Technical Report: What is a sound level meter 2

The frequency range of sound that humans can perceive (audible sound) is approximately 20 Hz to 20 kHz, and the range of sound pressure is from 20 μPa to 20 Pa, with the ratio of the smallest sound to the largest sound pressure reaching up to "10 ⁶" as discussed in Chapter 1. Generally, a logarithmic scale is used as a measure to efficiently represent a wide range of variations, and due to the very broad range of changes, this logarithmic scale is also used when expressing sound pressure and noise levels. Furthermore, there is Weber-Fechner's law, which states that "the sensory quantity of humans is proportional to the logarithm of the stimulus quantity," and since hearing is one of the sensory quantities, a logarithmic scale is employed.

The unit of the logarithmic scale is called the Bel (B), named after Alexander Graham Bell, who first used it to express the attenuation of power in telephony. However, since the value of the Bel itself is too large, the decibel (deci Bel = dB), which is one-tenth of a Bel, is actually used. In other words, 1 B is equal to 10 dB.

Note

In addition, the reason why decibels (dB) are widely used in the electrical and communication fields is that the gains of multi-stage connected amplifiers and attenuators can be easily calculated through addition and subtraction.

As mentioned earlier, decibels (dB) are used to represent the transmission loss (ratio) of power, and the definition formula is as follows.

Equation 4-1

As can be seen from the above formula 4-1, the decibel (dB) is a relative value that expresses the power ratio in common logarithm, and if the reference value (for example, the above E ₀) is clearly defined, it can be treated as an absolute value. Therefore, what is important with decibels is to always pay attention to "what the reference value is."

In the field of acoustics, since the square of the sound pressure is proportional to the strength of the sound, for example, one of the display values when measuring using a sound level meter is the sound pressure level L _p (dB), which is given by the following formula.

Equation 4-2

Furthermore, the formula to obtain the noise level L _A (A-weighted sound pressure level) (dB) from the sound pressure p _A weighted by the A characteristic, which corresponds to the human auditory response frequency (for details, see Section 8.3 "Frequency Correction Circuit"), is as follows.

Equation 4-3

In the world of sound (vibration), the term "level (practical unit as dB)" is used to represent its magnitude (strength), and instead of saying "loudness of sound," it is expressed as "sound (pressure) level" in the form of "what dB." Furthermore, as stated in the definition above, the absolute reference sound pressure of dB is clearly defined as p ₀ (20 μPa), so for example, the effective sound pressure value of a "100 dB sound pressure level" is uniquely determined in pascals. In this example, 100 dB corresponds to 2 pascals. The method of calculating decibels will be discussed later.

(Note) About dB SPL
Since sound pressure level is Sound Pressure Level (SPL), it was previously common to express it explicitly as "dB SPL" to indicate the unit of sound pressure level, which is dB (decibel). However, recent JIS standards and laws such as the Measurement Act have established that simply writing dB is the correct unit notation.

Under the old measurement law, the measurement unit 'hon' was used, but with the enforcement of the new measurement law in 1993, it has transitioned to the SI unit 'dB' in accordance with international standards, and the non-SI unit 'hon' has been completely prohibited.

Additionally, during the grace period until September 30, 1997, the use of both 'phon' and 'dB' was permitted, but please note that after October 1, 1997, it has been completely unified to 'dB' units. Furthermore, 'phon' is a unit that represents the sound level equivalent to 'dB', and although the unit names are different, they represent the same quantity (for example, 90 phon and 90 dB represent the same sound level).

(Note)
The unit for noise level (A-weighted sound pressure level) has often been expressed as dBA or dB(A) for clarity. However, according to current domestic and international standards (JIS and IEC) and the Measurement Act, the only acceptable unit for both sound pressure level and noise level is "dB". Therefore, please be cautious when using formal notation. The basic principle is to state that "all level units should be 'dB'. The type of quantity should be clearly specified as L _p (sound pressure level), L _A (noise level), etc." which is practical.

