Calculation of the sound warning system. Technical security systems Formula for determining the number of voice alarms

Kochnov Oleg Vladimirovich
head of the training and production department of the company ESCORT GROUP

The intensive economic transformations taking place in our country, the improved and strengthened regulatory framework contribute to the revival of industry, the growth in the number of manufacturing enterprises. In pursuance of the federal law of July 22, 2008 - FZ No. 123-FZ "Technical Regulations on Fire Safety Requirements", industrial premises with people working in them must be protected by fire safety systems. The most important part that ensures the comprehensive safety of buildings and structures are organizational measures, an element of which is electro-acoustic calculation. The purpose of this article is to acquaint the reader with the method of electroacoustic calculation (EA), to give it both normative and factual justification - to outline the specifics of the calculation in conditions of high noise typical for industrial enterprises, to demonstrate calculation examples.

In the event of a fire (or other emergencies) occurring inside the production premises (or on the territory of the protected enterprise), the warning system is activated (turns on automatically), broadcasting specially designed texts necessary for the effective evacuation of people to a safe place.

Industrial enterprises use the following types of warning systems:

■ warning and evacuation control systems (SOUE), designed on the basis of;

■ object (OSO) and local (LSO) warning systems in emergency situations, as well as public address systems designed on the basis of . The regulatory basis for the design of centralized, local and object warning systems is the federal law No. 68-FZ "On the protection of the population and territories from natural and man-made emergencies" dated 12/21/1994.

At especially large facilities, such as nuclear or hydroelectric power plants, command-and-search systems (complexes) are used.

The reliability of the transmission of an emergency message is determined by the characteristics, functionality and reliability of the technical means of warning systems, but the reliability of perception can only be confirmed by calculations.

Electro-acoustic calculation allows to determine the level of sound pressure with a sufficiently high accuracy at the so-called design point (RT) - the point (place) of the possible presence of people. Such points are selected in the most critical places in terms of both the removal and the noise present in them. Knowing the distance between the calculated point and the sound source, it is easy to determine the degree of sound pressure reduction at a distance, but this is not at all sufficient. According to the requirements of regulatory documentation, it is necessary to provide conditions under which the resulting level falls within certain limits.

In the specifics of industrial enterprises, the most important task is to determine the exact value of the noise level in the workplace. It should be noted that measuring instruments in such tasks can only be used as auxiliary means due to constantly changing conditions. Thus, the conditions for clear perception can be achieved by solving two problems - the effective placement of loudspeakers and protective acoustic measures.

Any of these systems uses a loudspeaker as a final actuating element - a device that converts an electrical signal at the input into an acoustic (audible) signal at the output. Depending on the requirements for the nature of the transmitted (broadcast) information, different requirements are imposed on the loudspeaker. So, according to the requirements set forth in, if the number of people working at a production facility: in a workshop, in a warehouse, in a laboratory, etc., exceeds 100 people, then type 3 SOUE is used to protect such an object - a voice warning system, broadcasting specially designed texts. In this case, the loudspeaker should operate effectively in the range from 200 Hz to 5 kHz. The concept of efficiency should be understood as the magnitude of the sound pressure (loudness) and the efficiency of the loudspeaker. To increase the degree of information content, the SOUE also includes a light notification method.

BASICS OF ELECTRO-ACOUSTIC CALCULATION

The concept of "acoustic calculation" (AR) in itself is quite capacious. In the context of ensuring the safety of people inside the production premises, the so-called electroacoustic calculation (EAA) is performed, during which:

■ the protected premises are analyzed;

■ design points (RT) are selected;

■ sound pressure in RT is calculated;

■ Noise levels (NL) in the RT are determined, which are typical for a given room;

■ additional sources of noise are identified;

■ the boundary conditions of the calculation are checked;

■ loudspeaker parameters are selected and their placement schemes are determined;

■ in case of non-fulfillment of boundary conditions, organizational measures are developed that increase the reliability of information transfer.

The requirements for the EDA can be found in, and the methodology - in Appendix A, to, however, it should be noted that the methodology available in this application is completely unsuitable for any serious calculation.

The name of the calculation - electro-acoustic - is due to the consideration of the electrical parameters of the sound path, which are input to the acoustic calculation. It should be noted that the calculation requirements set forth in are not entirely sufficient, however, they are necessary, therefore, the focus of this article will be on meeting these requirements. As for the specifics of this calculation, in particular, high noise, we will rely on the SNiP for Noise, which describes in sufficient detail both the design and organizational measures for calculating, recording and combating high noise.

