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

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
	4
dB
	3
higher
	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.

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