Basic Acoustics

Introduction to Acoustics

Bruel & Kjaer Norcross, Georgia www.bkhome.com

Agenda

2

z

Introduction to Theory and Terminology

z

The Decibel

z

Frequency of Sound

z

Measuring Sound

z

Applications of Acoustics

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Sound

3

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Sound and Noise

4

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Terminology of Sound Active Intensity

RMS Peak

Statistical analysis Fast Slow Impulse

Free Field/Pressure Field Percentile level

Sound Pressure dB Logarithmic scales Pascal

Weighting Leq

RMS

L10 L90

Constant percentage bandwidth

1/1 and 1/3 Octave Analysis Noise Dose

5

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Basic Parameters of Sound (cont.)

Receiver

Sound Pressure Level

p2 Lp = 10 log10 2 po

po = 2 ×10−5 N / m2 = 20µPa

Path

Sound Intensity Level

Source

Sound Power Level

I I0 2 Io = 1pW / m

Li = 10 log10

Lw = 10 log10 Wo = 1pW

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W Wo

Pressure vs. Power

Pressure p [N/m2 = Pa]

Analogy

Lp [dB]

Temperature t [°C]

Power P [W]

Power P [W] Sound Source Electrical Heater 7

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Sound Levels Under Free-field Conditions Example: r = 1.5 m

W p2 Ι= = 2 ρc 4πr

Sound Power = 0.01 Watt

Sound Power

Sound Intensity

W = 0.01 Watt

Ι=

p=

Ι L Ι = 10 log10 dB Ι0

p2 Lp = 10 log10 2 dB p0

L W = 10 log10

LW

W dB W0

0.01 = 10 log10 −12 dB 10 = 100 dB

Sound Pressure

W 0.01 = 2πr 2 2π ⋅ 1.5 2 = 0.000707 W m2

Ι ⋅ ρc = 0.000707 ⋅ 400

= 0.532 Pascal

7.07 ⋅ 10 − 4 = 10 log10 dB 10 −12 L Ι = 88.5 dB

= 10 log10

0.532 2

(20 ⋅ 10 )

−6 2

dB

Lp = 88.5 dB

LI = Lp under free-field conditions 8

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Sound Pressure Propagation

Pressure [Pa] 100 000 Pascal

Time 9

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Range of Sound Pressure Levels Sound Pressure, p [Pa] 100 10 1 0.1 0.01 0.001 0.000 1 0.000 01 10

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Sound Pressure Level, Lp 140 120 100 80 60 40 20 0

[dB]

Converting Pascals to Decibels

Lp = 20 log

⎛ p⎞ ⎜⎜ ⎟⎟ ⎝ p0 ⎠

dB re 20 µPa

(p0 = 20 µPa = 20 × 10-6 Pa)

Ex. 1: p = 1 Pa

Ex. 2: p = 31.7 Pa 1

Lp = 20 log 20 × 10 −6

11

Lp = 20 log

317 . 20 × 10 −6

= 20 log 50 000

= 20 log 1.58 × 10-6

= 94 dB

= 124 dB

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Human Perception of dBs Change in Sound Level (dB)

12

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Change in Perceived Loudness

3

Just perceptible

5

Noticeable difference

10

Twice (or 1/2) as loud

15

Large change

20

Four times (or 1/4) as loud

Types of Sound Sources Point source

Line source r: Lp 2r: Lp − 3 dB

Plane source r: Lp 2r: Lp − 6 dB r: Lp 13

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2r: Lp

Anechoic and Reverberant Enclosures

14

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Pressure Field

z

Loudspeaker

z

z

15

Microphone

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Enclosure

Sound Fields Lp

Near field

Far field Free field

Reverberant field

6 dB

Distance, r A1

16

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2 × A1

Frequency Range of Different Sound Sources

1

10 17

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100

1000

10 000

Frequency [Hz]

Wavelength and Frequency

c λ= f λ

λ

Wavelength, λ [m] 20

10

10

20

5

50

2

100

1

200

0.2

500

Frequency, f [Hz] 18

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1k

0.1

2k

0.05

5k

10 k

Why Make a Frequency Analysis

B

C Amplitude

Amplitude

A A

B

E D C

Time

E D

19

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Sound

Frequency

1/1 and 1/3 Octave Filters L B = 1/1 Octave

1/1 Octave f2 = 2 × f1 Frequency f2 = 1410 [Hz]

f1 = 708

B = 0 .7 × f0 ≈ 70%

f0 = 1000

L 1/3 Octave

B = 1/3 Octave

f2 = f1 = 891

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f2 = 1120 f0 = 1000

Frequency [Hz]

3

2 × f1 = 1.25 × f1

B = 0 .2 3 × f 0 ≈ 2 3 %

Third-octave and Octave Passband

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Band No.

