Basics    Absorption and diffusion    Reflection    Diffraction    Critical Distance    Sound Pressure Level

The perfectly diffuse sound field and the room modes

The theoretical goal of an acoustician is the perfectly diffuse sound field. Disturbing, for example, flutter echoes or discrete reflections. By diffuse scattering of the sound such phenomena can be prevented. But above all with long wavelengths in small rooms, the wave nature of the sound has great importance and the goal of perfect diffusibility remains unattainable. Small means that the room dimensions are in the range of the wavelength of the sound to be reproduced in the room. The oscillating air volume in a room also has natural frequencies as we already know from the single-shell components. These so-called room modes are often the most difficult problem to solve.

At 20 ° C room temperature, the speed of sound c is 343m / s. The useful sound usually corresponds to the entire hearing range and thus one obtains wavelengths λ in the range between 20m and 2cm. In small rooms, almost everything is in this area - furniture, objects and even the walls themselves and their projections.

Room modes are therefore at the frequencies at which the air volume in the rooms can be particularly easily excited to vibrate. Hermann von Helmholtz (1821-1894) used these properties of oscillating air volumes to amplify certain frequencies with the aid of hollow spheres (Helmholtz resonator). He put his ear to an opening in the ball, the sound penetrated into another opening and excited the volume of air in the vessel, especially at the frequency of the eigenmode to vibrate.

In rooms where you want to achieve the most uniform possible acoustics at all useful frequencies, this behavior of air volume is of course extremely disturbing. It requires that one and the same sound at different places in the room can have very different levels. In one and the same place (in terms of frequency) different tones, which are actually played equally loud, reach different volumes. You can not prevent this property of volume, but there are some ways to minimize the disturbing effects. The number of fashions of a cuboid space is fixed so to speak. If several modes are close together, this means that frequency ranges are created elsewhere where the density of the fashion is lower. If one has the opportunity to freely determine the dimensions of his space, one should try to choose the ratio of length, width and height so that the modes are distributed as evenly as possible.

Here I have combined these approaches in a computer that displays the mode distribution for arbitrary dimensions of rectangular spaces.


When vibration sound disturbs particles in the air or the other medium, then those particles displace other surrounding particles. This particle movement goes on continuously in the outward direction to form a wave pattern. The wave carries the sound energy through the medium and becomes less intense as it moves away from the source. The sound energy is also directly associated with the volume of the sound. Higher sound energy results in loud volume.
There are three aspects of a sound wave that cause different types of sounds to be produced: frequency, wavelength and amplitude. Sound waves vibrate at different rates or frequencies as they move through the medium. The wave may have a single frequency or many frequencies depending upon the vibration source.
Let us consider a sound wave of constant frequency generated by a source with displacement function on Y-axis and time function on X-axis (Fig. 1). The number of waves generated per second is the frequency of the sound and expressed in hertz (Hz). The maximum displacement of a peak is termed as amplitude while the distance from one peak to the other is the wavelength. The sinusoidal wave gen- erates only single frequency. A variety of non-repetitive sounds produce waves of different frequencies.

Fig. 1

Absorption and diffusion

Music is often performed in reverberant spaces; spaces were the sound bounces around many times before slowly dying away. Whether auditoriums, concert halls or stadiums, these spaces are intentionally designed to have lots of reflective surfaces. The best concert hall can have surprisingly little absorptive material. But your living room needs more. Its dimensions are smaller and so reverberation does not add the great sonic character of Boston Symphony Hall, it just adds sonic muddle. Besides, the recording that you paid good money for already has the sonic footprint of that large carefully designed performance space. Your living room does not need to add its footprint on top of that. In truth, your living room needs to absorb as much sound as possible. It needs to be acoustically dead.

A good room generally has a "quietness" to it. Your can carry on a soft conversation and fully understand the person you are talking to. Street noise may make it in to the room but it is well damped and unobtrusive. This quality of quietness comes from having a good percentage of all surfaces covered with acoustically absorptive materials. These can be heavy drapes, thick carpets, stuffed pieces of furniture, etc. Openings to the rest of the house absorb sound too, because they let it escape down the hall where it is more likely to be absorbed than reflected back to you.

