Room Acoustics and Treatment

In the ‘Acoustics and Psychoacoustics’ module in the second year of my degree, 50% of the grade was decided by two closely-linked reports. These reports also involved taking acoustic measurements of a room in the university and analysing the results. The first report is a brief guide to acoustics in general. In the second report, however, we were instructed to act as if we were an acoustic treatment firm hired to treat a room at the university.

 

Below are the two reports and the recordings made, which achieved a 2:1.

A brief guide to room acoustics and acoustic treatment

1. How sound works

What we perceive as sound is actually just vibrations in the air, they could be caused by a guitar string moving back and forth, vocal cords opening and closing or air blown across a reed. Assuming we’re only looking at sound travelling through normal air, the speed at which these vibrations travel through air is affected solely by temperature; sound travels faster through warmer air. This is because the air particles have more energy so they can vibrate back and forth a lot faster.

We can use this fact to make a good approximation of the speed, which becomes important when we look at some of the most important aspects of sound: the frequency and wavelength. The frequency of a sound wave is basically the pitch and the wavelength is the physical length it takes for the sound wave to form in the air, calculated by dividing the velocity of a sound wave by its frequency.

1.1 Measuring sound

One of the main ways in which engineers quantify sound level is through the Sound Intensity Level often quoted in decibels. Since the human ear can handle such a large range of sounds like a pin dropping to an explosion, we use the decibel scale to make the numbers more manageable and clearer. In the decibel scale, 0dB is about the quietest sound most people can hear, a change of 1dB is about the smallest change the human ear can perceive and every increase of 3dB is a doubling in intensity.

2. Why room acoustics are important

Most music is listened to within a room, which means it’ll be influenced by the presence of boundaries. We can split the reverberation in a room into 3 parts, the direct sound, the early reflections and the reverberant sound. Early reflections have bounced off of one or more surfaces and will vary as either the source of the sound or the listener moves within the space, which gives the listener an idea of the size of the space and the position of the source within the space.

Next, we have the reverberant sound; the sound that’s been reflected many times and so arrives at the listener from all directions, with each reflection arriving very close to its neighbours. The reverberant sound is desirable as it supports and adds richness to musical sounds. Also, since the reverberant sound waves arrive at the listener from all directions, at any one point in the room there will be a large number of sound waves whose intensities are being added together. This causes the reverberant field to be at the same level at any point in the room.

Furthermore, when listening to audio, the balance between direct sound and reverberant sound will change with your distance from the source. Even though the reverberant field level is constant, the level of direct sound diminishes the further you are from the source due to the inverse square law, increasing the relative level of the reverb.

 

The inverse square law is used because sound does not propagate in a single beam, it radiates outwards from a source in all directions, reducing in intensity by the square of the distance it travels. This is purely due to geometry and occurs before sound absorption even takes effect. Many factors cause sound, including reverberation, to decay over time. The time it takes for the reverberation specifically to die away is called the reverberation time and is often quoted as the RT60 value, the time it takes for the reverberant field to decay by 60dB. The RT60 is calculated like so:

R T60=0.161V/Sa

Where ‘V’ is the volume of the room and ‘Sa’ is the sum of the surface areas of absorbing surfaces multiplied by a number known as the absorption coefficient (a) and is usually a number between 0 and 1 which indicates how much sound the material absorbs or reflects, with ‘1’ being very absorptive.

2.1 Room Modes

As we can see, whenever sound hits a boundary and reflects, some of the sound is absorbed and therefore the sound in a room generally decays exponentially. However, when room dimensions allow for sound waves to be reflected in cyclic paths, with the length of the paths being a precise number of half wavelengths, a phenomenon known as standing waves are allowed to form, which cause certain frequencies to be louder or quieter depending on the listening position within the room. These standing waves fall into three major types.

