So where light travels over great distances in straight

lines, sound merely has a tendency to follow a

straight-line path, and readily spreads out from that path in an

ever-widening arc, particularly at low frequencies

[Regarding point sources - it is also worth considering

the example of a small loudspeaker emitting a low

frequency tone If the speaker is small in comparison

with the wavelength being emitted, then it will have

the characteristics of a point source and will obey the

inverse square law - sound pressure halves for every

doubling of distance from the source.]

Frequency

To compare the range of frequencies in human

experience, a satellite TV signal - for example - has

a frequency of around 10 to 14 GHz The Olympic

Games have a frequency of 8 nanohertz (they happen

once every four years!)

1 hertz (Hz) means one cycle of vibration per

Sound comes in virtually all frequencies but our

hearing system only responds to a narrow range

The upper limit of young human ears is usually

taken to be 20 kilohertz (kHz) (twenty thousand

vibrations per second) This varies from person to

person, and decreases with age, but as a guideline

it’s a good compromise If a sound system can handle

frequencies up to 20 kHz then few people will miss

anything significant

At the lower end of the range it is difficult to know

where the ear stops working and you start to feel

vibration in your body In sound engineering however

we put a figure of 20 Hz on the lower end We can

hear, or feel, frequencies lower than this but they are

generally taken to be unimportant

Frequency is related to wavelength by the formula:

velocity = frequency x wavelengthThis applies to any wave motion, not just sound The

velocity, or speed, of sound in air is a little under 340

meters per second (m/s) This varies with temperature,

humidity and altitude, but 340 m/s is a nice round

number and we’ll stick with it If you work out the

math, this means that a 20 Hz sound wave travelling

in air has a wavelength of 17 metres!

The extreme physical size of low frequency sound

waves leads to tremendous problems in soundproofing

and acoustic treatment At the other end of the scale,

a 20 kHz sound wave travelling in air has a wavelength

of a mere 17 mm Curiously, the higher the frequency

the more difficult it is to handle as an electronic,

magnetic or other form of signal, but it is really easy

to control as a real-life sound wave travelling in air

Low frequencies are easily dealt with electronically,

but are very hard to control acoustically

The decibel

The concept of the decibel a convenience that allows

us to compare and quantify levels in the same manner

through different media In sound terms, decibels can

be used for every medium that can store or transport

sound or a sound signal, for instance

real sound travelling in air

A change in level of 3 dB means exactly the same thing

in any of these media Without decibels we would have

to convert from newtons per square metre (sound

pressure), volts, nanowebers per square metre, etc

Decibels have another advantage for sound The ear

assesses sound levels logarithmically rather than

linearly So a change in sound pressure of 100 µN/m2

(micro-newtons per square meter) would be audibly

different if the starting point were quiet (where it

would be a significant change in level) then if it were

loud (where it would be hardly any change at all) A

change of 3 dB is subjectively the same degree of

change at any level within the ear’s range

[Sound pressure is measured in newtons per square

meter You may think of the newton as a measure of

weight One newton is about the weight of a small

apple.]

An important point to bear in mind is that the decibel

is a ratio, not a unit It is always used to compare two

sound levels

To convert to decibels apply the following formula in

your scientific calculator:

20 x log10 (P1 /P2 )

…where P1 and P2 are the two sound pressures you

want to compare So if one sound is twice the pressure

of another then P1 /P2 = 2 The logarithm of 2 (base

Optical film soundtracks, variable density and variable area Illustration by Iain F

10) is 0.3, and multiplying this by 20 gives 6 dB

Actually it’s 6.02 dB but we don’t worry about the odd

0.02

This is useful because we commonly need to, say,

increase a level by 6 dB, but it doesn’t actually tell us

how loud any particular sound is because the decibel

is not a unit The answer to this is to use a reference

level as a zero point The level chosen is 20 µN/m2

(twenty micro-newtons per square meter), which is,

according to experimental data, the quietest sound

the average person can hear

We call this level the ‘threshold of hearing’ and it can

be compared to the rustle of a falling autumn leaf

at ten paces We quantify this as 0 dB SPL (sound

pressure level) and now any sound can be compared

with this zero level Loud music comes in at around

100 dB SPL; the ear starts to feel a tickling sensation

at around 120 dB SPL, and hurts when levels approach

130 dB SPL

If you are not comfortable with math, it is useful to

remember the following, which apply to both sound

pressure and voltage (but decibels work differently

when referring to power):

-80 dB = one ten thousandth

Do you need to understand decibels to be a sound

engineer?

