[PPT] - Audio Theory What is Sound? Transfer of Energy Molecular PowerPoint Presentation

SLIDE 1

Audio Theory

SLIDE 2

What is Sound?

Transfer of Energy
Molecular Displacement
Wave Energy
Mechanical Wave
Pressure Waves
Longitudinal Pressure Waves

SLIDE 3

Sound Pressure Waves

Initial wave transmission
Compression
Rarefaction

Longitudinal Wave Transverse Wave

Sound waves in air

SLIDE 4

SLIDE 5

SLIDE 6

Sound Radiation

Free-field radiation
The output of a point source radiates in a perfect sphere whose

surface area is found by:

S = 4πr2
If we double our distance from a sound source we actually increase

the total area that the sound will radiate by 4 times

For each doubling in distance there is a 6 dB decrease in level.
A convenient reference point for acoustic measurement.

SLIDE 7

Sound Pressure Waves

Periodic Motion
The sine wave
One complete wave sequence is known as a Cycle (360˚)
The time interval to complete a cycle is known as the

Period(T)

SLIDE 8

The Sine Wave

Easily Measured and Predictable
Frequency (pitch)
Amplitude (loudness)
etc...

SLIDE 9

Waveform Characteristics

Frequency Amplitude Velocity Wavelength Phase Harmonic Content Envelope

7 of them

SLIDE 10

Frequency

How often the the pressure oscillation occurs
Expressed in Hertz or cycles per second (cps)
# of cycles / time (sec) = f in Hertz(Hz)
3cycles/3ms=1kHz or 3/.003 = 1000 Hz
The Period (T) of a wave is the time it takes to

pass through 360 degrees (one cycle)

T = 1/f

SLIDE 11

Volts/Div Sec/Div

0.1 V 2 ms

Frequency

# of divisions x Sec/Div
#cycles/sec = f
1 cycle = 4ms
f =1/.004=250Hz

SLIDE 12

Frequency

20Hz - 20kHz - Human range of hearing
Humans are sensitive to Proportional changes
2 to 1 Ratio = Octave interval
Each doubling provides twice the spectral content of

the previous octave

We use a logarithmic scale to describe it

SLIDE 13

Frequency - Bandwidth

All systems have a finite bandwidth
Human Hearing - 20 Hz to 20 kHz
Electronic Devices -

Variable

SLIDE 14

Frequency

Bandwidth is the range from the lowest to

the highest frequencies that are no more than 3dB down.

dB frequency Bandwidth 3 dB 40 Hz 10 kHz 20 Hz 20 kHz

SLIDE 15

Amplitude

Maximum displacement from a reference point
Magnitude of change in oscillaton
Pendulum
Electrical

Voltage or Alternating Current (AC)

SLIDE 16

Amplitude

RMS Peak Peak-to-Peak Amplitude +1V 0.707V

1V

SLIDE 17

Amplitude

Peak
= 1.414 x rms voltage
Peak to Peak
RMS - Root Mean Square
Type of averaging
Square root of the mean over time
= .707 x Peak

Voltage

RMS Peak Peak-to-Peak Amplitude +1V 0.707V

1V

SLIDE 18

Amplitude

Volts/Div Sec/Div

0.5 V 20 µs

# of divisions x

Volts/Div

Peak

V= 1V

Peak to Peak

V= 2V

RMS

V= .707V

SLIDE 19

Velocity

Speed at which something travels through a

medium

Speed of Sound
Variables
Density
Elasticity
Temperature

SLIDE 20

Velocity

Speed of sound in air (c) at 70°F (20°C) is:
c = 344 ±0.05 meters/sec
c = 1130 ±0.16 feet/sec
Equations for different temperatures
c = 331 + 0.607*TC (TC = °C)
c = 1052 +1.106*TF (TF = °F)
The rate will increase at a rate of 1.1 ft/sec for each

degree Fahrenheit and .607 m/sec for each degree Celsius.

SLIDE 21

Substance Temp(°C) Speed (m/s)

Gasses

Carbon Dioxide 259 Oxygen 316 Air 331 Air 20 343 Helium 965

Liquids

Chloroform 20 1004 Ethanol 20 1162 Mercury 20 1450 Water 20 1482

Solids

Lead – 1960 Copper – 5010 Glass – 5640 Steel – 5960

The speed of light in a vacuum is ~ 300,000,000 meters per second The speed of an electromagnetic wave in copper is ~ 90% of the speed

f light

SLIDE 22

Sound travels at the speed of the molecules
f the medium
All sound waves travel at the same speed, in

similar conditions

Frequency and Amplitude change the rate and

force at which the molecules move into each

ther

Velocity

SLIDE 23

Sound = energy transfer through longitudinal

compression waves

Period = Time it takes to complete 1 cycle

(oscillation) of a wave (T=1/f)

Frequency = Cycles per second (pitch)
Amplitude = Magnitude of displacement from

equilibrium (level or loudness)

Velocity = speed of wave propagation

(ft/sec or m/sec)

SLIDE 24

Wavelength

The measured distance between the

beginning and end of a cycle.