Let's consider the basic concepts necessary for the implementation of EAR.

BASIC SPEAKER PARAMETERS

According to regulatory documentation, loudspeakers must reproduce an audio or speech signal in the range: 200 Hz - 5 kHz.

The sound pressure of a loudspeaker is measured in decibels (dB) and is determined both by its sensitivity P 0 , dB, and the electric power, P W, W, supplied to its input:

R db \u003d R o + 10log (R W / Ppor), (1)

R o - loudspeaker sensitivity, dB; P w - loudspeaker power, W; P then - threshold power, = 1W.

Loudspeaker sensitivity, dB - sound pressure level measured on the working axis of the loudspeaker at a distance of 1 m from the working center at a frequency of 1 kHz at a power of 1 W. The loudspeaker power is taken from the passport provided by the manufacturer or supplier, while paying attention to the following circumstances:

1) If there are no special references or indications in the passport, then (in most cases) the so-called. RMS power measured at 1kHz.

2) On the so-called. "grades of inclusion".

A comment is required here. The fact is that the loudspeakers used in public address systems are transformer-based. The primary winding of the transformer has, as a rule, several taps with different impedances and allowing operation at different powers, therefore, in formula (1), it is necessary to indicate the specific switching power.

Execution. An important parameter of loudspeakers, typical for industrial premises, is a parameter called "performance". For various operating conditions (temperature, moisture, dust, aggressive environments), loudspeakers with different execution (protection) classes can be used. At low temperatures, frost-resistant loudspeakers are used. With an increased concentration of moisture and dust - loudspeakers with various degrees of protection, determined by the IP index:

■ IP-41 - closed premises;

■ IP-54 - outdoor version;

■ IP-67 - high degree of protection against dust and moisture. Additional speaker options will be discussed below.

INITIAL DATA FOR ELECTROACOUSTIC CALCULATION

The initial data for the EAR (at manufacturing enterprises) are:

■ plan and section of the premises with the location of technological and engineering equipment in order to select design points;

■ determination of the noise level at design points;

■ information about the characteristics of the enclosing structures of the premises (absorption coefficients);

■ technical characteristics and geometric dimensions of noise sources.

To calculate the sound pressure level at a design point, two important concepts must be considered:

■ the very concept of “design point” (RT);

■ the concept of "noise level" (NL) in the Republic of Tatarstan.

CALCULATED POINT

The calculated point is the place of possible (probable) location of people, the most critical in terms of position and distance from the sound source (loudspeaker). The RT is selected on the calculated plane - an (imaginary) plane drawn parallel to the floor at a height of 1.5 m (1.2 m for seats) in the place with the worst conditions - the point farthest from the loudspeaker or at the point with the highest Sn.

According to ND, RT are selected:

■ in the zone of direct sound;

■ in the area of ​​reflected sound;

■ in the middle of the crowd (place of maximum concentration of people).

This choice (method) is not suitable for EAR, except for the last point, and here's why. Under the direct sound zone, in the context, we mean a distance not exceeding the double size of the sound source. In sound (noise) sources are meant machines, turbines, units, etc. When using even the largest loudspeaker as a sound source, this distance will not exceed 1 m, which is not relevant.

In the area of ​​reflected sound. Here we mean a point located, firstly, near the reflecting surface and, secondly, as far as possible from the sound source. The choice of RT near the reflecting surface is explained by the specifics of the acoustic calculation as a calculation specifically for noise sources, for which both direct sound energy and diffusion energy are taken into account. When moving away from the noise source at a distance twice its size, the effect of the diffusion component begins to prevail sharply, see formula (7) below. The electroacoustic calculation, in its specificity, is close to the acoustic calculation performed for cinemas, concert halls, in which the characteristic information is music or speech. Such calculations, in order to ensure proper intelligibility, are performed using the so-called geometric-ray theory, which allows one to take into account reflections and determine the levels of direct sound coming (incoming) to the RT. According to this theory, known to the ancient Greeks, sound energy is identified with a thin beam (of light). When it hits objects, part of the sound energy is absorbed, and part is reflected at the same angle.

In acoustics, direct sound means both direct sound - sound propagating directly from the source to the RT, and primary reflections - sound entering the RT, reflected from surfaces (areas) no more than 1 time.

