ЗАХИСТ ВІД ШУМУ І ВІБРАЦІЙ

Acceptable room dimensions according to EBU/ITU, 1998 recommendations
 

This calculator helps to work out an acceptable proportion between studio line sizes, control rooms and music-rooms from point of view of reducing the impact of low-frequency resonances.

It’s based on a methodology, created by Robert Walker in 1993, after a series of researches, held in Research Department Engineering Division of ВВС. As a result, a formula has been introduced to regulate the balance of room’s line sizes in quite wide limitations.

In 1998 this formula was accepted as a standard by European Broadcasting Union (European Broadcasting Union, Technical Recommendation R22-1998) and International Telecommunication Union (International Telecommunication Union Recommendation ITU-R BS.1116-1, 1998), also, it was recommended for use while building studios and music-rooms. The proportion is the following:

Acceptable room dimensions calculator

Schroeder acoustic diffuser

   Schroeder diffusers, which construction is based on numbers theory, are an excellent tool for receiving diffuse sound field in different purpose rooms. Actually, Schroeder diffuser is a diffraction grid, which diffuses sound energy in wide range of frequencies, which falls to it, even at big size of falling angle.

   Schroeder diffuser consists of series of cells with different depth but equal width, made in a timber, MDF or other plate framing. Typical diffuser construction cut (p=7) is shown in the picture on the left.

 

   Diffuser’s construction is based on mathematical sequence of quadratic deductions from the numbers theory, which is evaluated as follows:

 

s_n = n² *mod(p), where

 

s_n – sequence of meanings of diffuser cells apparent depth,

n – nonnegative number {0, 1, 2, 3 ...}, determining the number of corresponding cell,

p – prime number {2, 3, 5, 7, 11, 13, 17...}. (Prime number is the one which is different from 0 and 1 and is divisible by 1 or itself)

    

  

   The cell’s actual depth dn in the diffuser’s construction depends on its project frequency meaning for:

d_n = s_n * с /(f_o * 2 * p), where

d_n –the depth of cell n,

f_o – diffuser’s project frequency,

с – speed of sound in the air,

p –prime number (diffuser order), corresponding to the quantity of cells.

 

   Schroeder diffuser has the highest effectiveness of diffusing sound energy at the project frequency. Working frequency diapason depends on line sizes of the diffuser cells. The bottom of diffuser’s working diapason (flow) depends on the deepest cell size. The high bound of working diapason (fhigh) depends on cell width meaning.

The diagram of sound energy dispersion at Schroeder one-dimensional diffuser is semi-cylinder.

  

Schroeder diffuser calculator

Room dimensions in compliance with international standards 
 

   The influence of main resonances in a small-size room often leads to increase of reverberation time and frequency characteristics irregularities, which in its turn often leads to sound coloration. Problems may occur at low frequencies due to comparatively low mode density.

Studio and music-room designers try to solve the problem by using rooms of relevant sizes, and also by situating listeners and loudspeakers in definite places. There have been introduced a lot of approaches to find optimal proportion in room sizes during recent decades. Mostly, these methods are aiming to avoid the cases where repeated modes are situated in narrow band.

The major assumption states that if there’s music playing in a room, lack or boost of definite tone elements will reduce the sounding quality and affect tone structure. Usually, the starting point for these methods is defining modes in an enclosed rectangular room with solid walls.

Richard Bolt (Richard H. Bolt, 1946) introduced a design chart, which allows defining preferred proportion of the room walls. Bolt was studying sound behavior in a camera, where enclosures in size were comparable with wave length. He introduced such group of proportions between height to length, and length to width, where modal frequencies were distributed sufficiently.

Louden (M. M. Louden, 1971) calculated modes distribution for lots of proportions of room sizes and published list of preferable sizes, based on one control chart. Due to this method the well-known proportion 1:1,4:1,9 was received. Louden made researches over 125 combinations of room sizes balance with step 1,0.

Robert Walker (Robert Walker, 1996) developed the criteria of room quality, based on calculating rms distance between mode frequencies. This method allows receiving range of practical and nearly optimal room sizes. In 1998 Walker’s formula was taken as a standard by European Broadcasting Union (EBU) and International Telecommunication Union (ITU).

Trevor Cox recommendations (Trevor Cox, 2004) are based on working with a room with the most even mode frequency characteristics. Computer algorithm is used for multiple seeking for the best room sizes. Similar seeking is used while defining the best placement for sound source and sound detector.

All the given methods, this way or another, have their own limitations. However, applying them in practice helps to identify the diapason of acceptable room proportions, avoid the worst cases and minimize the influence of room modes on tone balance and tone quality.

 

Room dimensions in compliance with international standards calculator

 

Axial room modes

Each room has its own acoustic resonances or, as they are also called, room modes. Room proportions, e.g. length, width and height proportions set the position of room modes in frequency spectrum, and also the density of their distribution. Sizes as they are define the frequencies, where resonances take place, i.e. whether important frequencies will be enhanced or suppressed. When a perfectly rectangular room has perfectly smooth reflecting surfaces (walls, ceiling and floor), these resonances can be easily calculated according to the following well-known formula:

where n_x, n_y and n_z – are whole numbers, and L_x, L_y and L_z – are relatively length, width and height of the room.

