1. Intensity, Intensity Level, and Intensity Spectrum Level
The spectrum level is the intensity level of the sound wave
within a 1 Hz band.

2. A Sonar System band pass filter #1 hydrophone band pass filter #2
acoustic pressure
hydrophone
Output

3. System Output Fourier Transform of the Time Domain Signal
frequency
band level
band #1
band #2
band #3
Fourier Transform of the Time Domain Signal
Frequency Analyzer

4. Example

5. Fourier Coefficients n fn (Hz) Pmax (Pa) P2rms (Pa) I (W/m2) L (dB) 11
0.5
3.3 x 10-7
117
110 5
12.5
8.3 x 10-6
131 2
220 3
330 4
110
220
330
440
f (Hz)
Pressure
(Pa) 1 2 3 4 5

6. Band Level
frequency
ISL f1 f2
ISLave
The Band Level is the intensity level over a band other than 1 Hz.

7. Example
100
200
282
355
frequency (Hz)
Intensity
Spectrum Level
(dB) 60 50 30
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

8. Types of Spectrums
frequency
Spectrum Level
broadband noise
tonals

9. Example
What is the total BL?

10. Common Bandwidths Constant Bandwidth Df = constant
Proportional Bandwidth
Octave Bandwidth
f2 = 21 f1
Half Octave Bandwidth
f2 = 21/2 f1
Center Frequency
100
200
282
355
frequency (Hz)
Spectrum Level
(dB) 60 50 30
fc=141

11. Preferred Octave Bands

12. 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