NOISE LEVELS

In order to perform EA, it is necessary to know the exact value of SS. There are a number of difficulties associated with the definition of WN. What value of AN should be used, at what frequency should it be measured, etc.

There are several ways to determine the value of SS:

■ direct measurement;

■ from normative tables;

■ additional calculations.

There is quite serious documentation regarding the USh in the form, however, for example, the designers of the SOUE do not rely on this (detailed) SNiP in their calculations. The absence of clear EAR methods does not make it possible to notice an unambiguous relationship between the two values ​​- the required sound pressure level in the RT and the USh, determined at the same point. This is the first. The second is that in order to determine the VSH, a rather specific calculation apparatus, unusual for the average statistical designer of the SOUE, is used, associated with octave levels, the calculation of diffusion energy. Such calculations, as a rule, are performed by acoustic specialists, while there is no direct requirement to perform the ESA and it is performed either at the request (according to the technical assignment) of the customer, or at the request of the designer. The direct measurement of SNR is associated with a number of difficulties. Firstly, for such a measurement, a professional, and most importantly, a verified USh meter (noise level meter) is required. Secondly, the measurement must be made not only at different frequencies, but also at different intervals (lengths) of time. According to , for manufacturing enterprises it is necessary to use the work shift period. If it is impossible to perform such measurements, it is necessary to use the already available data taken from the design documentation or from the customer's technical specifications, and if they are not available, it is necessary to refer to the Noise tables, for example, SP 51.13330.2011. Noise protection.

THE SPECIFICITY OF DETERMINING THE OCTAVE NOISE LEVELS

Levels are for 9-octave bands from 31.5 Hz to 8 kHz. According to paragraphs. 5.1 the calculation is made for 8-octave bands from 63 Hz to 8 kHz. According to the same, the frequency range of 0.2-5 kHz contains only 5 bands with geometric mean frequencies of -0.25 / 0.5/1/2/4 kHz. This discrepancy is overcome by the requirement to perform calculations in dBA - sound pressure levels corrected on the A scale. It can be shown that the total effect of perception, taking into account the correction on the A scale, of 8-octave (noise) bands is practically equivalent to the perception of 5-octave bands, which gives we have the right to use the equivalent levels of non-constant (intermittent and fluctuating in time) sound pressure /L Aeq, dBA, given in and in .

The NRs taken from the Noise Tables are only generalizing, they can be called intrinsic noises. So, for example, according to , for premises with permanent jobs at manufacturing enterprises /L Aeq = 80 dBA. However, for each specific enterprise, additional calculations are needed that take into account additional, introduced noise - noise resulting from the operation of any noise sources - units, machines, or noise penetrating through windows, doors, etc.

EXAMPLES OF ACOUSTIC CALCULATIONS UNDER HIGH NOISE CONDITIONS

Consider an example. On the figure 1 an elementary situation is depicted - a production room with two RT and two sound sources: a loudspeaker and a noise source.

The figure shows two calculated points RT 1 and RT 2. Let us assume that in RT 1 - the influence of the noise source shown in the upper right part of the figure is not significant due to the removal and shielding of the sound-absorbing structure.

Rice. one. An example demonstrating the features of accounting for noise levels

SOUND PRESSURE LEVEL AT CALCULATED POINT

Calculate the sound pressure level, dB, in RT, generated by the loudspeaker:

L\u003d P o + 10log P W - 20log ( r 1 - 1), (2)

r 1 - distance from the sound source (loudspeaker) to the RT, m. r o = 1 m, r> 2 m;

1 - coefficient taking into account that the loudspeaker sensitivity is measured at a distance of 1 m.

CALCULATION CRITERIA

The criterion for the correctness of the calculation will be the fulfillment of the following requirements:

The sound signals of the SOUE must provide a total sound level (the sound level of constant noise together with all the signals produced by the annunciators) of at least 75 dBAat a distance of 3 m from the siren, but not more than 120 dBA at any point of the protected premises. Sound signals of the SOUE should provide a sound level of at least 15 dBA above the permissible sound level of constant noise in the protected room.

This requirement contains 3 conditions:

1. Minimum level requirement. The sound pressure level of the loudspeaker must be at least 85 dB:

R db > 85 dB (3)

If this condition is not met, a loudspeaker with a high sound pressure must be selected.