When the effective value of the instantaneous sound pressure of a sound is p (Pa) and the reference sound pressure is p ₀ (Pa), the "sound pressure level" L _p (dB) is;

Equation 5-1

It is given in ; The reference sound pressure p ₀ for sound in air is 20 μPa, which is the minimum audible level for a 1 kHz pure tone for a person with normal hearing. Figure 5-1 below shows the relationship between sound pressure p (Pa) and sound pressure level L _p (dB), where a sound pressure of 20 μPa corresponds to a sound pressure level of 0 dB, 1 Pa corresponds to 94 dB, and 20 Pa corresponds to 120 dB. Note that although it is not audible, if there is a pressure fluctuation of 0.1 atmospheres (approximately 100 hPa = 10 ⁴ Pa), the sound pressure level would be 174 dB.

Let the effective value of the sound pressure propagating through the space be p (Pa), and the particle velocity of the medium particles vibrating due to the sound wave be u (m/s). The sound energy I (W/m ²) passing through a unit area perpendicular to the direction of sound wave propagation in a unit time is;

Formula 5-2

It is given in ;. This amount is called "sound intensity" I (W/m ²).

If the sound wave is a plane wave (a wave whose wavefront is a plane perpendicular to the direction of wave propagation), let the volume density of the medium be ρ (kg/m ³) and the speed of sound in the medium be c (m/s);

Equation 5-3

If we substitute the above equation into equation 5-2, the sound intensity I is;

Equation 5-4

It will be as follows. For example, at a temperature of 20 °C, the volume density of air ρ ₀ is 1.205 kg/m ³, and the speed of sound c ₀ is 343 m/s. Therefore, regarding sound waves propagating in air (specifically plane waves), the sound intensity I corresponding to the reference sound pressure p ₀ = 2×10^-5 Pa is;

Equation 5-5

This value is 10.^-12 W/m ² It is very close to the reference value of sound pressure p ₀ Reference value for sound intensity corresponding to I ₀ For this value (10^-12 W/m ² It is internationally agreed that this should be used.

Similar to sound pressure levels, the "level of sound intensity" L _I (dB) is as described above I ₀ Taking this as the reference sound intensity;

Equation 5-6

is defined by ;

The reference value of sound intensity I ₀ was obtained for plane sound waves, but the formula for the level of sound intensity 5-6 is also applicable to general sound waves. Additionally, for plane sound waves, formula 5-4 holds, so the level of sound intensity at a temperature of 20 ℃ is ;

Equation 5-7

The sound pressure level is almost equal to the sound intensity level. However, since the volume density of air and the speed of sound are functions of temperature, when the temperature is not 20°C, the sound pressure level and the sound intensity level do not match, resulting in a difference of about 0.2 to 0.3 dB. Furthermore, near sound sources, sound waves can no longer be considered plane waves, making it impossible to simply derive the sound intensity level from the sound pressure.

Sound waves propagating through a medium can be considered as a flow of energy, which is referred to as acoustic energy. Therefore, the quantity that represents the magnitude of this acoustic energy is the acoustic power P (W), defined as the acoustic energy passing through a specified surface per unit time.

If the sound wave is a plane wave, the acoustic power P passing through a plane perpendicular to the direction of sound propagation is given by the effective sound pressure p (Pa), the volume density of the medium ρ (kg/m ³), the speed of sound c (m/s), and the area of the plane S (m ²);

Formula 5-8

It is given by ;. Also, the quantity expressed as the level of acoustic power P relative to a reference value P ₀ is called the "acoustic power level" L _W (dB);

Equation 5-9

It is defined by;. Reference value for sound power level P ₀ is 10^-12 W is the sound intensity level L. _I Reference value I ₀ (10^-12 W/m ² This value is obtained by multiplying the unit area by the unit area. Acoustic power is primarily used to express the magnitude of acoustic energy radiated from a sound source. Within a specified frequency band, the total acoustic energy radiated by the sound source per unit time is called the "acoustic output (acoustic power of the sound source)" P (W), and the level of this acoustic power is called the "acoustic output level (acoustic power level of the sound source)" L _W It's called (dB).

When trying to capture the physical properties of sound, it is not enough to only consider the overall sound pressure level or the level of sound intensity; it is necessary to obtain the sound pressure levels and intensity levels for each frequency (frequency analysis).

In the case of frequency analysis of sound, analysis using fixed frequency ratio filters such as octave bands and 1/3 octave bands is widely conducted. These analyzers have been miniaturized and made more affordable through electronic circuit technologies like IC active filters, significantly contributing to improved measurement accuracy and ease of use. Further details about octave band filters will be explained in chapter 11.