Axial modes occur between two opposing surfaces and so are the function of the linear dimensions of the room. Tangential modes occur between four surfaces and so are a function of two of the dimensions of the room. Oblique modes occur between all six surfaces and so are a function of all three dimensions of the room. All three of these types of modes are exemplified below in a diagram from Everest and Pohlmann, (2009). Two parallel reflective surfaces can also cause a second acoustical defect known as flutter echo, which manifests as a series of rapidly spaced echoes.

Picture1

(Everest and Pohlmann, 2009)

Although human hearing covers frequencies from 20Hz to 20000Hz, modal behaviour does not apply to rooms across this entire range. There is a ‘critical frequency’ at which this behaviour stops dominating the characteristics of the room. Knowing this is important to make sure the right type of analysis is used in each discrete region. As well as these, there’s a cut-off region, in which the room is smaller than a half-wavelength in all dimensions, making it much harder for sound to radiate at these low frequencies. Finally, there’s the diffuse field region in which the concept of reverberation time is valid. In general, this region of the frequency spectrum will sound the best, providing the reverberation characteristics of the room are good, as the effects of room modes are minimal and the listener experiences an even reverberant sound level throughout the room.

3. How acoustic treatment can improve a room’s acoustics

Through various acoustic treatments, the acoustical defects of a room such as room modes and flutter echo can be significantly reduced and the reproduction of sound within a room made much more true to the source material. Clarity and intelligibility of speech and music can be greatly diminished by these defects but through use of sound absorbing and diffusing materials in proper arrangements, specific frequencies or room artefacts can be targeted and reduced to improve the overall acoustical quality of a room as well as a rooms suitability for any specific use.

4. Sound absorbers and diffusers

There are two basic types of absorption material; porous and resonant absorbers. Porous absorbers consist of soft fibrous materials with a high surface area for their volume, like your everyday carpets, curtains and rugs, as well as specially designed absorbers. This trait of the materials causes a large amount of friction with the velocity part of the sound wave, causing the loss in intensity. Unfortunately, as Cox (2015) states, “Foam and mineral wool on their own are ineffective for soundproofing, ie. stopping sound getting into or escaping from studios”. As well as this, they tend to affect very little of the low frequencies, where room modes might be problematic, lending them to be mainly used for treating mid to high-frequency issues.

The other means of absorption is through sound energy causing vibrations inside the absorbing structure itself, causing internal frictional losses. Resonant absorbers do this and it means they’re not affected by the velocity part of a sound wave but the pressure, making them good for mounting directly to walls, as this is where the velocity of a sound wave is lowest but pressure is highest. As Howard, D. and Angus, J. (2006) state, “The resonant characteristics of these absorbers allow them to be tuned to low frequencies and so allow them to have absorption characteristics which complement those of porous absorbers”. A similar form of resonant absorber, the Helmholtz absorber, uses the idea that resonance will occur in a tube above an air space (much like a person blowing across a bottle).

Both of these absorption types can also be combined to make a ‘Wideband Absorber’, as shown in the following diagram from Howard, D. and Angus, J. (2006).

Picture2

Typically, for reflective surfaces, the angle at which a sound wave hits a surface is the same as the angle at which it reflects. This leads to very predictable reflections which can cause room modes and other issues. A way to stop this, other than absorbing all the incident sound energy at the surface, is to diffuse the reflection, spreading the energy out to create a diffuse reverberant field. This is done with either reflective material arranged into specifically designed patterns, typically ‘bumps’ of various heights, or patterns of reflective material placed atop an absorber, giving the sheet a pattern of uneven absorption which can change across one dimension or several.

The former method, called a phase reflection grating, uses repeating patterns of varying depths which depend on the wavelengths of frequencies we wish to diffuse. In fact, the lowest frequency which can be effectively diffused like this is such that the maximum depth must be half the wavelength of the lowest frequency. This makes for very deep diffusers at low frequencies. The Latter method, amplitude reflection gratings, is almost the opposite in its effectiveness with varying frequency as it has no lower frequency limit but has a high-frequency limit. This limit is where the width of reflective strips is more than half the wavelength of the highest frequency we hope to diffuse.

5. cheat sheet for room acoustics

Obviously, room acoustics is a broad and complex subject, but there are some general tips one can follow to start in the right direction.

