Technical Report: What is a Sound Level Meter? (14)

If we have two sound sources, and their sound pressure levels when played individually are _L1 (dB) and _L2 (dB), then the sound pressure level when both sound sources are played simultaneously cannot be calculated using a simple arithmetic operation like _L1 + _L2. To calculate this, we need to calculate the sum of the dB values. This section describes the basic method for calculating dB.

We will find the combined sound pressure level L of multiple sound sources. If the sound pressure levels _L1, _L2, ..... Ln (dB) of the sound sources are _p1, _p2, ..... _pn, then:

Equation 12-1

Here, _p0 is the reference value (_p0 = 20 μPa). Expressing the above equation in exponential notation:

Equation 12-2

; and the dB value L of the sum of these is;

Equation 12-3

This results in L being the desired combined sound pressure level.
For example, the sum of 80 dB and 70 dB is calculated as follows:

Equation 12-4

Incidentally, calculating the sum of dB values in this way is sometimes called dB synthesis.

The average L of the n sums in term 12-1 is obtained by taking the sum of the powers and dividing by n to find the dB value. That is;

Equation 12-5

It is calculated as follows: Here, L is the sum obtained in the previous 12-1 section. Therefore, the average can be found by subtracting 10 log10 n from the sum of dB. For example, the average power of 80 dB and 70 dB is calculated as follows:

Equation 12-6

The difference L' between _L1 (dB) and _L2 (dB) is:

Equation 12-7

It can be calculated as follows: Therefore, for example, the difference between 80 dB and 70 dB is:

Equation 12-8

The calculation of the dB difference is used, for example, as background noise correction in specific noise measurements. The measured value including both specific noise and background noise is taken as _L1 (dB), and the measured value without specific noise (background noise) is taken as _L2 (dB). The level of specific noise can then be determined as the difference between these two values.

As explained in Section 4-1, a decibel (dB) is 10 times the logarithm of the ratio of a certain physical quantity (power) to a standard value, so understanding logarithmic calculations is important. Here, we will explain the basic properties of logarithms.

[Basic properties]
1000 can be expressed exponentially as 10 ^{^3}, and this relationship can be expressed using the base-10 logarithm log ₁₀ as log ₁₀ ^ ³ = 3. Generally speaking:

Equation 12-9

It is expressed as shown below. The relationship between the logarithm and the real number, which is often used in noise calculations, is described below.

JIS Z 8731 specifies the measurement method for equivalent sound level used in noise evaluation in general environments, work environments, etc. Equivalent sound level can be automatically determined using an integrating sound level meter with a built-in calculation function. However, even with a sound level meter that does not have an equivalent sound level calculation function, it can be determined by calculating the average value of dB from the measured noise level values, as follows.
To determine the equivalent sound level L _Aeq for a given measurement time (actual measurement time) from noise levels measured at regular time intervals, use the following formula:

Equation 12-10

Here, T is the measurement time, n is the total number of measurements, and L _A1, L _A2, and L _An are the measured noise levels (dB).

One method for measuring and evaluating fluctuating noise is the time-weighted noise level (TROQ). To determine the TROQ, first, set the dynamic characteristics to Fast and collect 50 measurement data points every 5 seconds, recording them in chronological order as shown in column A of Table 12-2. Next, determine the number of occurrences (frequency) for each level from this data and record it in the count column as shown in column B of Table 12-2.

Noise levels are usually read to one decimal place, but the division level is determined by the resolution to be evaluated, and the number of divisions is calculated. In this example, for ease of explanation, the division is made every 1 dB. Furthermore, the cumulative sum is entered in the cumulative column of B in Table 12-2, ordered from lowest to highest noise level, to obtain the cumulative frequency. Using this cumulative frequency data, the values in the cumulative column, in this case 1, 4, 7... are plotted on the Y-axis, and the corresponding noise levels 64.5, 65.5, 66.5... are plotted on the X-axis, as shown in Figure 12-1. A smooth curve (corrected curve) is drawn connecting each value to obtain the cumulative frequency distribution curve. The 95th percentile value of this distribution curve is read from the % scale to the right of the curve. This value is the upper limit of the 90% range, L ₅. Similarly, the 50% value is the median L ₅₀, and the 5% value is the lower limit of the 90% range L ₉₅.