Relation between Octave bands and Overall noise level

RELATION BETWEEN OCTAVE BANDS AND OVERALL NOISE LEVEL

 

Introduction

The word ‘octave’ is derived from the Latin word meaning ‘eight’. In the musical world where there are 7 notes, the 8^th note sounds twice as high as the 1^st note. The 8^th note is an octave higher than the 1^st note. Similarly in the octave band, the upper limit frequency is twice the lower limit frequency. Octave bands are very useful in engineering applications because they reveal the spectral content, meaning they represent the change in noise levels with respect to the frequency of sound. This helps in identifying which frequency is responsible for the noise which helps in nailing down the component in a machine responsible for the particular frequency.

Overall noise level is a single number value that describes a noise source. The overall noise level is the average of all individual noise levels emitted by the noise source. Since it is a single number value, it does not provide any information on the frequency content of the noise. However it is very useful to characterize and rank noise sources based on the overall noise level.

The Octave Band

Consider a machine which emits a steady noise. The noise emitted by the machine is captured by a suitable Real Time Analyzer (RTA) for a period of 10 second. The acquired raw data is then processed and the result is displayed as an Octave 1/1 plot.

Equations

The Sound pressure level equation is given by,

Where,

X_i – Sound pressure level in dB(A)

P_i – Sound pressure in Pa

P₀ – Reference sound pressure (P₀ = 20 x 10^-6 Pa)

 

The logarithmic addition or the total sound pressure level is given by,

X₁, X₂… X_n – Individual Sound pressure levels in dB(A)

X – Total Sound pressure level in dB(A)

 

Calculation

The average sound pressure level (SPL) in each octave can be inferred from the Octave 1/1 band considered in this example. The total SPL or the overall noise level is determined by logarithmically adding the individual SPL values.

Octave band tabular column

Frequency band (Hz)	Sound pressure level (dB(A))
31.5	30
63	35
125	40
250	35
500	55
1000	70
2000	50
4000	42
8000	26

 

Plugging in the individual SPL values from above tabular column in equation 2,

This is the overall noise level of the considered noise source. Notice that the overall level is very close to the peak sound pressure level from the tabular column which is 70 dB(A).

Graph

The overall noise level is a plot of sound pressure level versus time. Since the noise source is steady with respect to time, the overall noise level is constant and does not fluctuate.

Conclusion

Thus by logarithmically adding the individual sound pressure levels, the overall noise level is obtained. The overall level is very useful as it quantifies a noise source in a single value. The overall level does not offer any insight into the frequency composition of the sound which is a drawback. Two noise sources can have the same overall level but can sound pleasant and harsh. This is because frequency content and human hearing play a major role in determining the sound quality. For example, a noise source with lot of high frequency content would sound unpleasant despite having the same overall level as a source with less high frequency content.