# Building Acoustics – theory

The field of building acoustics consists of two parts; Room Acoustics which deals with sound propagation in a room and Building Acoustics, which deals with sound propagation between rooms.

Typically, room acoustics is related to the quality of sound, e.g. concert hall acoustics, while building acoustics is more related to unwanted sound, i.e. when you want to hear as little as possible of what is going on in adjacent rooms.

From a measurement technology point of view, the two have a lot in common which shall be outlined here.

### Sound in a room

Assume that we put our sound level meter in a fixed position in a room and that we start a sound source. The sound source could be a machine or a combination of a noise generator, a power amplifier and a loudspeaker or anything else making enough noise to make useful measurements.

What we will observe now is that the sound pressure level in the room will not rise indefinitely as the sound source continues to “pour” noise energy into the room. Instead, the sound level stabilises. Why is that?

Simply because the rate of sound energy input to the room is exactly compensated by the rate of energy absorbed in the room.

To be accurate, the absorbed energy consists of two parts; the energy actually absorbed by the room boundaries (the walls, ceiling and floor) and the energy transmitted through the boundaries into other rooms or out in the open.

Consequently,the sound level in the room will be reduced if more absorbing materials are brought into the room or more energy is transmitted through the boundaries.

We can increase the amount of absorption by bringing in carpets, soft furniture, curtains etc.

A very effective way of increasing the amount of transmission through the boundaries is simply to open a window!

### The nature of absorption

For practical rooms the absorption materials are parts of the decoration; furniture, carpets and curtains. These are all simple porous absorbers. By restricting air particle movements, the sound energy is converted into heat through the frictional forces.

Note that contrary to popular belief absorbers put directly on the wall are not as effective as those placed a bit apart from the wall.

The reason why is that since the absorption is due to particle movement restrictions, the most effective place to put an absorber must be at the point where the particle velocity is at its maximum. It can be shown that this takes place a quarter of a wavelength from the boundary (assuming that the angle of incidence is perpendicular to the wall). This means that an absorber’s ability to absorb will be frequency dependent qua its position.This property comes in addition to any frequency dependence of the material used in the absorber.

Consequently, a carpet lying on the floor will absorb better at high frequencies than at low frequencies. This follows from the fact that as the frequency is increased the wavelength becomes smaller. The quarter wavelengths at high frequencies become comparable with the thickness of the carpet and the absorption increases.

If the room is equipped with different absorbers absorbing different frequencies to different extents you may “tune” the room to a certain sound balance by adjusting the amount of the different type of absorbers.

Typically, rooms can in this way be more or less optimised to their uses such as for romantic orchestra music, baroque music, pop-music or speech.

### The reverberation time must match the use of the room

Rooms with highly reflecting surfaces such as bathrooms will have a relatively long reverberation time while rooms with lots of absorbing materials will have short reverberation times.

Sometimes we want to measure the acoustical properties of a material in a way that makes it independent of the room in which the measurement was made. We will then need a room where the reverberation time is as close to zero as we can get. Such rooms are called anechoic rooms. If you have ever been into such a room you may have noted that the room’s boundaries (walls, ceiling and floor) are completely covered with thick, conical absorbers.

The absorbers are made thick to be able to absorb over a wide range of frequencies. Otherwise, the absorption would be too frequency-dependent (cf. the aforementioned quarter wavelength requirement). The conical shape is there to prevent reflections.

Practical rooms cannot have too thick absorbers. Hence the absorption is bound to be frequency dependent. Typically, the reverberation time will be longer at lower frequencies due to the less effective absorption at these frequencies.

It is very important to design a room with an absorption matching the use of the room. A reverberation time too long makes speech intelligibility difficult. Anyone who as visited any of the Western World cathedrals will subscribe to that.

However, music will benefit from a certain amount of reverberation. Otherwise it will sound thin and staccato. How much reverberation depends very much on the type of music.

Gregorian chants, for example, should have quite a lot, while symphonic music must not have too much as it otherwise tends to become cacophonous and not at in line with the composer’s intentions.

Although the reverberation time must match the use of the room, this criterion alone is not enough to create what is often referred to as “good acoustics”.

### Sound distribution

Reverberation time is used in both building acoustics and room acoustics. Room acoustics uses it for “tuning” a room into the intended use (speech, music), while building acoustics uses it when measuring sound transmission through a wall.

However, the two depart when it comes to such things as sound distribution. This is purely room acoustics. A simple measurement of the reverberation time is not sufficient to determine if the acoustics conditions are adequate for the intended use of the room.

Sound distribution applies to large rooms where there may be significant differences in the sound quality about the room.