Wavelength =
Acoustical wavelength
λ = c/f
Also stated as
V= ƒ * λ

Velocity frequency

SLIDE 25

Same Velocity - Different Wavelength

SLIDE 26

Same Frequency - Different Velocity

SLIDE 27

Wavelength

Concert A = 440Hz
At 70º F, what is the length of one cycle

1130 440 = 2.56 feet

Bass Drum = 40Hz
At 70º F, what is the length of one cycle

1130 40 = 28.25 feet

SLIDE 28

Wavelength

Flute (High C)
2093 Hz
Piccolo (High C)
4186 Hz

0.54 feet 1130 2093 = 6.48 inches 0.27 feet 1130 4186 = 3.24 inches

SLIDE 29

Wavelength affect on Propagation

Wavelength determines how a sound wave will

react as it comes into contact with an object in its path

Diffraction
Refraction
Reflection

SLIDE 30

Wavelength

Diffraction
The bending of waves around obstacles and

the spreading out of waves beyond

penings.
Interaction dependent on wavelength

SLIDE 31

Diffraction

When the wavelength is

longer than the obstacle it acts as if it (the obstacle) isn’t even there

Long Wavelengths

SLIDE 32

When a wavelength is near to

the size of the obstacle both Shadowing and Re-radiation

ccur
Resonances

Diffraction

SLIDE 33

Wavelength shorter than
bject in its path
Pronounced Reflection
Very Clear Shadow Zone

Short Wavelengths

Diffraction

SLIDE 34

Small Opening = New

Source Point

Large Opening =

Continued waveform

Slight shadowing

Diffraction at Openings

SLIDE 35

Diffraction

SLIDE 36

Diffraction

Text http://hyperphysics.phy-astr.gsu.edu

SLIDE 37

Diffraction

http://hyperphysics.phy-astr.gsu.edu

SLIDE 38

SLIDE 39

SLIDE 40

Refraction

The bending of a waveform as it passes from
ne medium to another
Function of speed of sound in medium
Temperature changes affect velocity
Waves bend towards the slower (cooler)

side

SLIDE 41

Refraction

SLIDE 42

Refraction

S o u n d Source Cool Air Warm Air

When the air is cooler above a surface the wave will bend

upwards.

When the air is warmer then the surface the wave will

bend downwards.

SLIDE 43

Refraction

Inversion

SLIDE 44

Reflection

Sound waves reflect where angle of incidence

is equal to angle of reflection

Except that...
Convex surfaces deflect waves
Concave surfaces focus waves at one point

SLIDE 45

Reflection

SLIDE 46

SLIDE 47

Reflection

Considerations
Reflection will be strong if absorption is

low

Phase change upon reflection
Standing waves
If the surface is random, scattering occurs

SLIDE 48

Wave Interaction

Diffraction, Refraction, Reflection
Interference
Superposition
Constructive
Destructive
Beating
Moving Sources
Doppler Effect
Standing Waves

SLIDE 49

Interference

When two waves traveling through the same

medium collide they pass through each other

Superposition
Constructive Interference
Destructive Interference
Beating
ƒ(beat)= (ƒ1 - ƒ)

SLIDE 50

Phase and Phase Shift

The measurement of a cycle, in degrees,
Divided into 360°

SLIDE 51

Phase and Phase Shift

When two waveforms are completely in phase there is

0°phase difference.

100% coherent
If two waves are completely out of phase (180°) they will

completely cancel each other out.

0% coherent
Wire reversal = electrically out of phase
Acoustic phase cancellation might occur if two

microphones receive the same source one with a positive pressure and the other with a negative pressure.

SLIDE 52

Phase

Sum and Difference
Coherency
Interference
Beating
Alternating constructive/destructive interference
Two waves of near similar frequency combine to

produce a new wave

ƒ(beat)= (ƒ1 - ƒ)

SLIDE 53

Standing Waves

A wave that doesn’t move ???
Appears static
Two waves
Same Frequency
Same Wavelength
Traveling in the same plane

from opposite directions

Nodes
Antinodes

SLIDE 54

Standing Waves

Reflected energy
Resonance
The essence of tuned

instruments

SLIDE 55

Doppler Effect

Moving sound source
Shift in frequency and wavelength
Speed vs. Frequency
Observed pitch change as sound

source moves in relation to listener

SLIDE 56

Inverse Square Law

If we double our distance from a sound source we actually

increase the total area that the sound will radiate by 4 times (in a free field).