2. The requirement for the maximum level. The sound pressure level in the RT should not exceed 120 dB:

(R db - 20log ( r min - 1))

r min is the distance from the loudspeaker to the nearest listener.

If this condition is not met, you can reduce the sound pressure of the loudspeaker or use a distributed loudspeaker layout.

3. The condition for the correctness of the RAE:

L> WL + 15, (5)

VSH - noise level in the room, dB;

15 - sound pressure margin, according to , dB.

If this condition is not met, you can:

■ select a loudspeaker with greater sensitivity R o , dB;

■ choose a loudspeaker with a higher power R W, W;

■ increase the number of loudspeakers;

■ change the speaker layout.

ACCOUNTING FOR ADDITIONAL NOISE

In RT 2, the influence of the noise source is obvious. If the noise level generated by the noise source, NR and, dB in the RT, exceeds the NR, dB in the room, NR and ≥ SW must take into account the total effect of two noises SW sum, dB:

USh sum = 10log (10 0.1USh + 10 0.1UShi), (b)

and then substitute the result obtained into formula (5), equating WL = WS sum.

CALCULATION OF THE SOUND PRESSURE AT THE DESIGN POINT FORMED BY A NOISE SOURCE

From figure 1 it can be seen that the source of the sound is at some distance, r 3 , m, from RT. To calculate the Sn and, dB, we use the results presented in:

USH and = R ist + 10log (ΧΦ n /Ω r 2 2 + 4Ψ/ AT), (7)

P ist - octave (at a frequency of 1 kHz) the sound power level of the sound source, dB, is taken from the specifications or technical characteristics for the equipment;

Χ - coefficient taking into account the influence of the near field in cases where the distance from the noise source to the RT, r3 table 2, );

Φ n - directivity factor of the noise source (for sources with uniform radiation Ф = 1);

Ω - spatial angle of radiation source, rad. (taken according to table 3,);

r 2 - distance from loudspeaker to RT, m;

Ψ - coefficient that takes into account the violation of the diffuseness of the sound field in the room, Table 1;

AT- acoustic constant of the room, m 2 .

ROOM ACOUSTIC CONSTANT

Room Acoustic Constant Calculation AT is associated with the definition of the main sound absorption fund or the equivalent sound absorption area, A, m 2, formula (3), .

The coefficient that takes into account the violation of the diffuseness of the sound field in the room - Ψ depends on the ratio of the room constant B to the area of ​​enclosing surfaces S, table 1:

Tab. one. Coefficient that takes into account the violation of the diffuseness of the sound field of rooms (Ψ)

For an approximate definition AT you can use the following formula: AT\u003d μ * V 1000,

AT 1000 - room constant at a frequency of 1 kHz; μ - frequency multiplier, table 2.

Tab. 2. Frequency multiplier μ

Premises constant AT 1000 for a frequency of 1 kHz, depending on the volume of the room V, m 3, is determined in the following way:

AT 1000 = V/20 - for rooms without furniture with a small number of people (metalworking shops, machine rooms, test benches, etc.);

AT 1000 = V / 10 - for rooms with hard furniture or with a small number of people and upholstered furniture (laboratories, offices, etc.);

AT 1000 \u003d V / 6 - for rooms with a large number of people and upholstered furniture (working premises of administrative buildings, living rooms, etc.);

AT 1000 = V / 1.5 - for rooms with sound-absorbing lining of the ceiling and part of the walls.

Let us explain why VL determines the accuracy of calculations. The following approach (method) is used to select loudspeaker parameters or their arrangement:

1. Choose RT.

2. We determine VSH in RT.

3. Determine the expected sound pressure level in the RT.

4. We determine the installation location and the distance to the intended loudspeaker.

5. We calculate the minimum required sound pressure level of the proposed loudspeaker.

ADDITIONAL ORGANIZATIONAL MEASURES

At high noise levels, a situation arises when the use of a loudspeaker becomes irrational. In this case, organizational measures come to the fore. So, based on:

In protected premises where people are wearing noise-protective equipment, as well as in protected premises with a sound noise level of more than 95 dBA, sound annunciators must be combined with light annunciators. The use of light flashing annunciators is allowed.