The answer is, “Yes - to a point” You need to be able

to relate a change in decibels to a fader movement,

and from there to an image in your aural imagination

of what that change should sound like In addition to

that, you’ll get producers telling you to raise the level

of the vocal “a bit” How many decibels equal “a bit”?

Only the experience you will gain in the early years of

your career will tell you

The inverse square law

There is more to find out about the inverse square

law Here is an interesting point

The maximum rate of decay of a sound as you move

away from it is 6 decibels per doubling of distance

(the sound pressure halves) This is simply due to

the spreading-out of sound - the same energy has to

cover an ever greater area

If the sound is focused in any way, by a large source

or by reflection, then it will fade away at a rate less

than 6 dB per doubling of distance This fact is of great

importance to PA system designers

The ultimate focused sound source is the old-fashioned

ship’s speaking tube Sound is confined within the

tube and can travel over 100 meters and hardly fade

away at all

It’s going to be a long time before anyone invents a

way to transfer an electronic or digital signal straight

into the brain, bypassing the ears Until then, at some

stage sound must always pass through the air, and

this is the most difficult and least understood part of

its journey

When sound is created, whether it is the human voice,

speaking or singing, a musical instrument or plain

old-fashioned noise, it travels through the air, bounces

from reflecting surfaces, bounces again and mingles

with its own reflection, then enters the microphone

The same happens at the other end of the chain Sound

leaves the speakers, and although part of the energy

will be transmitted directly to the listener, much of it

will bounce around the room over a period of anything

from half a second or less in a domestic environment

up to several seconds in a large auditorium

Compare this with an electrical signal

Once created, the signal travels in a one-dimensional

medium – a cable or circuit track The signal can’t

escape until it reaches its intended destination, there

is nothing that it can bounce off (unless the cable is

several kilometers long when it will reflect from the

ends unless measures are taken), and the worst that

can happen is that electrical resistance will lower the

level slightly

This is a little bit of a simplification, but it’s fair to

say that everything about the behavior of electrical

signals can be calculated easily

This is not the case with acoustics Sound travels in

three dimensions, not one, and will readily reflect

from almost any surface When the reflections mingle,

constructive and destructive interference effects occur

which differ at every point in the room or auditorium

The number of reflections is, for all practical purposes,

infinite

Even with today’s sophisticated science and computer

technology, it is not possible to analyze the acoustics of

An audio cable is a dimensional medium

one-a room with complete precision, one-accounting for every

reflection It would rarely happen that the electrical

components of a sound system of any kind would be

installed (professionally of course) and then be found

not to work as expected

It is normal however to complete the acoustic design

of a room or auditorium, and then expect to have to

make adjustments when the building work is complete

Hopefully these adjustments will not cost more than

the margin of error allowed for in the budget

Acoustics is a complex science in practice, but in

theory it’s all very simple The acoustics of a room

(acousticians use the term ‘room’ to mean an

enclosed space of any size) are determined by just

three factors: the timing of reflections, the relative

strengths of reflections, and the frequency balance of

reflections

Look around you at the various surfaces in the room If

you speak to a colleague, the sound of your voice will

travel directly to his or her ears It will also bounce off

the nearest surface producing a reflection that arrives

at the ear after a certain number of milliseconds

(sound travels just under 34 cm in a millisecond –

one foot per millisecond is often used as a handy rule

of thumb in non-metric countries even though it is a

little bit on the low side) It will bounce off the next

nearest surface with a slightly longer delay, then the

next Then reflections of reflections will start to arrive

At first they will be spaced apart in time but soon

