ROOM ACOUSTICS Aravindha Karthik Chellappa
ABSTRACT Room acoustics plays a vital role in designing theatres and recording studios, for effective acoustic output and proper reproduction of the voices and the tones used. Better room acoustics result in making the processing of acoustic signals easier and efficient. The proper modeling of a room, or a studio, based on room acoustics, and hence its effect on the signal strength, are discussed in this paper. This paper aims at suggesting a better alternative to the already existing room acoustic methods, and aims at producing better signal output levels with more efficiency. Index Terms— Acoustics, Acoustic measurements. 1. INTRODUCTION Rooms, in general are reverberative in nature. In recordings, the presence of room acoustics, and the resultant sounds (mostly unwanted ‘noise’), just make it as an unwanted extra instrument playing along with the musicians. The design goal for a good music room is to minimize this coloration, which is strongest at bass frequencies between 20 and 200 Hz. At higher frequencies the room still has an influence, but resonances are much less of a problem since it is much easier to obtain high absorption at higher frequencies. Studies on this topic are mainly directed towards the design of professional sound studios, where the acoustics should be fairly uniform over the entire room. The ideal frequency response is flat with no peaks and valleys. This could only be obtained inside a perfect anechoic chamber - a room where the walls absorb sound without any reflections. This is not a feasible solution, and for almost any sound system the room will pretty much determine the frequency response at low frequencies. Room effects virtually always swamp out imperfections in drivers, enclosures and crossovers.
2. WHAT ARE SOUNDS? Sounds are often considered to be those sensations which the ear can detect; however, acoustics is concerned with much more than just hearing. Sound results from vibrations in the medium, whether it is a gas, a liquid or a solid.
For instance, let us consider a tuning fork - when it is 'sounded', the prongs vibrate back and forth creating fluctuations in the air pressure around the prongs. These fluctuations move away from the fork prongs, creating a sound wave. The bow causes a violin string to vibrate producing sound waves, while the bang coming from an explosion is caused by rapid changes occurring in the hot gas at the centre of the explosion. Similar function is effected when we ‘speak’. Speech is produced by the relatively complicated interaction of the lungs, vocal cords and passages in the throat, the resultant effect being the generation of alternatively compressed and rarefied regions of air immediately in front of the lips. Again, this region moves away from the speaker as a sound wave. 3. BASICS OF ACOUSTICS Acoustics includes the study of waves which range from infrasonic right through to ultrasonic waves - in fact any form of mechanical vibration in any media can be regarded as part of acoustics. This very broad definition is why acoustics is involved in practically all aspects of modern life. Every area of acoustics involves three aspects – (1) The production of the sound or vibration, (2) Transmission of the sound through some medium and, (3) The reception or detection of the sound. While the production and detection are important aspects, in many situations the most complicated area is often the transmission of the sound from source to receiver. This may involve reflection of the sound energy from a surface, diffraction where sound is bent around corners, interference where part of the sound wave interacts with other parts of the wave to cancel or enhance the overall effect and absorption where sound energy is changed into heat within the material. Often, many of these processes occur simultaneously.
4. DEFINITIONS 4.1 ANECHOIC CHAMBER A room is a place, or an area where the walls, ceiling, and floor have been covered with acoustic absorbing material to (nearly) totally eliminate reflections. Useful for engineering development of loudspeakers since it isolates the performance of the speaker. But the response in a real room will be very different. 4.2. REVERBERATION The echoes in a room that one hears after the original sound stops. The usual measure of reverberation time, denoted by RT60, is equal to the time it takes the sound to decay 60 dB after the sound source stops, in seconds. 4.2.1 Reverberation Time The absorption coefficient α is related to the reverberation time of the room, defined as the time in seconds required for sound pressure to decay 60 dB. A standard equation for reverberation time is given by,
Waetzmann- Schuster- Eyring reverb time formula
4.3 SPL SPL stands for Sound pressure level. A logarithmic dB scale is used, akin to the Richter scale for earthquakes. A 3-dB increase means doubling the power. Zero dB SPL is the threshold of hearing; a quiet room has a background SPL of about 40-dB; a loud rock concert can go to 120-dB; the threshold of pain is 135 dB. Peak sound pressure is 3 dB higher than root-mean-square (RMS) average pressure. SPL normally refers to RMS pressure. 4.4 SENSITIVITY Sensitivity is normally defined as the SPL level produced at a distance of 1 meter from the speaker, with 1 Watt of input power. However it is also common to specify an input of 2.83 volts instead of 1 watt of input power. This would be equivalent if the input impedance were 8 Ohms, but it is usually really closer to 6 Ohms.
5. ROOM RESONANCES Sound is conveyed through waves in the air. Waves that exist between a pair of surfaces can create standing wave resonances whenever the distance between the surfaces is any even multiple of one-half of the wavelength.
