Combining adding sound levels adding decibels 1/3 octave bands 1/1 octave band analysys finding number 1/3 octaves between frequencies filter oct calculator calculation band octave band conversion iso frequency bands EQ equalizer - sengpielaudio
 
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Adding decibels of one-third octave bands
to level of one octave band and vice versa
 
Spectral data analysis − spectrum analyzer − one-third octave band = 1/3 octave band
Filter Equalizer EQ

Three adjacent one-third octave bands (1/3 octave bands) belong to one octave band.
 
 Level of one-third octave band 1  dB 
Level of one-third octave band 2  dB
Level of one-third octave band 3  dB
 
                       
 
Combined octave band level  dB
 
 
Octave band level  dB 
 
                       
 
 Level of one-third octave band 1  dB
Level of one-third octave band 2  dB
Level of one-third octave band 3  dB
 
Should the level of an octave band be converted to one-third octave
bands, the energy of the octave band can be divided by three. This
corresponds to a reduction of (−)4.771 dB for each 1/3 octave band.

one-third octave

Calculate: Octave band level LΣ of three one-third octave band levels L1, L2, and L3:

Sum Level

Regenbogenlinie

Calculator: Adding of equal levels of 1/3 octave bands

Octave-band filters (1/1) and one-third octave-band filters (1/3)

Simply enter the value to the left or the right side.
The calculator works in both directions of the sign.

 
Number of 1/3 oct bands n 
 
 ↔  Increase of level Δ L 
dB
Formula1   Formula2
Three 1/3 octave bands are one octave band

The total level in dB is the level of one band plus the increase in level.

Octav bands     One-third octave bands
Octave bands                                      One-third octave bands

ISO
Band numbers
Octave band
Center frequency
One-third octave band
Center frequencies
11, 12, 13 16 Hz 12.5 Hz, 16 Hz, 20 Hz
14, 15, 16 31.5 Hz 25 Hz, 31.5 Hz, 40 Hz
17, 18, 19 63 Hz 50 Hz, 63 Hz, 80 Hz
20, 21, 22 125 Hz 100 Hz, 125 Hz, 160 Hz
23, 24, 25 250 Hz 200 Hz, 250 Hz, 315 Hz
26, 27, 28 500 Hz 400 Hz, 500 Hz, 630 Hz
29, 30, 31 1000 Hz 800 Hz, 1000 Hz, 1250 Hz
32, 33, 34 2000 Hz 1600 Hz, 2000 Hz, 2500 Hz
35, 36, 37 4000 Hz 3150 Hz, 4000 Hz, 5000 Hz
38, 39, 40 8000 Hz 6300 Hz, 8000 Hz, 10000 Hz
41, 42, 43 16000 Hz 12500 Hz, 16000 Hz, 20000 Hz

Standard frequencies for acoustic measurements according to EN ISO 266

1st octave cycle 31.5           63           125           250  
2nd octave cycle       45           90           180        
1st 1/3 octave cycle 31.5   40   50   63   80   100   125   160   200   250  
2nd 1/3 octave cycle   35,5   45   56   71   90   112   140   180   224   280
1st octave cycle         500           1000           2000      
2nd octave cycle   355           710           1400           2800
1st 1/3 octave cycle 315   400   500   630   800   1000   1250   1600   2000   2500  
2nd 1/3 octave cycle   355   450   560   710   900   1120   1400   1800   2240   2800
1st octave cycle     4000           8000           16000          
2nd octave cycle           5600           11200           22400    
1st 1/3 octave cycle 3150   4000   5000   6300   8000   10000   12500   16000   20000   25000  
2nd 1/3 octave cycle   3550   4500   5600   7100   9000   11200   14000   18000        

Center, lower, and upper frequencies for standard set of octave
and 1/3 octave bands covering the audible frequency range.

Octave Band 1/3 Octave Band
Lower
Frequency

f1 (Hz)
Center
Frequency

f0 (Hz)
Upper
Frequency

f2 (Hz)
Lower
Frequency

f1 (Hz)
Center
Frequency

f0 (Hz)
Upper
Frequency

f2 (Hz)
 22  31.5  44 22.4 25 28.2
28.2 31.5 35.5
35.5 40 44.7
 44  63  88 44.7 50 56.2
56.2 63 70.8
70.8 80 89.1
 88  125  177 89.1 100 112
112 125 141
141 160 178
 177  250  355 178 200 224
224 250 282
282 315 355
 355  500  710 355 400 447
447 500 562
562 630 708
 710  1,000  1,420 708 800 891
891 1,000 1,122
1,122 1,250 1,413
 1,420  2,000  2,840 1,413 1,600 1,778
1,778 2,000 2,239
2,239 2,500 2,818
 2,840  4,000  5,680 2,818 3,150 3,548
3,548 4,000 4,467
4,467 5,000 5,623
 5,680  8,000  11,360 5,623 6,300 7,079
7,079 8,000 8,913
8,913 10,000 11,220
 11,360  16,000  22,720 11,220 12,500 14,130
14,130 16,000 17,780
17,780 20,000 22,390

A, B, and C Electrical Weighting Networks for the Sound-Level Meter.
These numbers assume a flat, diffuse-field (random incidence) response for the sound level meter and microphone

Frequency
(Hz)
A-weighting
relative response (dB)
B-weighting
relative response (dB)
C-weighting
relative response (dB)
       25
          31.5
       40
−44.7
−39.4
−34.6
−20.4
−17.1
−14.2
−4.4
−3.0
−2.0
       50
       63
       80
−30.2
−26.2
−22.5
−11.6
−9.3
−7.4
−1.3
-0.8
-0.5
     100
     125
     160
−19.1
−16.1
−13.4
−5.6
−4.2
−3.0
−0.3
−0.2
−0.1
     200
     250
     315
−10.9
−8.6
−6.6
−2.0
−1.3
−0.8
0
0
0
     400
     500
     630
−4.8
−3.2
−1.9
−0.5
−0.3
−0.1
0
0
0
     800
  1,000
  1,250
−0.8
0
+0.6
0
0
0
0
0
0
  1,600
  2,000
  2,500
+1.0
+1.2
+1.3
0
−0.1
−0.2
−0.1
−0.2
−0.3
  3,150
  4,000
  5,000
+1.2
+1.0
+0.5
−0.4
−0.7
−1.2
−0.5
−0.8
−1.3
  6,300
  8,000
10,000
−0.1
−1.1
−2.5
−1.9
−2.9
−4.3
−2.0
−3.0
−4.4
12,500
16,000
20,000
−4.3
−6.6
−9.3
−6.1
−8.4
−11.1
−6.2
−8.5
−11.2

The total level adding of incoherent sound sources means power sum and power addition or sound power sum and sound power addition

Adding decibels - combining up to (10) ten acoustic levels
Adding decibels - combining up to (30) thirty acoustic levels
Calculate the center frequency of a frequency band - geometric mean
Calculate: Q Factor and center frequency - Find the −3 dB cutoff frequencies
Total level adding of incoherent sound sources
Sound measuring (Noise measuring) - Conversion: Frequency f to dBA and dBC

Generation law for octave and third octave bands

Octave band − oct. filter 1/3 Octave band − third oct. filter
Octave Band Formula Third Band Formula
 f1 = Lower cut-off frequency of the octave or 1/3 octave in Hz
 f2 = Upper cut-off frequency of the octave or 1/3 octave in Hz
 f0 = Center frequency of the octave or 1/3 octave in Hz
 B = Bandwidth (BW) of the filter f2f1 in Hz
 

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