Introduction to
Acoustics
dr inż. Michał Bujacz
bujaczm@p.lodz.pl
Visitng hours:
tuesday 15:00-16:00
wednesday 10:00-11:00
„Lodex” 207
Acoustics
[gr. akoustikós ‘related to
hearing’]
field of physics and
engineering that deals
with the study of all
mechanical waves in
gases, liquids, and solids
including topics such as
vibration, sound,
ultrasound and infrasound
http://www.physics.byu.edu/
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Sound
„phys. mechanical disturbance in a compressive medium
capable of inducing an auditory sensation, as well as the
auditory sensation itself” (Encyklopedia PWN)
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Longitudinal wave (wzdłużna)
Particles oscillate in the
direction of wave
propagation.
Areas of increased and
decreased pressure.
What’s the range of
movement of the air
particles moved by
sound?
0.008nm to 0.1 mm
http://www.physics.byu.edu/
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Harmonic signal
T
E   x(t ) dt
2
0
T
1
2
P   x(t ) dt
T0
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http://hyperphysics.phy-astr.gsu.edu
Physics vs. perception
Physical definitions:
Intensity (natężenie) or
amplitude (amplituda)
-
Psychoacustic definitions:
-
Loudness (głośność)
-
Pitch/tone (wysokość/ton)
-
Tembre (barwa)
-
Frequency
(częstotliwość)
-
Spectrum (widmo)
-
Speed (prędkość)
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Speed of sound
Liquids
Gases
 gestosc
Solids
c
C sztywnosc
c = 344 m/s
o
c = 331 + 0,6*T[ C]
Substance
Carbon Dioxide
Temperature (°C)
0
Speed (m/s)
259
Oxygen
0
316
Helium
0
965
Ethanol
20
1162
Mercury
20
1450
Water
20
1482
Copper
-
5010
Glass
-
5640
Steel
-
5960
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Intensity of sound
Intensity = the amount of energy passing
through an area in time
P W 
I
2 
2
4r  m 
How does amplitude change
with distance?
P ~ E ~ p 2 ~ A2
1 1
A~ I ~ 2 ~
r
r
http://hyperphysics.phy-astr.gsu.edu
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Measures of sound level
Pressure (rms)
from 0.00002 N/m2 (threshold of hearing)
to
20
N/m (threshold of pain)
atmospheric pressure
100000
N/m2
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Decibel scale
Ratio of power:
 P1 
LdB  10 log 10  
 P0 
Ratio of amplitude:
 A12 
LdB  10 log 10  2 
 A0 
 A1 
LdB  20 log 10  
 A0 
dB
power ratio
60
1 000 000
50
100 000
40
10 000
30
1 000
20
100
10
10
amplitude ratio
1 000
316.2
100
31.62
10
3.162
6
3.98
2
3
2
1.414
0
1
1
-3
0.5
0.7071
-6
0.251
0.5
-10
0.1
0.3162
-20
0.01
0.1
-30
0.001
0.03162
-40
0.000 1
0.01
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Confusing „sound levels”
Sound Power Level (SWL)
- energy emitted by sound source per second (cause)
Sound Pressure Level (SPL)
- pressure (amplitude) changes at receiver (effect)
Sound Intensity Level (SIL)
- energy delivered to receiver area per second (effect)
p0  20μPa
P0  10 12 W
m
2
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12
http://www.physics.byu.edu/
Loudness
1Fon = 1dBSPL at 1kHz
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Frequency
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Audio frequency ranges
Tones
Examples
Low bass:
20 – 80 Hz
Lowest two octaves.
Explosions, storms, lowest church organ notes
Upper bass:
80 – 320 Hz
3th – 4th octaves
Drums, bass, cellos, wind instruments
Lower mid:
320 – 2560 Hz
5th – 7th octaves
Most instruments and human speech
Upper mid:
2560 – 5120 Hz
8th octave
Highest notes on most instruments, whistles, most
sensitive perception range
High/treble:
5120 Hz – 20000 Hz
9th -10th octave
Percussion (hi-hat, cymbal), higher harmonics of
sounds, noise
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Human perception
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Musical tone (pitch)
Musical scales
– divided into octaves
(intervals),
e.g. C (dur)
A4 = 440Hz
Psychoacoustic scales
– Mel or Bark
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http://www.sfu.ca/
Freq. components
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Fourier transform
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Spectrum of a sound
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Amplituda (dB)
Real spectrum
Częstotliwość (Hz)
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Cutting the spectrum into
octaves
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Tembre/quality
Set of features distinguishing sounds of the
same base frequency on different instruments
Spectrum dependent (harmonics and noise)
and transients (sudden changes)
Described semantically (np.brightness, warmth,
coarsness, clarity)
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Sound envelope
24
Anatomy of hearing
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Cochlea
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Future topics
-
Psychoacoustics
- Spatial audio
- Room acoustics (wave phenomena)
- Spectrum analysis (Fourerier, DFT, FFT)
- Noise and sound standards
- Math of Music
- Electroacoustics
- Studio equipment
- Sound synthesis
- Speech signals
- Speaker sets
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