• Wherever possible, walls and ceilings should be slightly off-parallel. This helps avoid uneven frequency responses due to room modes and flutter echoes, as sound will not be able to reflect back and forth along the same axis.

• “As the room size increases, the reverberation time increases proportionally, if the average absorption remains unaltered.” (Taken from: Howard, D. and Angus, J. (2006). Acoustics and psychoacoustics. 3rd ed. Focal Press.)

• To help avoid room modes, rooms should not have dimensions which are integer multiples of one another or else some modal frequencies will be shared between multiple dimensions, causing issues.

• Mid to high frequencies will be greatly absorbed by soft fibrous materials. While specially designed absorbers can be bought, carpets, curtains and rugs will have a similar effect. Curtains or thinner wall-mounted absorbers should, however, be placed some distance away from the wall to maximise effectiveness, as per Troldtekt (Undated).

• Placing porous absorbers across the corners of rooms will increase the number of quarter- wavelength points passing through it, increasing absorption at lower frequencies while minimising useable space taken up by the absorber itself.

• Phase reflection grating diffusers will work at very high frequencies but have a low-frequency limit where the depth is half the wavelength. Amplitude reflection grating diffusers will work at very low frequencies but have a high-frequency limit where the width of reflective strips is half the wavelength.

Technical Report on Proposed Acoustic Treatment for P/T/003

1. Introduction

In January 2018, a team of five students including myself booked the room ‘P/T/003’ to take in impulse response as an example. Herein, the taking of this impulse response will be documented, with the results displayed and analysed. Suggestions will then be made based on the current acoustics of the room to improve them. Hopefully, these suggestions will be welcomed and increase the room’s suitability for purpose and perhaps even extend its usefulness in regard to the acoustics.

2. Physical Description of the Example Room

The room (P/T/003, pictured right) has a height of 3.7 meters, a width of 5.9 meters and a length of 7.6 meters. These dimensions give the room a volume of 165.91 meters cubed and wall surface area of 189.58 meters square. 

27016907_1977199182298811_805216055_o

The room is an active seminar/meeting room and as such was suitably cluttered. Items were moved to the side but tables lined two ends of the room with boxes on and under the tables on one side. A few chairs and a coatrack were moved to the sides of the room and the sliding divider bisecting the room was opened as fully as possible.

The walls are a mix of painted brick, plasterboard and windows while the floor is entirely carpeted. The bricks and window, of course, are hard, reflective surfaces which will extend reverberation times in the room as they have a very low absorption coefficient. Plasterboard is unusual as it is relatively absorptive around 125Hz (with a coefficient of around 0.3) but very reflective at frequencies above this. The carpet, however, will act as a porous absorber and while there are windows they are covered with blinds. While these blinds are very thin, it should be noted that they will have a small absorptive effect and diminish the reflectivity of the windows. Overall, the room is made of mostly reflective surfaces with some porous absorbers, making for a room which should have a generally low average absorption which increases slightly with frequency. The number of tables in the room, which act as hard reflective surfaces, will also increase the reflectivity of the room, especially as they may cover sections of the floor which might otherwise be absorptive. The divider in the middle of the room, being reflective but corrugated, could also act as a type of diffuser, potentially diminishing some modes down the length of the room.

Using the dimensions of the room, potential room modes can be estimated as mentioned previously. I have estimated the first ten room modes to be as follows in Hz: 22.5658, 29.0678, 36.7988,  45.1316, 46.3514, 51.5525, 53.6824, 54.7118, 58.1356, 59.1828. I’ve also estimated the RT60 using the Sabine equation. From two tables of absorption coefficients from Howard, D. and Angus, J. (2006) and Soundproof Your Home (2014), I was able to roughly estimate the absorption coefficients of each surface, multiply each by their respective surface areas and substitute them into the Sabine equation below.

Where V is the volume of the room and Sa is the summation described previously. Doing this gives a value of 1.1s. This is, of course, an estimation with rough absorption coefficients and no consideration to the furnishings within the room.

