Basic Room Acoustics

Sound Waves

Sound waves are essentially pressure variations traveling through the air.

When the sound wave travels, it compresses air molecules together at one point. This is known as the high pressure zone.

After the compression, an expansion of molecules occurs. This is known as the low pressure zone.

This process continues along the path of the sound wave until the energy becomes too weak to hear.

Frequency and Wavelength

The frequency of a sound wave indicates the rate of pressure variation or cycles. One full cycle is a change from high pressure to low pressure and back to high pressure.

The number of these cycles completed in one second is called the Hertz (Hz). A tone of 1000Hz frequency has 1,000 cycles per second.

The wavelength of a sound is the physical distance from the start of one cycle to the start of the next cycle. Wavelength is related to frequency by the speed of sound.

Sound velocity in air depends on atmospheric pressure and temperature, with the latter being the more significant factor.

The velocity at 0°C is 332 metres per second, rising by 0.6 metres per second for each °C increase in temperature.

Loudness

The fluctuation of air pressure created by sound waves is a change above and below normal atmospheric pressure.

This is what the human ear responds to.

The varying amount of air molecule pressure compressing and expanding is related to the apparent loudness arriving at the ear.

The greater the pressure change, the louder the sound. The ear is capable of detecting a pressure change as small as 0.0002 microbar. One microbar is equal to one millionth of atmospheric pressure.

The threshold of pain is around 200 microbars. This wide amplitude range of sound is often referred to in decibels.

Sound Pressure Level (dB SPL), relative to 0.0002 microbar (0dB SPL). 0dB SPL is the threshold of hearing and 120dB SPL is the threshold of pain.

1dB is about the smallest change in SPL that can be heard.

A 3dB change is generally noticeable and a 6dB change is very noticeable. A 10dB SPL increase is perceived to be twice as loud.

Reflections

A sound wave can be reflected by a surface or object if that surface is physically as large, or larger, than the wavelength of the sound wave.

Because low-frequency sounds have long wavelengths they can only be reflected by large surfaces or objects.

Reflection is the source of echo, reverb, standing waves and diffusion.

Echo

This occurs when an indirect sound is delayed long enough (by a distant reflective surface) to be heard by the listener as a distinct repetition of the direct sound.

Reverberation

This consists of many reflections of a sound, maintaining the overall sound in a room for a time even after the direct sound has stopped.

Standing Waves

These occur in a room at certain frequencies related to the distance between parallel walls.

The original sound and the reflected sound will begin to reinforce each other when the wavelength is equal to the distance between the two walls.

Typically, this happens at low frequencies due to their longer wavelengths and the difficulty in absorbing them.

Refraction

This is the bending of a sound wave as it passes through some change in the density of the transmission medium.

This change may be due to physical objects or it may be due to atmospheric effects such as wind or temperature gradients.

Diffraction

A sound wave will bend around obstacles in its path which are smaller than its wavelength.

Because a low frequency wave is much longer than a high frequency wave the low frequencies will bend around objects that the high frequencies cannot.

Passive Absorption

When sound passes through an acoustically absorptive material like mineral wool insulation or acoustic foam, the sound waves are forced to change directions many times and travel great distances before the sound passes completely through the absorptive material. 

Each time the sound waves change direction a percentage of the energy is absorbed by conversion to heat. 

When there is a reflective surface behind the absorber (such as a wall) the sound which passes through the absorber will be reflected back and through the absorber once again.

Absorbers work best when there is some sort of a reflective surface behind them.

Absorbers behave differently as they are moved away from the wall surface. In recording studio situations it is ideal to have an air gap behind the absorber to increase the mid and low frequency absorption. 

Long wavelength, low frequency sound waves are much more difficult to attenuate with porous absorptive materials.

This is because the thickness of the absorptive material must be at least 1/4 of the wavelength of the lowest frequency to be absorbed.

This is because at 1/4 wavelength from a reflective surface the sound pressure is zero but the acoustic particle velocity is at maximum.

For 200Hz the wavelength is 1.7 metres so a theoretical thickness of 425mm is required to absorb or attenuate this.

Adding plenty of cheap 25mm thick acoustic foam in a small studio space is not that great an idea. The reason is explained above, in that, it will only provide effective absorption down to around 3kHz.

The high frequencies are easily absorbed but with limited mid-range absorption the room may well end up sounding a bit boomy and muddy.

Absorption Coefficient

The Absorption Coefficient of a material can be expressed as a value between 0 and 1 where 0 represents no absorption (perfect reflection) and 1 represents total absorption. It can also be represented as a percentage.

Direct vs Ambient

Direct sound becomes weaker as it travels away from the sound source at a rate controlled by the inverse square law. 

When the distance from a sound source doubles, the sound level decreases by 6dB.

The ambient sound in a room is at nearly the same level throughout the room. This is because the ambient sound has been reflected many times within the room until it is essentially non-directional. Reverberation is an example of non-directional sound.

The ambient sound in a room becomes increasingly apparent as a microphone is placed further away from the direct sound source.

The amount of direct sound relative to ambient sound can be controlled by the distance of the microphone from the sound source and to a lesser degree by the polar pattern of the microphone.

If the microphone is placed beyond a certain distance from the sound source the ambient sound will begin to dominate the recording and the desired balance may not be possible to achieve.

This is known as the critical distance and becomes shorter as the ambient noise and reverberation increases forcing a closer placement of the microphone to the source.

Phase Relationships

The phase of a single frequency sound wave is always described relative to the starting point of the wave or 0°. The pressure change is zero at this point.

The peak of the high pressure zone is at 90°, and the pressure change falls to zero again at 180°. The peak of the low pressure zone is at 270° and the pressure change rises to zero at 360° for the start of the next cycle.

Two identical sound waves starting at the same point in time are called in-phase and will sum together creating a single wave with double the amplitude but otherwise identical to the original sound wave.

Two identical sound waves with one starting point concurring at the 180° point of the other wave are said to be out of phase and the two waves will cancel each other out completely.

When two sound waves of the same single frequency but different starting points are combined the resulting wave is said to have phase shift.

This new wave will have the same frequency as the original waves but will have increased or decreased amplitude depending on the degree of phase shift.

Most sound waves are not a single frequency but are made up of many frequencies. When identical multiple-frequency sound waves combine there are three possibilities for the resulting wave:

• doubling of the amplitude at all frequencies if the waves are in-phase.
• complete cancellation at all frequencies if the waves are 180° out-of-phase.
• partial reinforcement or partial cancellation at various frequencies if the waves have an intermediate phase relationship.

The latter case is the most likely and the audible result is a seriously degraded frequency response called comb filtering.

The pattern of peaks and dips resembles the teeth of a comb and the depth and location of these notches depends on the degree of phase shift.

With microphones this effect can occur in two ways. The first is when two (or more) microphones pick up the same sound source at different distances.

Because of the increased time delay of the sound arriving at the more distant microphone there will be a phase difference between the signals from the microphones when they are combined at the mixer.

The second way for this effect to occur is when a single microphone picks up a direct sound and also a delayed version of the same sound. The delay may be due to a reflection of the original sound or to multiple sources of the original sound.

When this effect is heard it is usually possible to move the sound source, use a microphone with a different directional characteristic or physically isolate the sound source further to improve the situation.