EFFICIENT SPEAKER POSITIONING

To fulfill a full-fledged RAE, regulatory requirements alone are extremely insufficient, so additional characteristics have to be introduced. Let's demonstrate some of them:

Beam Width (BPA) is the opening angle, determined from the (circular) speaker pattern, at which the sound pressure level is reduced by 6 dB relative to the working (geometric) axis of the loudspeaker.

The effective range D, m, of the sound of the loudspeaker is the distance from the loudspeaker to the point, sound pressure r, dB, at which the USh by 15 dB.

The effective range can be defined as:

D= 10 1/20 (Rdb - USh -15) + 1, (8) where

R db - sound pressure developed by the loudspeaker at a certain power, dB.

1 - coefficient taking into account that the sensitivity of the loudspeaker is determined at 1 meter.

Operating with the above characteristics (parameters) allows, depending on the types of loudspeakers - ceiling, wall, horn - to build various diagrams - contours of sounded areas. So, for example, for a ceiling loudspeaker, the effective sounded area (contour) is the area of ​​a circle. For SDN = 90°, the radius of such a circle is: R= H- 1.5 m, where H-ceiling height . For wall or horn loudspeakers, the relevant parameter is the effective range. D, m.

EXAMPLE OF ACOUSTIC CALCULATION FOR A WAREHOUSE

On the figure 2 a simplified diagram of a warehouse is shown, for the sounding of which three horn loudspeakers are used.

Horn loudspeakers have a number of advantages over other types:

■ protection class not lower than IP54 and can be used in unheated premises;

■ high sound pressure, allowing to work in conditions of high noise;

■ universal mount that allows you to vary the resulting radiation pattern. Placing speakers on one wall (Fig. 2),

has a practical basis, however, it must be confirmed by calculations.

POSSIBLE CALCULATION ALGORITHMS

The EAP (verification) algorithm for RT 1 can be as follows:

1. The calculated point RT 1 is chosen correctly - in a place as far as possible from the second loudspeaker GR 2.

2. Let's make sure that RT 1 falls into the area of ​​the radiation pattern (SDN) of the second loudspeaker (GR 2).

3. Let's define WN in RT 1 .

4. Calculate the sound pressure level in RT 1 , L 1 , dB, according to formula (2).

5. Let us check the fulfillment of boundary conditions (3), (4), (5).

6. If conditions (3), (4), (5) are met, the calculation for RT 1 is completed.

7. If conditions (3), (4), (5) are not met, another loudspeaker is selected, the loudspeaker layout is changed, and additional organizational measures are taken.

However, it is possible to justify the RAE for RT 1 in a simpler way:

■ determine the effective range D, m, for the second loudspeaker;

■ compare the received value D, m, with distance r1, m;

■ if D> r1, RAE for RT 1 completed.

For RT 2, the EAR algorithm can be as follows:

1. The calculated point of PT 2 is chosen correctly - in the place most critical in terms of the location of the loudspeakers.

2. Let's define WN in RT 2 .

3. Let's make sure that RT 2 falls within the scope of the radiation patterns of the second (GR 2) or third (GR 3) loudspeakers.

4. Since RT 2 does not fall into any of the areas of the diagrams, let us turn to the geometric-ray theory.

5. From figure 2 it can be seen that 2 beams of sound energy, formed by GR 2 and GR 3, and reflected from the second rack, enter RT 2.

Rice. 2. Example of loudspeaker placement for a warehouse

b. The sound pressure level L 2, dB, in RT 2 can be calculated in the following way:

■ calculate the sound pressure level at point A, L A, dB, according to formula (2);

■ calculate the sound pressure level at point B, L B, dB, using the following formula:

L B = L A - 20log r 3 + 10log(1 - K absorb),

K absorb - absorption coefficient of the reflective surface;

■ similarly calculate the sound pressure level generated by the third loudspeaker (GR 3) at points B, L B , dB, and G, L G, dB;

■ calculate the sound pressure level in RT 2 , L 2 , dB: L 2 = 10log (10 0.1LB + 10 0.1Lg).

ORGANIZATIONAL MEASURES

Noise protection by building acoustic methods should be ensured by:

■ rational from the acoustic point of view solution of the master plan of the object, rational architectural and planning solution of buildings;

■ application of enclosing structures of buildings with the required sound insulation;

■ use of sound-absorbing structures (sound-absorbing linings, wings, piece absorbers);

■ use of soundproof observation and remote control booths;

■ use of soundproof casings on noisy units;

■ use of acoustic screens;

■ use of noise suppressors in ventilation and air conditioning systems and in aerogasdynamic installations;

■ vibration isolation of process equipment.