Other potential issues could be sound isolation. The door facing the inside of the building does not form a particularly tight seal, meaning that sound from outside the door has space to get into the room. Furthermore, having several parallel walls which are very reflective (painted brick is even more reflective than exposed brick) there could be issues with flutter echo.

3. Auditory Properties of the Example Room

3.1 The room’s acoustic properties

The room is very small and as such has a short reverberation time. The RT60 (T30) of the room at 1KHz, I’ve calculated as being 862 milliseconds. This was calculated by separating the recording impulse response into eight frequency bands and acquiring the time it takes for the sound to decay by 30dB in each band and multiplying this time by two. The RT60 values of each band are quoted in the table of obtained results on page 9. This is slightly lower than my previous estimate, as expected, which is probably primarily due to furniture in the room absorbing and diffusing sound waves, which the Sabine equation does not account for.

Viewing time decay across frequency bands show a strong flutter echo in the 63Hz and 125Hz bands. It is slightly visible in the preceding bands however it is much weaker. This echo manifests itself as a bumpiness to the reverberation decay where the sound would usually decay exponentially. These bumps are the distinct echoes as they arrive and sum with the general reverberation in the room to cause the peaks visible on the graph below on the following page. The graph shows the Shroeder Curve of the of the Impulse response in the 63Hz band, along with the T30 and a line at dB = -60, to highlight exactly when the signal decays by 60dB.

63Hz graph

3.2 Audio Illustration

Below is a visual representation showing amplitude against samples for both an anechoic recording of a clarinet playing staccato and the same material but convolved with the impulse response taken for the example room. From this, we can see the effect convolution has on the signal. For example, the most obvious difference is that the anechoic material is now reverberating, giving the staccato notes a longer tail as suggested by the RT60 time previously derived. The second most important difference is the range of amplitudes. The original material was not perfectly consistent in the amplitude of the peaks but we can see that as the player plays through a scale, certain notes of different fundamental frequencies cause different changes in apparent gain, which is especially apparent with the largest spike seen, hinting at the non-flat frequency response of the room.

anechoic vs convolution

3.2 Room acoustic properties

Shown in the table below are values of important acoustic properties of the room, derived from the impulse response taken of the example room. All values were calculated by using the Matlab acoustic parameters toolbox by Alex Southern. Calculations are made for 8 frequency bands, though these measurements are rarely quoted for frequencies below 125Hz due to the effect of modal behaviour.

Freque-ncy (Hz)

T20 (ms)

T30 (ms)

C50 (dB)

C80 (dB)

D50 (%)

D80 (%)

EDT (ms)

63

1028.21

946.68

-5.27

4.00

22.90

71.53

705.66

125

816.07

841.81

1.87

4.59

60.59

74.21

778.80

250

971.69

986.33

-0.58

4.62

46.68

74.61

969.64

500

920.42

971.68

-0.27

4.69

48.46

74.68

855.46

1000

888.89

862.24

0.58

4.75

53.35

74.92

848.87

2000

781.94

815.64

2.36

5.74

64.72

78.93

799.27

4000

701.02

709.44

4.73

7.90

74.83

86.06

654.27

8000

527.95

551.56

8.56

12.70

87.78

94.90

443.58

T20, T30 and EDT are all values of RT60 where the T20 is the time for the signal to decay by 20dB which is then multiplied by 3 to approximate the RT60, the T30 is the 30dB decay time multiplied by two and the Early Decay Time (EDT) is the 10dB decay time, again extrapolated to approximate the RT60.

Clarity is the subjective measure of how ‘clear’ a signal is; how distinctly each note or syllable can be heard versus how much they blend into their neighbours. This subjective quality can be objectively defined as the ratio of early sound energy to late sound energy present in a signal and is presented as the stated C50 and C80 values of the table. These values are especially good at quantifying speech intelligibility. C50 is the logarithmic ratio of sound energy in the first 50 milliseconds to later sound energy and C80 is the same but with the threshold moved to 80 milliseconds.