 

Для вычисления всех мод необходимо перебрать все возможные комбинации из трех целых чисел Nx, Ny, Nz. На практике же достаточно вычислить только низкочастотные моды, т.е. ограничиться максимальным N=4.

It’s necessary to try all the possible combinations of three whole numbers Nx, Ny, Nz. in order to calculate all the modes. In practice, it’s enough to calculate only low-frequency modes, i.e. to confine to the maximal N=4.

f (1,0,0) = c/2/L

these modes are called axle or axial and, as a rule, are the most intense.

Tangential modes emerge when sound wave is repeatedly reflected by the four surfaces, where pairs are parallel to each other. These modes can be calculated by combining two whole numbers and zero. For instance, array (1,1,0) allows to calculate a first-order mode in x-y (length-width) dimension. Such stationary modes emerge between the four walls of the room and are situated in parallel with the ceiling and the floor.

Oblique modes emerge between all the six walls of the room. As mode energy accumulation takes place during each sound circle (a wave here locks itself after six re-reflections, losing part of its energy each time) oblique modes affect the sound less than any other stationary wave. It’s possible to calculate frequencies enhanced by these modes if you combine the set of three (1, 1, 1 – oblique mode of first order).

 

Axial modes are, as a rule, the most intense and you can ignore the influence of tangential and oblique modes while giving rough estimates for room resonances distribution.

 

Axial room modes calculator

Simplified analysis of axial room modes

Colorations largely determine the quality of sound for a small studio or listening room. The big task then is to determine which, if any, of the hundreds of modal frequencies in a room are likely to create colorations.

How close together must adjacent modal frequencies be to avoid problems of coloration? Christopher Gilford's studies (Gilford, C.L.S., The Acoustic Design of Talks Studios and Listening Rooms) showed that an axial mode separated more than 20 Hz from the next axial mode will tend to be isolated acoustically. It will tend not to be excited through coupling
due to overlapping skirts but will tend to act independently. In this isolated state it can respond to a component of the signal near its own frequency and give this component its proportional resonant boost.

Zero spacings between modal frequencies are also a source of coloration. Zero spacing means that two modal frequencies are coincident (so called "degenerate" modes), and such degeneracies tend to overemphasize signal components at that frequency.

Presence of the isolated modes is the cause of dips in the amplitude-frequency response curve, whereas zero spacings between modal frequencies lead to peaks in the curve. High irregularity of amplitude-frequency response below 300 Hz causes unwanted acoustical defects, such as "boxy" or "boomy" sound.

This acoustic calculator allows to calculate the near field length and determine the characteristic bands within the sound range bounded by F1-F5 frequencies.

F1-F2
Sound pressure region. No resonant support for sound in the room.

F2-F3
Room resonances region. Wave acoustics principles apply. The region is bounded above by Schroeder's frequency.

F3-F4
Transition region. Wavelengths are too long for ray acoustics and too short for wave
acoustics. Diffraction and diffusion of sound waves.

F4-F5
Reflection of sound waves region. Geometric acoustics principles apply.

This calculator is only applicable for evaluation of problematic modal frequencies in rooms of simple rectangular shape with little absorption. 

Simplified analysis of axial room modes calculator

Reverberation time calculation

Reverberation time (T, s), a concept introduced by W.C. Sabine at the end of 19th century, remains one of the most important acoustic properties of the room. Standard reverberation time is defined as that time required for the sound-pressure level in a room to decay 60 dB after a source stops generating sound. It characterizes degree of boominess of the room.
 
In general, shortening of reverberation time leads to better clarity and speech articulation, i.e. increases the degree of acoustic comfort. Shortening of reverberation time is achieved by using sound absorbing materials on the walls, floor, and ceiling.
 
This acoustic calculator designed to estimate reverberation time of the room depending on its purpose, and to preselect required quantity of sound absorbing materials. Besides using internal database of sound absorbing materials, the program allows to enter sound absorption coefficients of any arbitrary materials taken from reference books.
Sound absorption coefficients table
 
Calculations with Reverberation time calculator are based on online input. Results are displayed on a diagram. Calculation is performed in accordance with Eyring's formula:
 

Т (sec) = 0,163*V / (−ln(1−α)*S + 4*µ*V)

V – volume of the room, m3
S – total surface area of the room, m2
α - average absorption coefficient of room surfaces
µ - a coefficient which takes account of attenuation of sound in air
 

Calculated value of reverberation time is graphically compared to recommended (optimum) values are in compliance with international standards:
 
DIN 18041 Acoustic quality in rooms – Specifications and instructions for the room acoustic design, 2016
EBU Tech. 3276 – Listening conditions for sound programme, 2004
IEC 60268-13 (2nd edition) Sound system equipment - Part 13, 1998

Reverberation time calculator

 

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