Trane TRG-TRC007-EN manual Logarithmic Addition of Decibels, 50 dB + 44 dB = 51 dB

Page 21

period one

Fundamentals of Sound

notes

Lp = 20 log10

sound pressure, µPa

---------------------------------------------------------

20 Pa

or 10 log10

sound pressure, µPa

---------------------------------------------------------

20 Pa

2

Again, these reference values can be considered the threshold of hearing. The multiplier 20 is used in the sound-pressure level equation instead of 10 because sound power is proportional to the square of sound pressure.

Logarithmic Addition of Decibels

value	5
value	4
dB	4
dB	3
higher	3
higher	2
to the	2
to the	1
add	0	0	5	10	15
			dB difference between values being added

50 dB + 44 dB = 51 dB

Figure 17

Measuring sound using a logarithmic scale means that decibel values cannot be added arithmetically. Instead, logarithmic addition must be used to add two or more sound levels. This involves converting the decibel values into ratios of sound intensity, adding these ratios, and then converting the sum back into decibels. The mathematics become rather involved—the graph in Figure 17 has been developed to simplify the procedure.

To demonstrate the use of this figure, consider the example of adding a 50 dB sound to a 44 dB sound. The difference between these two sounds is 6 dB. Therefore, 1 dB is added to the higher of the two sounds (50 plus 1) to arrive at the logarithmic sum of 51 dB.

Also, notice that the logarithmic sum of two sounds of equal magnitude (0 dB difference) results in a 3 dB increase. Therefore, adding two 50 dB sounds would result in a combined sound level of 53 dB.

14	TRG-TRC007-EN

Image 21

Contents Air Conditioning Clinic Fundamentals of Hvac Acoustics Business Reply Mail One of the Fundamental Series Comment CardFundamentals of Hvac Acoustics Fundamentals of Hvac Acoustics PrefaceContents TRG-TRC007-EN Fundamentals of Sound Fundamentals of SoundWhat is Sound? What is Sound?Sound Wave and Frequency Wavelength Broadband Sound and Tones Broadband SoundOctave Bands Octave BandsLogarithmic sums One-Third Octave Bands Sound Power and Sound Pressure Sound Power and Sound PressureAn Analogy Decibel DB = 10 log10 ´ log Logarithmic ScaleEquation for Sound Pressure Equation for Sound Power50 dB + 44 dB = 51 dB Logarithmic Addition of DecibelsSound Perception Rating Methods Human EarHuman Ear Response Loudness Contours Response to Tones Single-Number Rating MethodsSingle-Number Rating Methods Sound Perception and Rating Methods C WeightingWeighting Example Weighting Noise Criteria NC Curves NC-39 Room Criteria RC Curves MPa DB ref Pressure Sound Perception and Rating Methods RC-31 R Phon and Sone Octave-Band Rating Method Octave-Band Rating MethodAcoustical Analysis Acoustical AnalysisSetting a Design Goal Setting a Design GoalAcoustical Analysis Source-Path-Receiver Analysis Acoustical AnalysisSource-Path-Receiver Model Airborne Typical Sound PathsExample of Multiple Sound Paths Examples of a Single Sound PathIdentifying Sound Sources and Paths Sound-Path Modeling Modeling Sound PathsSupply Algorithms for Sound-Path Modeling Computerized Analysis Tools Terms Used in Sound-Path Modeling Attenuation and RegenerationSound Transmission Insertion loss IL Noise reduction NR Transmission loss TL Absorption Reflected Sound Receiver Sound Correction Equipment Sound Rating Equipment Sound RatingFields of Measurement Free FieldDistance Correction in a Free Field = L p1 20 logLot Near Field Reverberant Field Semireverberant Field Hvac Equipment Sound Rating Rating Hvac EquipmentReverberant-Room Method Free-Field Method Industry Standards Ducted Air-Handling Equipment Air Handler Test Configurations Former Methods of Sound Testing ARI Standard Sound Power by Octave Band Review-Period One ReviewNoise criteria NC Room criteria RC Review-Period TwoReview-Period Three Review-Period Four Review Questions for Period QuizOctave-band frequency, Hz Answers Glossary Glossary Room effect See receiver room correction Glossary Trane