Figure 5.1 Frequency regions in a musical keyboard At resonant frequencies (tones), the sound is louder and decays much more slowly than at non-resonant frequencies, causing uneven tonal quality and interference with clarity. Resonant frequencies occur mainly in the bass range, due to the relationship between the wavelengths of low-frequency sounds and the typical sizes of listening rooms. Every room has its associated resonant frequencies. Rooms built using preferred dimensions ratios have potentially more even distributions of these resonant frequencies. Room built with angles walls or ceilings have more complicated resonant modes than typical rectangular rooms and the resonances can be potentially less severe. Although the acoustic treatment required to optimize the sound is different for every room, every setup, and each unique application, there are still some basic acoustic concepts that are applied universally in a properly treated room. Some of the fundamental acoustic topics needed for a properly treated listening room are - Room Resonance Control, Bass Traps, Comb Filtering, Flutter Echo, Reflection Control, and Reverberation Time. The bass response is sharply boosted for a narrow frequency band near resonance, and then is depressed between resonances. The sharpness and height of the resonant peak depends on the sound absorbing properties of the room. A room with a lot of soft furniture, heavy carpeting and drapes will be relatively "dead," and the peaks and valleys of the frequency response typically vary by 5-10 dB. A room with bare walls and floor will be very "live," and the peaks and valleys vary 10-20 dB or more. The absorption coefficient of 0.2 is about average, corresponding to a reverberation time of about 1/2 sec.
6. OPTIMUM ROOM DIMENSIONS The standard modal approach for designing a room with good acoustics is to create as many different resonances as possible, and to spread them as evenly as possible across the frequency spectrum. There is even a complicated "Bonello Criterion" to evaluate the spread. The lowest resonance is determined by the largest dimension of the room. In general, the lower the better for the first resonant frequency, because this region is where the frequency response is most variable. For a 19-foot long room the first resonance is about 30 Hz. Every harmonic of this frequency (60, 90, 120, etc.) is also a resonance. The width and height of the room each give rise to another series of resonances. These are the primary "axial" resonances, involving reflections from two opposing surfaces. Additional resonances are created by reflections that ricochet off four different surfaces. To spread these resonances as uniformly as possible, various ratios between the room height, width, and length have been proposed. Three such sets from the Handbook for Sound Engineers are shown in the table below. The optimum room dimensions are:
Figure 7.1.1 Model - Floor Plan
7.2 MEASURED RESULTS The measured results have lower peaks at somewhat shifted frequencies. The lines across the top show the modal resonances of the room. The calculated results show a peak at the 1st and 4th resonances. One significant difference is that the levels of the computed echoes are much higher than the measured values. This might be due to any one of the following factors: (1) The position in which the microphone was held at the speaker, varying the echo responses, and, (2) Almost all of the calculated echoes are perfect responses to the inputs given, which is not the case in real-time. 8. POSITION OF SUBWOOFER
7. MODEL CONSTRUCTION 7.1 Floor Plan
Modal theory tells us that a subwoofer in a room corner will excite all modes, as shown below:
The floor plan of the room is shown below. The image and hence the related calculations assume an empty rectangular room, and the same absorption coefficient at all surfaces. As a studio does, this room plan also contains furniture, and the absorption coefficient of the floor and walls is different. In the measured data, I used a standard microphone (with the normal heart-shaped response), directed towards a standard speaker; the image calculation assumes a perfect speaker. The room has a measured (approximate measurement) reverberation time of around 1/4 sec at 125 Hz, and this corresponds to an absorption coefficient between .18 and .25 (from the table in the image analysis section from The Handbook for Sound Engineers).
Figure 8.1 Modal Theory for positioning a Subwoofer It turns out that on paper the smoothest low-frequency response is obtained when the subwoofer is as close as possible to the listener, which, when tested with real-time
audio, was found to spoil the mood of the listener, brining mostly noise, along with some music that was played. The dominant feature of room response at subwoofer frequencies is near-chaotic variation vs. frequency, and vs. room position. However, I come to terms with this setup, and it is enjoyable to listen to music under these conditions. 8.1 SPATIAL RESPONSE OF THE ROOM To illustrate spatial variations at low frequencies, I calculated the response in a plane at four frequencies, for a normal room using the image analysis program. Many modes are present at each frequency, but at the lower frequencies often a single mode dominates. As the frequency increases, more modes tend to be excited and the spatial variation becomes more complex, resembling the pattern of a single mode less and less. Our listening position decides the response of the subwoofer. If we are at a position there is a null of one of these modes, at that resonant frequency, we will hear no response instead of hearing a strong resonant response. 8.2 TEMPORAL RESPONSE OF THE ROOM Room reflections are significant for the reverberation time, typically 1/2 second or so. The number of reflections grows geometrically with time. The echoes which were computed according to the response demonstrated the temporal behavior. The echoes were represented in the form of dots in the response curve. With each dot in the figure representing a discrete echo, there were almost 1500 echo-dots in the first 100 milliseconds. (An absorption coefficient of 0.25 was used in this calculation). When the echoes were added incoherently, the resulting decay in dB was very nearly linear vs. time, and the reverberation time can be calculated from the decay rate. 9. CONCLUSION In summary the existing methods of room acoustics and their limitations were demonstrated. The constructed model of a studio and its advantages compared to the existing models was explained. The model has the advantages of making the design simple, but still efficient in the presence of all the unwanted noise and in environments with practically unlimited acoustic instruments and/or devices. The applications of the various models for room acoustics filters and their usage in the fields of audio and electro acoustics, and hence sound engineering should be investigated in the future.
10. REFERENCES [1] H. Kuttruff, Room Acoustics, Applied Science, 3rd ed., 1991. [2] Glenn M Ballou, Handbook for Sound Engineer, Third Edition, Focal Press, 2002.
