Introduction to Acoustics

dr inż. Michał Bujaczbujaczm@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/2

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.

http://www.physics.byu.edu/

What’s the range of movement of the air particles moved by sound?

0.008nm to 0.1 mm

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Harmonic signal

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

T

dttxE0

2)(

T

dttxT

P0

2)(

1

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Physics vs. perception

Physical definitions:

- Intensity (natężenie) or

amplitude (amplituda)

- Frequency (częstotliwość)

- Spectrum (widmo)

- Speed (prędkość)

Psychoacustic definitions:

- Loudness (głośność)

- Pitch/tone (wysokość/ton)

- Tembre (barwa)

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Speed of soundc = 344 m/s

c = 331 + 0,6*T[oC]gestosc

sztywnoscCc

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Intensity of soundIntensity = the amount of energy passing through an area in time

224 m

W

r

PI

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

How does amplitude change with distance?

22 ~~~ ApEP

rrIA

1~

1~~

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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 scaleRatio of power:

Ratio of amplitude:

dB power ratio amplitude ratio

60 1 000 000 1 000

50 100 000 316.2

40 10 000 100

30 1 000 31.62

20 100 10

10 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

0

110log10P

PLdB

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10log10A

ALdB

0

110log20A

ALdB

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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)

μPa200 p 212

0 mW10P

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http://www.physics.byu.edu/

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Loudness1Fon = 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 octavesDrums, bass, cellos, wind instruments

Lower mid: 320 – 2560 Hz

5th – 7th octavesMost instruments and human speech

Upper mid: 2560 – 5120 Hz

8th octaveHighest notes on most instruments, whistles, most sensitive perception range

High/treble: 5120 Hz – 20000 Hz

9th -10th octavePercussion (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 Barkhttp://www.sfu.ca/

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Freq. components

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Fourier transform

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Spectrum of a sound

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Real spectrumA

mpl

itud

a (d

B)

Częstotliwość (Hz)

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Cutting the spectrum into octaves

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Tembre/qualitySet 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

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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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