4πr2
For each doubling in distance there is a 6 dB decrease in level.
dB = 20Log d1/d2
Example: A speaker has a level of 95 dB at 5 ft, What level can

we expect at 14 ft?

20Log 5/14 = -8.9 dB
95 - 8.9 = 86.1 dB

SLIDE 57

Harmonics

The world does not exist of pure tones exclusively.
Timbre
Enables us to distinguish between musical instruments
Fundamental
The note being played
Partials or Overtones or Harmonics
Every other frequencies present including the

fundamental.

SLIDE 58

Harmonics

Most musical instruments overtones consist
f whole number multiples of the

fundamental frequency.

First harmonic = the fundamental
Second harmonic = 2f
Third harmonic = 3f
And so on . . .

SLIDE 59

Overtone Series

SLIDE 60

SLIDE 61

Harmonics

Some instruments have partials that are not

harmonically related to the fundamental (bells, xylophone and other percussive instruments).

The different combination of partials and

their amplitudes give us different timbre

SLIDE 62

Harmonics

There are two basic categories of waveforms:
Simple
Sine
Square
Triangle
Sawtooth
Complex

SLIDE 63

Harmonics

Sine Wave
No Harmonics

SLIDE 64

Harmonics

Square Wave
Odd Harmonics of 3f, 5f, 7f, ...
Amplitude with a ratio of 1/n

(A/3, A/5, A/7...)

SLIDE 65

Harmonics

Triangle Wave
Odd harmonics of 3f, 5f, 7f . . .
Amplitude with a ratio of 1/n2

(A/9, A/25, A/49...)

SLIDE 66

Harmonics

Sawtooth
All harmonics
Amplitude with a ratio of of 1/n

(A, A/2, A/3 . . .)

SLIDE 67

SLIDE 68

Harmonics

Complex waves do not necessarily repeat and

are not necessarily symmetrical about the zero line.

Since they do not repeat it is difficult to

divide these waves into cycles or categorize them as to frequency by waveform.

SLIDE 69

Harmonic Distortion

Most electronics add some harmonic components that are not a

part of the original signal.

This distortion is measured in percentage.
If a 1 volt sine wave with frequency f has an output that

contains a 0.1 volt at 2f, the output is said to contain 10% second harmonic distortion.

Second and fourth harmonic distortion are 1 and 2 octave

intervals

add some richness.
Third harmonic distortion may add some nice color (a twelfth

above the fundamental).

Musical instruments are full of rich harmonic distortion so we

need to be careful when adding additional harmonic distortion.

SLIDE 70

Frequency Amplitude Velocity Wavelength Phase Harmonic Content Envelope

SLIDE 71

Envelope (ADSR)

The envelope works with the timbre to give each

instrument it's own sound.

Attack: How the sound begins
Transients
Decay: How the sound comes off the attack.
Sustain: How long the sound holds out.
Release: How the sound ends.
Human ears average intensity, so high amplitude portions
f an envelope will not make an instrument loud unless it

is sustained long enough. Short high amplitude contributes to the character rather than loudness.

SLIDE 72

Frequency Amplitude Velocity Wavelength Phase Harmonic Content Envelope

SLIDE 73

Frequency

cps - cycles per second - Hertz (Hz)
Period = 1 cycle = t=1/ƒ
All systems have a finite bandwidth
Proportional changes

SLIDE 74

Velocity of Sound

Varies depending on medium
Velocity affects wavelength
Sound travels the speed of the molecules
1130 ft/sec or 344 m/s

SLIDE 75

Wavelength

Affects interaction properties
Reflection, Diffraction, Refraction,

Absorption

Varies depending on

Velocity

Acoustical wavelength
λ = c/f

SLIDE 76

Phase

Measured in degrees (º)
Sum and Difference
Coherency
Interference

SLIDE 77

Harmonics

Harmonics, Overtones, Partials
Multiples of the fundamental ƒ
Timbre
Simple waves
Sine, Square, Triangle, Sawtooth
Complex Waves
Can be constructed with a combination of
Sine and Cosine waves w/ varying amplitudes
Fourier Series

SLIDE 78

Amplitude

Displacement, from equilibrium
Peak & RMS
Volts, Pascals, Newtons
Dynamic Range

SLIDE 79

Dynamic Range

70 dB S/N Ratio 20 dB Headroom 90 dB Dynamic Range 70 dB S/N Ratio 20 dB Headroom 90 dB Dynamic Range 120 dBSPL Maximum Sound Level 100 dBSPL Average 30 dBSPL Ambient Noise Level +24 dBu Clipping Point +4 dBu Nominal Level