there will be so many reflections that they turn into a

general mush of reverberation

Some surfaces will be more absorbent, so reflections

are lower in level Some surfaces will favour certain

ranges of frequencies These three factors almost

completely determine the acoustics of a room

There is a fourth factor that is worth mentioning –

movement If anything moves in the room – source,

listener or any reflecting surface – then the Doppler

effect comes into play

The Doppler effect is best demonstrated by the siren

of a passing police car, which appears to drop in pitch

as it goes past Sound can’t travel faster than its

natural velocity in any given medium, so if the sound

source moves, then velocity of the source converts to

a rising in pitch for an approaching source, a lowering

of pitch (acoustic red shift if you like) for a source that

is moving away

In most contexts where acoustics are important, neither

the source nor listener will be moving significantly,

nor will the reflecting surfaces

What will be moving however is the air in the room

due to convection effects and ventilation You can see

this quite clearly if you anchor a helium balloon so

that it can float midway between floor and ceiling

Even in a living room it will move around more than

you would expert

This effect is often modelled in digital reverberation

units where it adds useful thickening to the sound, or

‘chorusing’ as some sound engineers might say

Standing waves

Although acoustics is a science, the ultimate arbiter of

good acoustics is human judgment There are certain

basics that must be adhered to, derived from common

knowledge and experience, and also statistical tests

using human subjects

Firstly, a room that is designed for speech must

maintain good intelligibility Too much reverberation

obscures the words, as do reflections that are heard

by the listener more than 40 milliseconds or so after

the direct sound

Late reflections cause phonemes (the sounds that

comprise speech) to overlap Short reflections actually

aid intelligibility by making unamplified speech

louder

For both speech and music there is the requirement

that the reverberation time (normally defined as the

time it takes for the reverberation to decrease in

level by 60 dB – the RT60 ) is in accordance with that

commonly found in rooms of a similar size

A small room with a long reverberation time sounds

odd, as does a big room with a short reverberation time

We can thank the British Broadcasting Corporation

(BBC), who probably own and operate more purpose

designed acoustic spaces than any other organization

in the world, for codifying this knowledge

One of the most common problems in acoustics, that

particularly affects ‘room-sized’ rooms, rather than

concert halls and auditoria, is standing waves The

wavelength of audible sound ranges from around 17

mm to 17 m Suppose that the distance between two

parallel reflecting surfaces is 4 m Half a wavelength

of a note of 42.5 Hz (coincidentally around the pitch

of the lowest note of a standard bass guitar) will fit

exactly between these surfaces As it reflects back and

forth, the pattern of high and low pressure between

the surfaces will stay static – high pressure near the

surfaces, low pressure halfway between The room will

therefore resonate at this frequency and any note of

this frequency will be emphasized The reverberation

time at this frequency will also be extended

Standing wave demonstration using a string

This will also happen at integral multiples of the standing

wave frequency Smaller rooms sound worse because

the frequencies where standing waves are strong are

well into the sensitive range of our hearing

Standing waves don’t just happen between pairs of

parallel surfaces If you imagine a ball bouncing off all

four sides of a pool table and coming back to where it

started; a standing wave can easily follow this pattern

in a room, or even bounce off all four walls, ceiling

and floor too

Wherever there is a standing wave, there might

also be a ‘flutter echo’ Next time you find yourself

standing between two hard parallel surfaces, clap your

hands and listen to the amazing flutter echo where all

frequencies bounce repeatedly back and forth It’s not

helpful either for speech or music

[At higher harmonics than the fundamental frequency,

the pattern of high and low pressure can be such

that there is high pressure in the centre between the

boundaries and low pressure elsewhere The pressure

is always high at the boundaries.]

