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Basic Frequency Analysis of Sound

Contents: Frequency and Wavelength Frequency Analysis Perception of Sound

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[Hz]1 10 100 1000 10 000

Frequency

Frequency Range of Different Sound Sources

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1 10 100 1000 10 000 [Hz]

Frequency

Audible Range

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Wavelength, [m]

Speed of sound, c = 344 m/s

Wavelength

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c

f

20 10 5 2 1 0.2 0.1 0.05

10 20 50 100 200 500 1 k 2 k 5 k 10 k

Frequency, f [Hz]

Wavelength, [m]

Wavelength and Frequency

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b

Diffraction of Sound

Example:

b = 1 m

= 0.344 m (f = 1 kHz)

Example :

b = 0.1 m

= 0.344 m (f = 1 kHz)

b

b b

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Example:

b = 0.5 m

= 0.344 m (f = 1 kHz)

b b

Example :

b = 0.1 m

= 0.344 m (f = 1 kHz)

b bDiffusion of Sound

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Imaginary Source

Source

SourceSource

Reflection of Sound

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Basic Frequency Analysis of Sound

Contents: Frequency and Wavelength Frequency Analysis Perception of Sound

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p Lp

time

Frequency

time

time

p

p

Lp

FrequencyLp

Frequency

Waveforms and Frequencies

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p Lp

time

Frequency

time

time

p

p

Lp

FrequencyLp

Frequency

Typical Sound and Noise Signals

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FastSlow

Impulse

87.2

RMSPeakTime

pFrequency

Lp

Frequency

Lp

Time

p

Filters

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B0

0

- 3 dB

Frequency Frequency

Frequency

Ideal filter

Practical filter anddefinition of 3 dB Bandwidth

Ripple

f1 f0 f2

f1 f0 f2

=

Bandwidth = f2 – f1

Centre Frequency = f0

f1 f0 f2

Practical filter anddefinition of Noise Bandwidth

Area Area

Bandpass Filters and Bandwidth

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0 1k 2k 3k 4k 5k 6k 7k 8k 9k 10k

B = 400 Hz

Linear Frequency Axis(primarily used in vibration analysis)

2 4 8 16 31.5 63 125 250 500 1k 2k 4k 16k8kFrequency[Hz]

Logarithmic Frequency Axis(primarily used in acoustic analysis)

B = 400 Hz B = 400 Hz

B = 1/1 Octave B = 1/1 Octave B = 1/1 Octave

Frequency[Hz]

L

L

1

Filter Types and Frequency Scales

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Frequency[Hz]f1 = 891

f0 = 1000

f2 = 1120

f f2 12

B f 0 7 70%0.

f f f23

1 12 125 .

B f 0 23 23%0.

B = 1/1 Octave

f1 = 708

f0 = 1000

f2 = 1410

B = 1/3 Octave

Frequency[Hz]

L

L

1/1 Octave

1/3 Octave

1/1 and 1/3 Octave Filters

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500 1000 2000

800 1000 1250

L

L

Frequency[Hz]

Frequency[Hz]

B = 1/1 Octave

B = 1/3 Octave

3 × 1/3 Oct. = 1/1 Oct.

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Band No. Nominal CentreFrequency Hz

Third-octavePassband Hz

OctavePassband Hz

123456

1.251.62

2.53.15

4

1.12 – 1.411.41 – 1.781.78 – 2.242.24 – 2.822.82 – 3.553.55 – 4.47

1.41 – 2.82

2.82 – 5.62

272829303132

500630800

100012501600

447 – 562562 – 708708 – 891891 – 1120

1120 – 14101410 – 1780

355 – 708

780 – 1410

40414243

10 K1.25 K16 K20 K

8910 – 1120011.2 – 14.1

14.1 – 17.8 K17.8 – 22.4 K 11.2 – 22.4 K

Third-octave and Octave Passband

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L

Frequency[Hz]

1/1 Octave

1/3 Octave

The Spectrogram

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Basic Frequency Analysis of Sound

Contents: Frequency and Wavelength Frequency Analysis Perception of Sound

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Infra Audio Ultra

0.02 0.2 2 20 200 2000 20.000 200K HzFrequency

Sound Frequencies

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140

dB120

100

80

60

40

20

0

20 50 100 200 500 1k 2k 5k 10k 20 kFrequency [Hz]

Sou

nd P

ress

ure

Leve

l

Thresholdin Quiet

Limit of Damage Risk

Threshold of Pain

Speech

Music

Auditory Field

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Sound

pressure

level, Lp (dB re 20 Pa)

120

100

80

60

40

20

Phon0

1020

3040

50

6070

80

90

100110

120130

20 Hz 100 Hz 1 kHz 10 kHzFrequency

970379

Equal Loudness Contours for Pure Tones

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Change in Sound Level (dB)

Change in Perceived Loudness

3

5

10

15

20

Just perceptible

Noticeable difference

Twice (or 1/2) as loud

Large change

Four times (or 1/4) as loud

Perception of Noise

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40

20

0

20 Hz 100 1 kHz 10 kHz

40

0

-20

-40

20 Hz 100 1 kHz 10 kHz

40

Lp (dB)

Lp (dB)

A-weighting

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

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

40 dB Equal Loudness Contours and A-Weight

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0

-20

-40

10 100 1 k 10 k

Lp [dB]

AB

CD AB + C

D

Lin.

Frequency[Hz]

-60

20 k2 k 5 k200 50020 50

Frequency Weighting Curves

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0

-20

-40

10 100 1 k 10 k

Lp [dB]

A-weighting

Frequency[Hz]

-60

20 k2 k 5 k200 50020 50

L = 8.6dB

Calibration and Weighting!

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FastSlow

Impulse

87.2

RMSPeak

Weighting

Use of Frequency Weighting

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FastSlow

Impulse

RMSPeak

87.2

321 n

Serial Analysis

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FastSlow

Impulse

RMSPeak

87.2

321 n

Parallel Analysis

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FastSlow

Impulse

87.2

RMSPeak

Weighting1/1, 1/3 oct

125 250 500 1k 2k 4k 8k L A20

40

60

80

100dB 1/3 Octave Analysis

The Sound Level Analyzer

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L[dB]

Frequency[Hz]

1/1 Octave

1/3 Octave

LA [dB(A)]LB [dB(B)]LC [dB(C)]LD [dB(D)]LLin. [dB]

The Spectrogram and Overall levels

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Conclusion

Headlines of Basic Frequency Analysis of Sound

Basic introduction to audible frequency range and wavelength of sound

Diffraction, reflection and diffusion of sound Frequency analysis using FFT and Digital filters Fundamental concepts for 1/1 and 1/3 octave filters Human perception of sound and background for A,B,C

and D-weighting Signal flow and analysis in Sound Level Meters

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Literature for Further Reading

Acoustic Noise Measurements

Brüel & Kjær (BT 0010-12)

Noise Control - Principles and Practice

Brüel & Kjær (188-81)