The simplest way of looking into sound distribution is by putting up a sound source in the position to be used by the musicians or the speakers and then measure the sound pressure levels at various positions about the room. Your measurements may, or may not include frequency analysis.

More sophisticated analysis will include time-domain measurements in order to look for echoes and how the sound is distributed both as a function of time & frequency and as a function of position. The aim is to investigate when and from which direction the audience receive the sound. There is an ISO standard on this, viz. the ISO 3382.

### Sound insulation

In building acoustics where we concentrate on the noise level due to what goes on in adjacent rooms (or outside) an important parameter is the sound insulation.

Values in building acoustics should be normalised and objective, i.e. independent of the current conditions (amount of absorption) of the room. Primarily we want to characterise a wall’s ability to insulate rather than the current sound level in the receiving room. This is very much because most countries have regulations on how good the insulation at least should be.

We are here talking about the source room – which is where the noise originates – and the receiving room – where we measure the amount of noise coming through the wall.

By correcting the measured level difference in a certain way, we compensate for the effect that the reverberation time has on the sound level in the receiving room.

Note that many buildings have homogenous structures of low loss factors, typically solid concrete walls. In such constructions sound energy is transmitted with very little attenuation. This calls for impact sound insulation measurements in addition to the airborne sound insulation.

## Level difference measurements

When measuring airborne sound insulation between two rooms, we normally do as follows:

One of the rooms is defined as the source room. In this room we put a signal generator/power amplifier/loudspeaker combination and at least one microphone connected to our analysing system.
If we use one microphone only, we must make several level measurements at different positions about the room to calculate a spatially averaged sound pressure level. The loudspeaker must also be used in at least two positions otherwise we cannot guarantee that the measured sending room level is representative for the sending room.
The other room is defined as the receiving room. In here we put at least one microphone which we move about the room to calculate a spatially averaged level even here.
The excitation signal used is normally white or pink noise, used broad band or in octaves/third-octaves.
Pink noise is a broadband noise with a spectrum whose level changes by -3dB/octave as the frequency increases. To explain why we use pink noise let us first look at White noise which is the term for a broadband noise signal whose spectral desity does not vary with the frequency. It contains all frequencies, like light reflected from a white coloured surface.

White noise is said to have a flat spectrum. Since the bandwidth of an octave (or third octave) becomes progressively wider by doubling the width for each octave, the use of white noise will cause the total energy content of a given octave to be the double of the energy content of the octave preceding it.

If we instead use pink noise we reduce the energy by a factor 2 for each octave. This is because -3dB corresponds to halving the energy. The amount of energy per octave will then remain constant since 2×0.5=1.

Red noise has a spectrum falling off by -6dB/octave as the frequency increases. The pink noise is called pink because it represents a spectrum between white noise.

In the receiving room we measure the sound pressure level in octaves or third-octaves, depending on the Standards applicable to our measurement.
Sometimes, the wall has so good insulation properties that the sound pressure level measured in the receiving room remains buried in the background noise of the receiving room. In these cases the source room level should be increased.
However, sometimes the level needed will be prohibitively high for practical loudspeakers. One way to circumvent this is by exciting the sending room with bandpass-filtered noise instead of broadband noise. The loudspeaker’s maximum permissive output level can then be spent on a single frequency band, which will result in an improvement of 10-15dB which may be what is needed to achieve successful results.

This will require instrumentation capable of making serial analysis. Needless to say, perhaps, that most Norsonic building acoustics instrumentation has been designed with this in mind.

The measured receiving room level is subtracted from the source room level and a correction for the receiving room reverberation time is then made. This latter correction is because we want to characterise the sound insulation between two rooms independent of the receiving room’s furniture condition.

## Reverberation time measurement

### A little theory

The reverberation time is defined as the time it takes for the sound level to decay by 60dB after a sound source has been switched off.

Rooms with small amounts of absorbing materials will have longer reverberation times than rooms with more absorbers.

For normal rooms, with reasonable amounts of absorbers, the reverberation time is approximately given by:

T=0.16V/A

in which T is the reverberation time in seconds; V is the room volume in cubic metres; A is the absorption of the room, measured in equivalent square metres open window (i.e. if the absorber has half the absorbing property as an open window, it should be used with half its surface area in the formula) and finally 0.16 is an empirical constant determined by Wallace C. Sabine and published in 1898.

This model cannot be used in rooms with excessive amounts of absorbers, such as anechoic chambers.

### Measuring the reverberation time

To measure the reverberation time you will need a sound source and instrumentation able to capture the sound decay.

