Technical Report: What is a sound level meter?

There are two sound sources, and when pronounced individually, their sound pressure levels are L ₁ (dB) and L ₂ (dB). When both sound sources are pronounced simultaneously, the sound pressure level cannot be simply calculated as L ₁ + L ₂. To determine this, it is necessary to perform the calculation of the sum of dB. Here, we will describe the basic calculation method for dB.

We will calculate the sound pressure level L of multiple sound sources combined. Now, let the sound pressure levels L ₁, L ₂,..... L _n (dB) of the sound sources correspond to the sound pressures p ₁, p ₂,..... p _n:

Formula 12-1

Here, p ₀ is the reference value (p ₀ = 20 μpa). Expressing the above equation in exponential notation;

Formula 12-2

Next, the sum of these dB values L is;

Formula 12-3

This L represents the required combined sound pressure level.
For example, the sum of 80 dB and 70 dB is calculated as follows.

Formula 12-4

Furthermore, the process of finding the sum of dB is sometimes referred to as dB synthesis.

The average of the sum of n items in section 12-1 L is obtained by dividing the value of the sum of powers by n and finding its dB value. That is;

Formula 12-5

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

Equation 12-6

The difference between L ₁ (dB) and L ₂ (dB) is L' ;

Equation 12-7

The difference between 80 dB and 70 dB can be determined.

Equation 12-8

It will be ;. The calculation of the difference in dB is used, for example, as a correction for background noise in specific noise measurements. The measurement value that includes specific noise and background noise is denoted as L ₁ (dB), and the measurement value without specific noise (background noise) is denoted as L ₂ (dB), allowing us to determine the level of specific noise as the difference.

Decibels (dB), as mentioned in section 4-1, are ten times the logarithm of the ratio of a certain physical quantity (power) to a reference value, so it is important to understand logarithmic calculations. Here, we will explain the basic properties of logarithms.

[Basic Properties]
1000 can be expressed in exponential form as 10 ³, but when expressed using the logarithm log ₁₀ with base 10, it becomes log ₁₀ 10 ³ = 3. In general;

Equation 12-9

It is expressed as follows. Below is the relationship between true values and logarithmic values commonly used in sound level meter calculations.

JIS Z 8731 specifies the measurement method for equivalent sound level used for noise evaluation in general environments, working environments, etc. The equivalent sound level can be automatically determined using an integrating sound level meter with built-in calculation functions; however, even sound level meters without equivalent sound level calculation functions can determine it by calculating the average dB value from the measured sound level values as follows.
To determine the equivalent sound level L _Aeq for the measurement time (actual measurement time) from the sound level measured at regular time intervals, it is calculated using the following formula.

Formula 12-10

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

One method for measuring and evaluating fluctuating noise is the time rate noise level. To determine the time rate noise level, first set the dynamic characteristics to Fast, then collect 50 measurement data points every 5 seconds, and record them in the order of collection as shown in column A of Table 12-2. Next, from this data, calculate the frequency of each level and enter the counts in the frequency column as shown in column B of Table 12-2.

The display of noise levels is usually read to one decimal place, but the division level is determined by the resolution being evaluated, and the number of divisions is calculated. In this example, for ease of explanation, it is divided every 1 dB. Furthermore, in the cumulative column B of Table 12-2, the cumulative values are recorded in ascending order of noise levels, and the cumulative frequency is determined. Using the cumulative frequency data here, the values in the cumulative column, which are 1, 4, 7... are taken on the Y-axis, and the corresponding noise levels 64.5, 65.5, 66.5... are taken on the X-axis, and plotted as shown in Figure 12-1, connecting each value to draw a smooth curve (modified curve) to obtain the cumulative frequency distribution curve. From the % scale on the right side of this distribution curve, the 95% value of that curve is read. This value is the upper limit L ₅ of the 90% range. Similarly, the 50% value is the median L ₅₀, and the 5% value is the lower limit L ₉₅ of the 90% range.