Finally, the definition is much like the clarity but where the clarity is good for speech intelligibility, ‘definition’ is good for distinction of musical articulation. The D50 and D80 are percentages of early to late sound energy and again correspond to energy in the first 50 and 80 milliseconds respectively. 3.3 Recommendations

From the table of acoustic parameters and calculated modes, it’s apparent that there are several issues to address if this room where to be used as a music venue. These issues can also affect speech intelligibility in the room’s normal application. Each definition and clarity can be improved by reducing the amount of late sound energy arriving at the listener. As we can see in the table, the 63Hz, 4KHz and 8KHz bands require the most attention in these. Absorption of sound in the 63Hz band can improve the clarity and definition in these ranges by increasing the relative energy of early sound.

Absorption in this band could be achieved using resonant absorption, with the absorbers being placed in corners to maximise points of 1/4 wavelength contact and decrease wasted space. Due to the layout of the room, the ceiling to wall corners would be the least intrusive place to attach these. Using the ceiling to wall corners in the half of the room opposing the whiteboard (henceforth known as ‘the listening area’) will be entirely unobtrusive and help increase clarity and definition for the audience. Using resonant absorption would be best for this as porous absorption like the ‘superchunk’ approach would use over a meter deep of material.

The window behind the listening area is also an issue and is currently only covered with a thin blind. As such, very little of its high reflectivity is negated. Placing shutters over the window with Amplitude reflection grating diffusers will work at very well to diffuse a broad band of frequencies, especially the lower frequencies causing an issue. Using diffusion rather than absorption will also enhance the diffuse field reverberation, making for a more pleasant, musical listening environment. Using reflective strips 80 millimetres wide will give the panels a high-frequency limit of 20KHz, the top range of human hearing.

Absorbing at higher frequencies, to combat the issues at 4-8KHz can be easily done with porous absorption. Beams bisect the ceiling rather handily into a performance/presentation and listening area. The unused space above the listening area could have a sheet of porous absorber suspended from the ceiling. Rockwool in itself would provide good absorption of high frequencies and suspending it from the ceiling would increase its effective frequency range by creating space behind it.

A more musical reverberation could be achieved by replacing the floor with a more reflective material like wood and placing an absorptive rug in the listening area. This will have an effect almost like ‘live-end, dead-end’ in that a performer or presenter can stand on a wooden floor and have a pleasant reverberation to their voice or music, with the aforementioned absorption and diffusion alongside an absorptive rug reducing early reflections to the listeners, making the reverberation pleasant while retaining clarity and definition.

All of these treatments will greatly improve the rooms suitability for its current purpose as increasing clarity will improve speech intelligibility when hosting small presentations. As well as this, greater definition and a more pleasant diffuse reverberant field will also allow for the room to be used as a small acoustic music venue. While doing this, the small size of the room is taken into account by making the changes unobtrusive, placing extra materials in corners and already disused cavities or replacing features like the floor which will not change its physical size. Typical corner bass traps can cost around £50 for two 4’ lengths, wooden flooring around £1200 for a 40m2 area and a set of suspended cloud panels could cost roughly £200.

4. Conclusion

From my measurements and analysis, it’s evident that the room has problems with clarity and definition, specifically in the very low end and high end. The reverberation in the room is also uneven across the frequency spectrum. All of these contribute to making a room in which both speech and music are not properly represented when they reach the listener, especially as the position of the listener moves around the room and is affected by various modes. All of these things, however, can be corrected or significantly reduced with the prescribed treatments. For less than £2000, the acoustic characteristics of the room can be tweaked and fixed without any obstruction, which is especially impressive when thinking of the rooms already small size.

My firm is the clear choice to make these alterations as we’ve taken one of your smallest useable rooms and made suggestions which will not affect the capacity or make any obstruction at all to occupants. Other firms may provide a slightly more even response but at a huge cost to space, installing large ‘superchunk’ porous absorbers to absorb low frequencies, where much smaller absorbers can be applied to corners of the room to the same effect.

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