The solution to standing waves is firstly to choose the

proportions of the room so that the standing wave

frequencies are spread out as much as possible

Square rooms concentrate standing waves into a

smaller number of frequencies A cube shaped room

would be the worst Non-parallel walls are good, but

these damned clever standing waves will still find a

way We need

Acoustic Treatment

The function of acoustic treatment is to control

reverberation time and to reduce the levels of

standing waves We’ll come back to standing waves

in a moment

If surfaces can be made more absorbent then

obviously reflections will be reduced in strength,

hence reverberation time will be less

Soft materials such as carpet, drapes and especially

mineral wool all find applications as porous absorbers

Porous absorbers however only work well when they

are at least a quarter of a wavelength thick

This means that they are only really practical for

high and high mid frequencies If the only acoustic

treatment used in a room is porous absorption, then

the room will sound incredibly dull and lifeless

Another type of absorber is the panel or membrane

absorber A flexible wood panel (around 4 mm to 18

mm thick) mounted over a sealed air space (around

100 mm to 300 mm in depth) will resonate at low

frequencies, and as it flexes will absorb energy

If damping material (typically mineral wool) is added

inside, or a flexible membrane is used, then this

type of absorber can be effective over a range of low

frequencies Drill some holes in the panel and the

absorption becomes wide band

Ideal! Panel absorbers with little damping can be

tuned to the frequencies of standing waves and control

them very effectively The other way of dealing with

standing waves, and at the same time waving a magic

wand and making the room sound really great, is to

use diffusion Irregular surfaces break up reflections

creating a denser pattern of low level reflections

than would occur with mirror-like flat surfaces The

irregularities however have to be comparable in size

to the wavelengths you want to diffuse Sound is

always difficult to control

Panel absorber

There has always been a lot of confusion between the

role of materials that reflect sound, and materials that

absorb sound Sound-absorbing materials are NOT

good at blocking sound transmission

This is not to say that they have no function in

soundproofing Just that the general public consensus

is that to provide soundproofing, all you need is lots

of absorbent material This is 100% absolutely not so

Here’s an example

Suppose a partition is created from a very thick

layer of mineral wool (the most cost-effective sound

absorber there is) Suppose it is so thick that it absorbs

75% of the sound pressure that falls upon it, leaving

only 25% to transmit through to the other side This

seems good, since the sound pressure has dropped to

a quarter

However, when you consider this in decibel terms,

reducing sound pressure to a quarter is a change of

minus 12 dB So if the sound pressure on the side

where the sound originates is 100 dB SPL, the sound

pressure on the other side of the partition is still a

very significant 88 dB SPL

This is a noticeable difference, but it’s hardly

soundproofing For really effective soundproofing we

need a drop of at least 45 dB, and preferably more

Even then, the sound will very likely be audible on the

other side of the partition

Materials

Effective soundproofing can only be provided by

materials which reflect sound energy Such materials

would be massive and non-porous, such as concrete,

or a well-made brick or blockwork wall Here is a list

Plywood and dense particle board

The two characteristics that all of these have in common

is mass and non-porosity The last item, ‘proprietary

flexible soundproofing materials’ covers an immense

range of potential solutions, some of which - when

you look at their advertising material - seem to work

by magic rather than physics They will only work if

they are massive and non-porous - simple as that

The three requirements for good

soundproofing

Having looking briefly at the materials, we can

now consider the three requirements for good

Mass means what it says Double the mass of a

partition and you get 6 dB more insulation

Continuity of structure not only means non-porosity,

it means that the soundproofing should enclose the

room in question absolutely 100% If there is any

place where sound can get through, it will You could

spend a lot of money and see it wasted because of

‘acoustic holes’ in the structure

‘No defects’ really means the same as continuity

of structure Except that it is one thing to design a

room with no acoustic holes, quite another thing to

see it through to completion successfully Builders

do not always comply with architects’ plans 100%,

and the short-cuts they take could well compromise

consideration is that it should be vibrated effectively

to make sure there are no air pockets

Bricks

A house brick often has a hollow in one surface,

known as the ‘frog’ BBC practice is to lay bricks with

their frogs uppermost (which is not always the case

in conventional building practice) because then they

have to be filled completely with cement This makes

the wall heavier than it may otherwise have been, and

therefore a little bit better at soundproofing

Plasterboard (drywall)

Plasterboard consists of a layer of gypsum plaster

around 12 mm thick sandwiched between two sheets

of thick paper With it you can make a ‘dry partition’

