Intensity, Intensity Level, and Intensity Spectrum Level

2a max

2 2a a rms

pI or,

2 c

p pI

c c

ref

IL 10log

I

ref ref

I in 1 Hz band I in 1 Hz band 1HzISL 10log 10log

I in 1 Hz band I

The spectrum level is the intensity level of the sound wave within a 1 Hz band.

A Sonar System

band pass filter #1

band pass filter #2

band pass filter #3acoustic

pressure

hydrophone

Output

refband Rf

V

2

refband Rf

V

2

refband Rf

V

2

System Output

• Fourier Transform of the Time Domain Signal

• Frequency Analyzer

frequency

band level

band #1 band #2 band #3

Example 1

p t 5cos 2 110Hz t 3cos 2 2 110Hz t 4cos 3 2 110Hz t Pa2

0 1 2

1 2

1f t a a cos t a cos 2 t

2 b sin t b sin 2 t

0.01 0.02 0.03 0.04 0.05Timesec

-5

-2.5

2.5

5

7.5

10

12.5

Pressure Pa

Fourier Coefficientsn fn (Hz) Pmax (Pa) P2

rms (Pa) I (W/m2) L (dB)

0 0 1 0.5 3.3 x 10-7 117

1 110 5 12.5 8.3 x 10-6 131

2 220 3

3 330 4

110 220 330 440 f (Hz)

Pressure(Pa)

1

2

3

4

5

1p t 5cos 2 110Hz t 3cos 2 2 110Hz t 4cos 3 2 110Hz t Pa

2

2 2 2max n nP a b

22 maxrms

PP

2

2 2rms maxP P

Ic 2 c

Band Level

frequency

ISL

f1 f2

ISLave

tot

ref ref

I in a 1 Hz band fIBL 10log 10log

I I

ref

ave

2 1

I in a 1 Hz band 1Hz fBL 10log 10log

I 1Hz

BL ISL 10log f

where Δf f f

The Band Level is the intensity level over a band other than 1 Hz.

Example

• Using the plot of ISL as a function of frequency shown, calculate – the band level of every band– the total band level – the total band level in a band from 150 Hz to 300 Hz

100 200 282 355

frequency (Hz)

IntensitySpectrum Level(dB)

60

50

30

Types of Spectrums

frequency

Spectrum Level

broadband noise

tonals

tot ave BB tonal #1 tonal #2BL ISL 10log f L L ...

Example

Spectrum containg both noise and tones

0

10

20

30

40

50

60

70

450 500 550 600 650

Frequency (Hz)

ISL

(d

B)

What is the total BL?

Common Bandwidths• Constant Bandwidth

f = constant• Proportional Bandwidth

– Octave Bandwidth• f2 = 21 f1

– Half Octave Bandwidth• f2 = 21/2 f1

• Center Frequency100 200 282 355

frequency (Hz)

Spectrum Level(dB)

60

50

30

fc=141

c 1 2f f f

Preferred Octave Bands

Why do we care?

Source Level (SL) and Noise Level (NL) are both examples of Band Levels (BL) where the frequency band(s) are defined by the frequencies of our Sonar System