Noise protection measures should be provided in the projects:

■ in the section "Technological solutions" (for manufacturing enterprises), when choosing technological equipment, preference should be given to low-noise equipment;

■ the placement of technological equipment should be carried out taking into account noise reduction at workplaces, in premises and on territories through the use of rational architectural and planning solutions;

■ in the "Construction solutions" section (for industrial enterprises), based on the acoustic calculation of the expected noise at workplaces, if necessary, construction and acoustic measures to protect against noise should be calculated and designed;

■ noise characteristics of technological and engineering equipment should be contained in its technical documentation and attached to the section of the project "Protection from noise";

■ take into account the dependence of noise characteristics on the mode of operation, the operation performed, the material being processed, etc.;

■ possible variants of noise characteristics should be reflected in the technical documentation of the equipment.

AS A CONCLUSION

We have considered only a part of the issues related to acoustic calculations. Separate consideration is required for the placement of loudspeakers, determining the reverberation time of the room, and calculating intelligibility. Here are some recommendations for improving overall speech intelligibility.

1. Natural noise has the greatest impact on speech intelligibility.

2. Significant influence on speech intelligibility is exerted by reverberation interference, the reduction of which is achieved by additional (special) measures.

3. Good intelligibility in reverberant rooms with a limited sound path can be achieved with a difference between the sound pressure in the RT and the noise level of at least 6 dB.

4. Intelligibility is significantly affected by the quality of the speakers you choose. With the uneven frequency response of the loudspeaker approaching 10%, intelligibility deteriorates by 7%.

5. A significant increase in speech intelligibility can be achieved by increasing the proportion of direct sound in the total sound energy inside the room, due to:

■ increasing the localization of sound sources;

■ competent placement of sound sources (loudspeakers), taking into account their directivity and location, in which the PT point is not very far from the source and is not in the shadow.

LITERATURE

1. Federal Law No. 123, set of rules SP 3.13130.2009. Fire safety requirements for sound and voice warning and evacuation management.

2. Federal Law No. 123, set of rules SP 133.13330.2012. (Appendix A. Simplified calculation of the number of loudspeakers in public address systems).

3. Kochnov O. V. Electroacoustic calculation performed in the design of SOUE// Proceedings of the XV scientific and practical conference "Integration of science and practice as a mechanism for the development of modern society." April 8-9, 2015.

4. SP 51.13330.2011. Noise protection. Updated edition of SNiP 23-03-2003. M., 2011.

5. SNiP 23-03-2003. Noise protection (Sound protection) dated 01-01-2004.

6. Kochnov O. V. Calculation of speech intelligibility // Proceedings of the XVIII scientific and practical conference "Integration of science and practice as a mechanism for the development of modern society." December 28-29, 2015.

The lack of generally accepted methods for calculating sound pressure when designing warning systems often leads to design errors (insufficient sound pressure level), because the number and installation locations of annunciators are determined by the designer "by eye". Accordingly, in case of an insufficient level of the sound signal, it is necessary to redo the already mounted system.

We tried to simplify the task for designers and installers - we developed software for calculating the required number of sounders in a room, which is available for download. The program automatically calculates the minimum required number of sirens and their installation locations for wall and ceiling mounting options.

In addition to the lack of methods, the complexity in the calculations is the lack of technical parameters - the amplitude-frequency characteristic and the radiation pattern for the vast majority of sound and speech annunciators. Therefore, this software is intended only for sound detectors, since for most of them the sound pressure level at a deviation from the annunciator axis of 90° is known and amounts to -5 ÷ -10 dB (can be changed in the program).

Method of calculation

Knowing the sound pressure of the sound source in a given direction Р 0 , it is possible to determine the sound pressure in this direction at the calculated point Р 1 located at a distance L>1 m from this source using the formula:

The audio signals of the SOUE should provide a sound level of at least 15 dB above the permissible sound level of constant noise (N) in the protected room. Sound level measurement should be carried out at a distance of 1.5 m from the floor level.

where P 0 and P 90 are the sound pressure of the annunciator at a distance of 1 m at 0 ° and 90 °, respectively.
In accordance with (1) and (2) we obtain the inequality:

Consider the equivalent inequality

The function on the left side of inequality (6) on the interval φ° of interest to us)