Different than absorption, but equally desirable, is the scattering of sound. A large flat surface bounces sound waves back as an undisturbed front. These large reflections may be heard as an echo, at the very least they up the sonic harshness, degrade stereo clarity and upset the balance of sound. Anything that breaks up the surface will take that sonic wave and scatter it in multiple directions. Not only does that reduce the severity of reflections, it tends to promote energy loss by giving the sound a longer path (hence more chances to hit an absorptive area) before it gets back to your ears, all good stuff.

So the two main components determining room acoustics are absorption and diffusion.

Make a mental tally of what percentage of the rooms surfaces are hard and flat, what percentage have scattering surface irregularities.
  • Front wall has drapes by windows (good)
  • Drapes are open revealing a lot of glass (bad)
  • Nothing but sheetrock on that ceiling (bad)
  • Thick carpet on the floor, with under padding (very good)
  • Large sofa in front of side wall (good)

By now you should be starting to get a sense of what good and bad sounding rooms consist of. If you want a great example of a bad sounding room, pick up any architectural magazine. See that designer-look room with hardwood floors and nary a throw rug, minimalist furniture, expansive glass walls (nice view) and clean uncluttered walls? Bad acoustics, I guarantee it.

So what can we do with our room to improve its acoustics, short of bringing in the wrecking crew and starting over?

Add absorption. As a rule of thumb, try to cover 1/3rd of all surfaces with something soft. Purpose built audio absorbers are available but are frequently ugly and not the only solution. A large empty wall can have a rug hung on it. I knew a person that collected oriental rugs. They did not want to walk on the silk rugs in their collection so they hung a few on the walls. (Hint: hide a layer of carpet backing behind it to further increase its absorptive properties.) At least put a large area rug over the center of that hardwood floor. Put a thick pad underneath it. Drapes for the windows add a lot of absorption, especially if they are heavy or thickly lined.

Add diffusion. Again, commercial solutions are available but there are many domestic solutions. One of the best diffusers of sound is a bookcase half full of books. Some three dimensional art objects can diffuse sound. Decorative room dividers (the zigzag kind) can absorb or diffuse sound. Anything that breaks up that big expanse of hard plaster or drywall will help diffuse sound.

The drawing below shows the path of the primary bounces of sound in a typical rectangular room. Although placing these absorptive and diffusive sound objects anywhere in the room will have some effect, you can maximize the effect by placing them directly in the path of these primary sonic paths. This guarantees that strong hard reflections are scattered or absorbed. These early reflections are especially dangerous to the clarity of sound and to the stereo effect. Absorbing or scattering them will up the clarity of movies or music.

Here you will find some calculators, related to acoustical calculations,

  • Standing Waves,
  • Cancellation Frequencies,
  • Reverberation Time,
  • Room Modes,
  • Room Dimensions,
  • Bass Trap,
  • Panel Absorber,
  • Slot Absorber,
  • Skyline Diffusor and Quadratic Residue Diffusor
Sound waves are principally longitudinal waves. It means the wave medium, for instance, air, oscillates parallel to the wave’s direction. Let us consider a soft coil is stretched and fixed at one end. If the coil is quickly pushed and pulled from the other end, it will compress and elongate along with the force direction. The same thing happens in longitudinal sound wave. Air particles get oscillated back and forth in the direction parallel to the sound wave movement. This create compression and rar- efaction waves alternately. Longitudinal waves begin with compression followed by rarefaction. The wavelength can be determined by measuring the distance between two consecutive compressions, or rarefactions.

The sound wave interact with the material or object surface and may be absorbed, transmitted, reflected, refracted or diffracted form the surface depending on type of the surface. These phenomenons are described in Fig. 3. When all the emitted sound waves are absorbed by the receiver, sound absorption occurs. It is exactly like sponge absorbing water. Sound absorption is an important phenomenon as far as sound insulation is concerned. There are different materials available for sound absorption. The sound absorbers may be porous or resonant type. Porous absorbents are classified as fibrous materials and open-celled foams. Fibrous materials convert acoustic energy into heat energy when sound waves impinge the absorber. In case of foam, sound wave displacement occurs through a narrow passage of foam and causes heat loss. Resonance absorbents are of mechanical type, where there is a solid plate with a tight air space behind. It is noteworthy that some material such as foam absorbs sound waves whereas the glass blocks it. The selection of material to be used depends on the end use application. For example, the office room in a building can be designed as sound absorbing or sound proofing.