Theoretically, you have two options with respect to the sound source; impulse excitation or noise excitation. However, the old ISO 140 Series of Standards as well as the new laboratory version called ISO 10140, require the use of noise excitation. It is important that the noise is broadbanded enough to cover the entire frequency range of interest.

Although the reverberation time is defined as the time it takes for the sound to decay 60dB, this is seldom possible to measure due to the unavoidable background noise. Further, the initial part of the reverberation decay is usually the most interesting part. The reverberation time is therefore normally based on the decay rate for a range of 20 or 30 dB starting 5dB below the stationary level. The value is afterwards extrapolated to 60dB assuming that the part of the decay that we used is representative for the entire decay. It is common practise to specify the range used as T20, T30, etc., all having the same numeric value if the decay is linear.

One way of checking the consistency is by comparing e.g. T20 and T30. Any discrepancies between the two will normally originate from a non-linear decay (when plotted as a graph with a logarithmic level scale). All the Norsonic building acoustics instrumentation currently available has this capability of presenting at least two ways of calculating the decay simultaneously.

The frequency range required for field measurements is 100-3150Hz, but many measurements are now made up to 5000Hz which is the requirement for laboratory measurements. Optionally, you may extend the frequency range downwards to 50Hz, which would make the requirement even tougher with respect to output levels.

### How reverberation time is measured in Norsonic instruments

An ideal sound decay will form a straight line when drawn in a coordinate system as level (logarithmic) versus time. In reality, however, sound decays will always contain fluctuations. Two problems will then immediately arise; viz. how to have the analyser accurately determine the initial level and when to start the calculation.

Using noise as excitation, the calculation starts at 5dB below the mean level (the Leq that is) of the noise measured at the microphone position before the noise is switched off.

As long as the noise then stays below this -5dB threshold the time elapsed is counted. Once the level drops below a second, much lower (i.e. 20dB or 30dB below) the counting is discontinued. Should the level for any reason again exceed the second line, the counting will be resumed and go on until the level again drops below this second threshold.

Likewise, should the level exceed the first threshold any time after the counting was started, the counting will be discontinued until the level drops back below this threshold.

The first threshold is as said above positioned at -5dB, while the second threshold is positioned at -25dB, corresponding 20 dB below where the calculation started fro T20 calculations, or 35 dB below for T30 calculations and so on.

Norsonic normally apply one of two different methods for the reverberation time calculation: The triangular method and the least-square-fit method. The triangular method is a weighted time measurement where the weighting reduce the influence of fluctuations at the start and end of the time measurement. The name is adopted from the triangular shape of the weighting function. More emphasis is then applied to the middle part of the decay and correspondingly less to its extremes. The least-square-fit method is based on a time measurement on a straight line fitted to the decay my linear regression.

In order to minimise any possible influence from the background noise level, you may – in Norsonic instruments – specify a minimum distance to the noise floor. Should, for example the background noise level suddenly rise this will cause the reverberation time to seem longer than it actually is.

Some International Standards, such as the ISO354 require a minimum of 15dB distance to the noise floor. This is a tough requirement actually. From a signal theory point of view a distance of 5dB will suffice in most cases.

## Reverberation time measurement

Historically, sinusoidal signals were used for measurement of the most common building acoustic properties like airborne sound insulation and reverberation time. However, as the obtained result may change considerably by even a small change in the frequency, it was soon realised that band limited noise, with a bandwidth of one- or one-third octave, was more convenient to obtain the mean value for a certain frequency range. The wanted property for the noise is the spectral distribution, the unwanted is the stochastically distribution of the result due to the randomness of the excitation. The system to be measured can, however, in most cases be regarded as deterministic, linear and time invariant. This allows general signal theory to be applied for the measurement.

Stochastic signal analysis methods for the measurement of sound transmission phenomena started to be developed around 1960, but lack of available computing power excluded the use of these methods outside the most equipped research laboratories. The recent development of digitising circuitry, powerful personal computers and the use of digital signal processing components in sound measuring equipment for field use, have made the application of measuring equipment based on extended digital signal analysis readily available even in handheld instruments.

Norsonic applied the new measurement technique in Nor840 in the form of the MLS-option (Maximum Length Sequence). The “swept-sine method” is implemented in Nor140 (Nor118/Nor121) as an option. These methods are less sensitive to extraneous noise than the classical methods and can be used for extending the measurement of low levels by 10–30dB downwards. This may be important for the measurement of the level in the receiving room as well as measurement of the reverberation time in large rooms or in rooms heavily polluted by extraneous noise.

ISO 18233 describes the requirements and guidelines for the use of new measurement methods in building acoustic measurements and room acoustics.