Technical Report: What is dB (Decibel)? 3

As explained earlier, there are two types of decibel values: relative level values and absolute level values. How can we add or subtract these two types of values?

The following combinations are possible:

In this case, you can simply add or subtract decibel values.

[example]
When an A dB amplifier and a B dB amplifier are connected, the combined amplification factor is (A + B) dB.

In this case as well, numerical addition and subtraction of decibel values is possible.

[example]
When a microphone with a sensitivity of -30 dB (re. 1 V/Pa) is connected to a preamplifier with an insertion loss of -2 dB, and a sound pressure of 1 Pa (sound pressure level of 94 dB) is measured, a voltage of -32 dBV (approximately 25 mV) is output.

In this case, simple numerical addition or subtraction of decibel values is not possible. Regardless of whether it is an electrical or acoustic vibration system, addition or subtraction of power values is required. That is, the decibel values are converted back to numerical values, addition or subtraction is performed using numerical values, and then converted back to decibel values. This type of addition is called energy addition (power addition, decibel summation).

For example, the sum (or subtraction) of the absolute levels of L1 dB and L2 dB, L dB, is:

This can be calculated as follows.

However, adding absolute level values together doesn't make much sense, but subtracting them corresponds to the ratio of the argument numbers, so the difference in absolute decibels with the same reference value becomes meaningful as a relative decibel value. For example, the inter-room sound pressure level difference D, which is often used in the acoustic performance of buildings, can be calculated as a difference in decibels as follows.

[example]
The combined sound pressure level of 60 dB and 63 dB can be found by substituting these values into equation (5-1):

When measured under an ambient noise level of 40 dB, the sound pressure level was 45 dB. The sound pressure level corrected for the ambient noise can be obtained by substituting this into equation (5-1):

In a 1/3 octave band filter analysis, when the levels are 72 dB at 800 Hz, 76 dB at 1 kHz, and 74 dB at 1.25 kHz, the level of the 1/1 octave band filter analysis with a center frequency of 1 kHz is obtained by band synthesis:

【Note】
The method used is to add up the absolute level values and then take the average. This type of average is called an energy average (power average, decibel average). For example, the average sound pressure level L dB of sound pressure levels L ₁ dB, L ₂ dB, and L ₃ dB is:

For example, the average level of 80 dB, 82 dB, and 84 dB can be calculated by substituting these values into equation (5-3) to get 82.3 dB. However, some existing standards may require calculating the numerical average of the decibel values. This method is sometimes called the arithmetic mean of the decibel values. In this example:

This corresponds to 82 dB. For more information on calculating decibel values, please refer to Chapter 12, "Calculation of Decibels (dB)," on Ono Sokki website under "What is a Sound Level Meter?".