Fig. 2

Sound absorption measures the amount of energy absorbed by the material and expressed as sound absorption coefficient (α). The coefficient ranges between 0 and 1 where 0 is no absorption and 1 is highest or total absorption. The higher coef- ficient yields lower reverberation time. The reverberation time is persistence of sound in a space after a sound source has been stopped. It is the time lag, in seconds, for the sound to decay by 60 dB after a sound source has been stopped. Sound absorption is important to make the acoustic environment suitable for a specific purpose; for instance, in recording studios, lecture halls, concert rooms, lecture theatres, etc. The low frequency sound of 500 Hz is relatively difficult to absorb than high frequency sound.


When sound waves impinge on hard or smooth surface they may reflect back with their full energy without altering their characteristics. The reflection angle of sound wave from the reflecting surface is equal to the angle of incidence. The angles are defined between a normal to the reflecting plane and the incident and reflected waves. The reflected sound waves, thus, follow Huygen’s geometry where both the incidence and reflection angles are equal.
The reflection phenomenon of sound waves finds many applications. For example, a reflected sound wave is used to measure the depth of water from sea level with the help of echo produced from the reflective surface. The geological composition at the bottom of the ocean and inside the earth crust is also identified using the reflection of sound wave. Echo is a simple example of sound reflection phenomenon. Echo can be heard when the sound wave, perpendicular to the sound source, hits a flat and smooth surface.

For more read the article listening room reflections and the ETC.


Diffraction involves a change in the direction of sound waves as it strikes through a surface. Sound waves when impact on a partial barrier, some of them get reflected, some propagate without any disturbance and some bent or diffract over the top of the barrier. As sound source moves closer to the barrier, less sound diffraction is obtained. The sound at lower frequencies tends to diffract more easily than sound at higher frequencies

Critical Distance

Critical Distance is where the direct and reverberant sound energies are equal. Critical Distance is different at all frequencies. The more reverberant a room, the closer is Critical Distance. The more absorbent a room, the further is Critical Distance. (Critical Distance is different at all frequencies).

For good acoustic design the Critical Distance should be as far as possible from the sound source, and the resultant reverberation minimal and even at all frequencies. Direct sound from the speaker system diminishes in level, as a function of the distance (inverse square law) whereas reverberation constantly spreads throughout the room. Because there is new incoming sound from the speakers, reverberation keeps building up, until the new incoming sound, equals the sound absorbed (steady-state).

When the reverberant sound becomes 12db or greater than the direct sound all intelligibility is lost. The simplest way to find 'Critical Distance' is to play compressed pop music through the sound system.
Begin with one speaker (left or right). Walk back and forth around the room, and you will be surprised how easy it is to identify the critical distance. Repeat the exercise with the other speaker, then both speakers.
Its surprising how accurate our ears are, when compared with acoustic measurement microphones.

  • The more reverberant the room is the closer the Critical Distance.
  • The more absorbent the room is the further the Critical Distance.
  • Near field or Direct field is inside the Critical Distance.
  • Far field or Reverberant field is outside the Critical Distance.

Sound Pressure Level

Sound pressure level is a measure of volume (loudness) of the sound in terms of the sound pressure. The level can be determined by measuring the sound pressure disturbance from the equilibrium pressure value. The pressure disturbance is the difference between the instantaneous pressure and the static pressure. The mean pressure deviation from the equilibrium is always zero, since the mean compression waves are equal to mean rarefaction waves. These positive and neg- ative effects are converted into positive using the root mean square (RMS) value of sound pressure (Prms) over a period of time. However, RMS value of sound pres- sure is not convenient to use as it varies over a wide range of magnitudes. The decibel (dB) is the easiest and a more convenient way to measure the volume (loudness) of the sound in terms of the sound pressure.
  • dB = Sound pressure level
  • rms = Root mean square value
  • po = Reference pressure
Decibel is a value on a logarithmic scale and it is based on the capacity of humans to sense sound pressure. Sound perception by humans is subjective in nature. Different exposure times of the same sound pressure may have different effects on hearing. In general, it is recommended that sound pressure levels should not exceed 30 and 40 dB in resting room and kitchen. The sound pressure level beyond 90 dB may be harmful for human hearing, especially when the exposure time is high.

On the Calculator page you wil find 19 useful Calculator Modules...

About Standing Waves one of the Listening Room Problems...

How to Create a Killer Sweet Spot in Your Room

Early Reflections 101