A wooden framework is constructed and layers of

plasterboard nailed on

The BBC’s ‘double Camden partition’ consists of two

such frameworks, onto which are nailed a total of

eight layers of plasterboard

The advantage of dry partitions is that they can be

constructed while the rest of the studio complex is

still operational Concrete and bricks are very much

more messy, making it more likely that operation

will have to be closed down totally Dry partitions

are sometimes called ‘lightweight partitions’ This is

because you can divide a room into two using just two

sheets of plasterboard on the wooden framework But

by the time you have added enough extra layers for

good soundproofing, it is no lighter than a brick wall

providing the same degree of insulation

Plywood and particle board such as

chipboard and MDF

These are all good materials - obviously the denser,

and therefore heavier, the better They are more

expensive than plasterboard however, so they are

only used where they are needed

Glass

Glass is a very good material for soundproofing, but it

is expensive Therefore it is only used when you need

to see through the soundproofing

Metal

Once again, this is a very good material for

soundproofing, but it is expensive in comparison to the

alternatives It is only used where its high density is

important in achieving a relatively thin soundproofed

partition It is most commonly found in soundproofed

doors, which may have a lead lining

Proprietary flexible soundproofing

materials

With regard to the comments made above, these are

generally expensive in comparison with their acoustic

worth They should only be used where flexibility or

ease of installation is important They may also be

used as damping material

For instance a metal panel in a car may vibrate and

transmit energy to the passenger compartment If it

were damped, then not only would the vibration would

be reduced, but significant energy would be taken out

of the sound wave

Construction techniques

A room is made up from a variety of surfaces and

components, all requiring their own construction

Whatever material the wall is made out of, it is better

to use two thin walls spaced apart rather than one

thick one of equivalent mass

Remembering that soundproofing is best achieved by

reflection, and that reflection occurs at the boundary

between one material and another, it makes sense to

provide four boundaries rather than two

At first thought, it may seem that if a partition has a

sound transmission class (STC) of say 35 dB, and two

such partitions are provided, then the overall STC will

be 70 dB This is not the case

By doubling the mass you get an extra 6 dB, and by

spacing apart the two leaves of the partition you might

gain another 3 dB

This may not sound like much, but it costs hardly

anything so it is worth having

The reason why you don’t get twice as many decibels of

sound reduction is that the two leaves remain coupled

together In fact the more closely they are coupled,

the more the object of the exercise is defeated

Double-leaf brick walls (‘cavity walls’) are often

constructed using wire or plastic ties which couple the

leaves together for mechanical strength For a wall

that is designed for good soundproofing, the use of

such ties should be minimized Care should be taken

not to allow cement to fall onto the ties In normal

building, this would not matter

Also, builders are known to have a habit of depositing

rubbish between the leaves of a cavity wall This of

course must not be allowed to happen as it couples

the leaves of the partition

The space between the partitions should be filled

with absorbent material such as mineral wool This

is where absorbent material does have a place in

soundproofing If the cavity is left empty, sound will

bounce back and forth between the leaves and some

of the reflected energy will end up being transmitted

If this can be absorbed significantly, then the insulation

will be better

Ceiling

The difficulty in building a sound proofed ceiling is

mounting sufficient mass horizontally The brute force

solution is to lay concrete on top of metal shuttering,

preferably as a double-leaf construction The concrete

could be up to 175 mm thick in total As always, mass

wins

For a less heavily engineered solution, the BBC

recommend woodwool slabs Woodwool is a sheet

or board made from a mixture of thin strips of wood

and cement, which are bound together through

compression within a mould Layers of plasterboard

can be used too, providing they are adequately

supported

‘Acoustic tiles’ are virtually useless as sound

insulation, although they do find application in acoustic

treatment

Floor

Once again, mass rules But also there is a technique

known as the ‘floating floor’, which is widely used in

studio construction

The fully engineered floating floor would consist of a

concrete slab formed on metal shuttering, supported

on rubber pads or even heavy-duty springs The mass

of the slab is important as the mass-spring system