66 dBu

Noise Floor

Dynamic Range, Headroom, & Signal-to-Noise Ratio

The ratio between the smallest and largest possible values of a changeable quantity

SLIDE 80

violin viola violincello contra-bass flute

boe

clarinet tenor saxaphone bassoon french horn trumpet trombone tuba soprano alto tenor bass piano harsichord

rgan

guitar

rchestra

timpani bass drum snare drum cymbals 70 dB

Dynamic Range

100 80 60 40 dB Hz 100 200 500 1000 2000 100 80 60 40 dB Hz 100 200 500 1000 2000 100 80 60 40 dB Hz 100 200 500 1000 2000 100 80 60 40 dB Hz 100 200 500 1000 2000

Pitch Dependence

f Dynamic Range

violin trumpet recorder clarinet

SLIDE 81

Loudness

Perceived - Subjective Measurement
Frequency dependent
The ear is not equally sensitive to all frequencies
Fletcher-Munson Curves - original
Equal Loudness Curves - updated
Loudness level is measured in phons
phon- A unit of apparent loudness, equal in number

to the intensity in decibels of a 1,000 Hz tone judged to be as loud as the sound being measured.

SLIDE 82

Equal Loudness Curves

SLIDE 83

The human ear is not equally sensitive to all

frequencies

Listening level determines perception
The lower the listening level, the greater the

discrepancies

The higher the listening level, the lower the

discrepancies

The ear is most sensitive to mid-range frequencies

and least sensitive to low frequencies.

The sensitivity to high frequencies falls in between

its sensitivity to low and mid-range frequencies.

SLIDE 84

Common Decibel Relationships in Audio Engineering Volts dBu dBV dB VU nWb/m

AC Pro Audio Consumer see below*

0.001

57.8
60.0
61.8

0.0015

54.3
56.5
58.3

0.0025

49.8
52.0
53.8

0.005

43.8
46.0
47.8

0.01

37.8
40.0
41.8

0.0125

35.8
38.1
39.9

0.015

34.3
36.5
38.3

0.02

31.8
34.0
35.8

0.025

29.8
32.0
33.8

0.05

23.8
26.0
27.8

0.10

17.8
20.0
21.8

0.15

14.3
16.5
18.3

0.20

11.8
14.0
15.8

0.25

9.8
12.0
13.8

0.3

8.2
10.5
12.3

0.35

6.9
9.1
10.9

0.425

5.2
7.4
9.2

0.475

4.3
6.5
8.3

Mic 0.50

3.8
6.0
7.8

Preamp 0.55

3.0
5.2
7.0

Gain 0.59

2.4
4.6
6.4

0.65

1.5
3.7
5.5

0.70

0.9
3.1
4.9

0.725

0.6
2.8
4.6 185 nWb/m

0.75

0.3
2.5
4.3 200 nWb/m

0.765

0.1
2.3
4.1

0.775

2.2
4.0

VU METER 0.87 1.0

1.2
3.0 250 nWb/m

1.00 2.2 0.0

1.8

1.09 3.0 0.7

1.0

1.15 3.4 1.2

0.6

1.23 4.0 1.8 0 370 nwB/m FS METER 1.38 5.0 2.8 1.0 1.55 6.0 3.8 2.0 1.73 7.0 4.8 3.0 520 nWb/m 1.95 8.0 5.8 4.0 2.18 9.0 6.8 5.0 2.45 10.0 7.8 6.0 3.00 11.8 9.5 7.7 3.10 12.0 9.8 8.0 3.45 13.0 10.8 9.0 4.00 14.3 12.0 10.2 5.00 16.2 14.0 12.2 6.00 17.8 15.6 13.8 7.00 19.1 16.9 15.1 8.00 20.3 18.1 16.3 9.00 21.3 19.1 17.3 10.00 22.2 20.0 18.2 11.00 23.0 20.8 19.0 12.00 23.8 21.6 19.8 13.00 24.5 22.3 20.5

Maximum

14.00 25.1 22.9 21.1

Output

15.00 25.7 23.5 21.7

Range

16.00 26.3 24.1 22.3

for

17.00 26.8 24.6 22.8

0 dBFS

18.00 27.3 25.1 23.3

*RCA Studio B Alignment using MRL Test Tape with a Reference Fluxivity of 250 nWb/m, machine aligned for +3/250 nWb/m

Consumer Line Level dBu Reference Level dBV Reference Level Professional Line Level Low Mic Sensistivity High