Studio Acoustics part 1/3

In this Multi Parts Post, I will try to help you build the acoustic of your room. I will start with some theory of acoustic and then I will take an example and build the acoustic from zero to an empty room. I will also share the excel calculation sheet that I use so you don t have to spend hours doing mathematical equations and formulas, I use excel to keep it simple for everyone.


Acoustics is the field of science that deals with the generation, propagation, and reception of waves in elastic environments, whether they are gaseous, liquid, or solid. The most peculiar aspects are those associated with auditory sensation and therefore concern sound waves, the sounds that can be perceived by the human hearing system.Many types of waves can propagate in solids: Longitudinal waves, shear (transverse) waves, flexural waves, torsional waves, etc.

In ideal fluids (absence of viscosity) only longitudinal sound waves can propagate (the vibratory oscillation of the particles occurs in the same direction of wave propagation) as they do not have elastic resistance to shear deformation.

Free-field propagation

A “free field” is defined as the sound, generated by a source, which propagates in an unlimited, homogeneous, and isotropic medium without discontinuity or obstacles. 

Two situations can be determined in which the free-field conditions can be approximated more or less well and within certain limits:

• An open space;

An outdoor space without reflection from the ground, in stable and homogeneous atmospheric conditions, where there are no surfaces or obstacles in a sufficiently large area around the source.

• The anechoic chamber.

It is a large room in which all surfaces completely absorb the sound that affects them; the sound present inside the chamber is only that produced by the source, with no sound reflected from the surfaces. In these rooms you can even hear your blood through your veins, people can’t stay too long inside, can drive you crazy.

You can also compare how sound travels in a free field with the trail of a ship in the sea, at the start, there are a lot of waves a lot of activity more detailed waves, and then slowly they disappear if there is nothing to disturb them.

The free acoustic field can be divided into two regions:

– the near field: the sound intensity can have a complicated trend, depending on the type of source and its dimensions, which does not necessarily follow a monotonous trend as a function of distance, and also the directional characteristics of the source must be interpreted with great caution

– the far field: from the near field in theory to infinity; the sound intensity, on the other hand, assumes a linear trend and is reduced with the inverse of the square of the distance from the source; the intensity level is attenuated by 6 dB with every doubling of the distance. Furthermore, the directivity of the source can also be uniquely defined.

Sound sources and directivity

Sound sources

Real sound sources are generally very complex and difficult to describe analytically in detail. in most practical cases, it is possible to resort to substantial simplifications;

Acoustic MONOPOLE: the most drastic simplification consists in treating as infinitely small (point-like) a real source whose dimensions are much smaller than the wavelength of the sounds it produces;

Other more complex ideal sources, such as the dipole, higher-order multipoles, linear sources can still better account for the properties of a real source, or at least highlight the most salient emission characteristics.


The simplest possible source is the point source, which can be represented as a pulsating sphere whose radius tends to zero;


In far-field conditions, the average sound intensity of the dipole is:

  • depends on the square of the distance, as in the case of the monopole;
  • varies much more rapidly with frequency;
  • the low-frequency emission of a dipole is much less efficient;
  • the acoustic field produced by the dipole is strongly directional: the greatest intensity is found along the axis of the dipole, while it is zero along the direction normal to the axis passing through its center

A source that emits in a certain direction with double intensity, compared to the ideal omnidirectional source, has a directivity factor 2 and a directivity index of 3 dB in that direction. Directivity factor and directivity index of a real source almost always vary according to the frequency of the emitted sound;

For example, a loudspeaker can be considered almost omnidirectional at sufficiently low-frequency values and become strongly directional at higher frequency values.

Indoor propagation

Wave propagation interacts with all objects and people present and with the boundaries of the environment; phenomena of absorption, reflection, transmission, refraction, diffraction and interference of waves occur; The acoustic field emitted by any source is altered by the surrounding environment; In mathematical terms it means imposing boundary conditions (geometries, absorptions, etc.) to the propagation equation; Only in simple cases there are exact solutions, while in complex cases we resort to experimental measurements and computer processing.

Dimensions of the rooms

Acoustically, an environment is defined as “large” if its size is much larger than the wavelength under examination and “small” if its size is comparable to the wavelength under examination.

For example in the air a 20 Hz have a wavelength ~ 17 m, while a 20 kHz have a wavelength ~ 1.7 cm: the environment is “seen” differently by the high and low frequencies.

There is a limit frequency, called the Schroeder frequency: this separates:

  • low frequencies f <f lim  modal behavior (“small rooms”)
  • high frequenciesf> f lim  statistical behavior (“large rooms”)

    Standing waves

Occur in closed or partially enclosed environments, where the direct field interferes with the reflected field. The particular phenomenon that occurs is the fact that the extreme points of this interference are stationary, ie fixed in space.

  • The stationary points of maximum constructive interference are called antinodes; in them, the pressure reaches the maximum oscillation value.
  • The stationary points of maximum destructive interference are called nodes; in them, the pressure reaches the minimum oscillation value.

Standing waves are established in the room at precise frequencies, called resonant frequencies or natural frequencies.

Three-dimensional standing waves:

Modal indices and types of modes

Depending on the values of the three modal indices (nx, ny, nz) it is possible to define three types of modes:

  • axial modes: they have only one index other than zero;
  • tangential modes: they have two indices other than zero;
  • oblique modes: all three have non-zero indices.

Axial modes

Depending on the room size you can find where the frequencies of these modes are in your room.  To avoid having a lot of modes is better to use these optimal ratios between length width and high of the room.

Bolt Optimal Ratios (1946): he studied the problem assuming that there would be a better frequency response, having a lower ROS, by requiring the modes to be equally spaced in frequency. He obtained as ratios between the dimensions of the sides 2: 3: 5 and 1: 21/3: 4 1/3 (ie 1: / 1.26: / 1.59).

The room has to meet BONELLO Criteria, you can check HERE by entering the room dimensions

For example, in my studio calculation sheet, the axial modes are the ones with red color in a room with the dimensions in the orange line on top. You can also see the axis where the modes are in the link HERE or in my calculation sheet (nx W; ny L; nz H)

They have the highest average energy, 4 times greater than the tangential modes; these are the most “dangerous” modes in a room, that after the sound hits a parallel wall returning will meet the sound in an inverted phase and can create a boost or a null in a room so you might NOT hear a frequency in your listening point, or you can hear that frequency way higher. This can affect your mixdowns and how you hear the sound in your room.

The Schroeder frequency roughly divides the frequency response of the sound pressure level into three zones:
  • Modal zone: it has a deterministic behavior in which the modes are few and distinguishable 
  • Diffusion zone: the statistical behavior of the modes that makes the field diffuse begins
  • Absorption zone: the modes are many and completely indistinguishable, the phenomenology is determined by the absorption of the environment.

Trev = Reverberation time of UNTREATED room at 1000Hz (have to measure the room with microphone) we will do that in part 2
V = Total Volume of the room

Why is this helpful? 

Because after we calculate the Schroeder frequency we can see the frequencies of these modes so we can build RESONATORS for this area to fix the problem and also to know from what frequency upwards we need to build the diffuser of the room and lastly to control the reverberation of the room with absorption materials.

See you in the next part where I will start to build the acoustic project for an empty room. I hope this was helpful SUBSCRIBE to receive notification when the post will be up in the next few days and also get discount codes for the music store and many more to come.

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