Nominal Centre Frequency Hz

Third-octave Passband Hz

1 2 3 4 5 6

1.25 1.6 2 2.5 3.15 4

1.12 – 1.41 1.41 – 1.78 1.78 – 2.24 2.24 – 2.82 2.82 – 3.55 3.55 – 4.47

27 28 29 30 31 32

500 630 800 1000 1250 1600

447 – 562 562 – 708 708 – 891 891 – 1120 1120 – 1410 1410 – 1780

40 41 42 43

10 K 1.25 K 16 K 20 K

8910 – 11200 11.2 – 14.1 14.1 – 17.8 K 17.8 – 22.4 K

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Octave Passband Hz

1.41 – 2.82 2.82 – 5.62 355 – 708 780 – 1410

11.2 – 22.4 K

Auditory Field 140 dB 120

Threshold of Pain

Sound Pressure Level

100 80

Music

60

Speech

40 20 0 20

22

Limit of Damage Risk

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Threshold in Quiet 50

100

200

500 1k 2k Frequency [Hz]

5k

10k

20 k

Equal Loudness Contours for Pure Tones 130 120 110 100 90 80 70 60

120

Sound pressure level, Lp

100

(dB re 20 µPa)

80 60

50 40 30

40 20

20 10

0

Phon 20 Hz

23

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100 Hz

1 kHz Frequency

10 kHz

40 dB Equal Loudness Contours and A-Weight L p

z

40 dB Equal Loudness Contour normalized to 0 dB at 1kHz

(dB) 40

40

20 0

Lp z

20 Hz

1 kHz

10 kHz

1 kHz

10 kHz

(dB) 0

40 dB Equal Loudness Contour inverted -20 and compared with A-weighting -40

40 A-weighting

20 Hz 24

100

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100

Frequency Weighting Curves Lp

D

[dB] Lin. 0 D

C B+C

A

-20 A B -40

-60

10

25

20

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50

100

200

500

1k

2k

5k

10 k 20 k

Frequency [Hz]

The Sound Level Analyzer

dB 100 1/1, 1/3 oct

1/3 Octave Analysis

Weighting 80 RMS Peak Fast Slow Impulse

60 40 20 125 250 500 1k

87.2 26

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2k

4k

8k

LA

Time Weighting p

Time

Lp

Lp

Impulse (1.5 ) Slow (1 s) Fast (125 ms)

Slow (1 s) Fast (125 ms) Impulse (35 ms) 27

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Time

Equivalent Level, Leq

Leq = 10 log10

1 T ∫0

T

⎛ p(t ) ⎞ ⎜ ⎟ dt ⎝ p0 ⎠ 2

Lp

Leq Time

T 28

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Sound Power z z z z

Product noise labeling Government regulations ‘Apples to Apples’ comparison of noise Can predict SPL with knowledge of sound field

Z z

Three ways to calculate sound power: z Free Field z Reverberant Field z Sound Intensity

Y

X 29

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Intensity Mapping

z

z

z

30

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Visually identify where sounds come from Rank sound power contribution of individual components Make modern art?

Sound Quality L = 63 dBA

zz

L = 63 dBA

L = 63 dBA

Sound SoundQuality Qualityisisaaparameter parameterthat thatsells sellsthe theproduct product zz A-weighted A-weightednoise noiselevels levelsand andsound soundpower powerare arenot notsufficiently sufficiently sensitive sensitiveto tofully fullycharacterize characterizethe the“quality” “quality”of ofproduct productsound sound zz Sound SoundQuality Qualityisisfunction functionof ofconsumer consumerexpectations expectations

31

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Building Acoustics z z z z z

32

Reverberation Time Transmission Loss Leakage between rooms Impact Isolation Speech Intelligibility

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Environmental Noise Models

Large Plane Smaller size

Mid Sized

Noise Contours

Mid Sized

Smaller

33

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Conclusion

34

z

Clear understanding of the three basic acoustic parameters: pressure, intensity, power

z

What a decibel is and why we use it in acoustics

z

Differences between Anechoic, Reverberant, and Pressure sound fields

z

How wavelengths are calculated and the importance of frequency analysis in acoustics

z

Introduction to some different acoustic applications

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Literature for Further Reading References z z z z z z z z

35

Acoustic Noise Measurements Journals and Magazines Brüel & Kjær (BT 0010-12) z Journal of the Acoustical Noise Control - Principles and Practice Society of America Brüel & Kjær (188-81) z Noise Control Engineering Noise and Vibration Control z Sound and Vibration Magazine L. L. Beranek, ed. INCE z Bruel & Kjaer Magazine Industrial Noise Control Websites Louis Bell, Dekker z www.bkhome.com The Science and Application of Acoustics z asa.aip.org Daniel Raichel, AIP Press z www.inceusa.org Industrial Noise and Vibration Control z www.nonoise.org Irwin and Graf, Prentice Hall Acoustics L.L. Beranek, Acoustical Society of America Acoustical Designing in Architecture V. Knudsen, C. Harris Acoustical Society of America

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