Practical class on room acoustic for sound and recording degree program in Santa Fe, Argentina

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1 ED Education in acoustics: Paper ICA Practical class on room acoustic for sound and recording degree program in Santa Fe, Argentina Pablo Delmonte Zalazar (a), Paula Ayelén Gareis (b), Ernesto Accolti (c) (a) Instituto Superior de Música, Universidad Nacional del Litoral, Argentina, (b) Instituto Superior de Música, Universidad Nacional del Litoral, Argentina, (c)1 Instituto Superior de Música, Universidad Nacional del Litoral, Santa Fe; 2 Instituto de Automática, Universidad Nacional de San Juan, Comisión Nacional de Investigaciones Científicas y Técnicas, eaccolti@inaut.unsj.edu.ar Abstract In this article the final work of students of the course in Room Acoustics for Sound and Recording degree program of the Instituto Superior de Música from Universidad Nacional del Litoral, Argentina, is described and results are shown. They designed, implemented and aurally tested pseudo random sequence diffusers. One group of students designed a onedimensional quadratic residue diffuser, the second group an MLS and the third group a twodimensional quadratic residue diffuser. They tested aurally for themselves and then in a practice shared with all the class in the recording studio facilities. The students experienced how to build diffusors and how do they sound. Keywords: Diffusor, Education, Acoustic Solutions. 1

2 Practical class on room acoustic for sound and recording degree program in Santa Fe, Argentina 1 Introduction In this article we show the final work of students of the course in Room Acoustics for Sound and Recording degree program of the Instituto Superior de Música from Universidad Nacional del Litoral, Argentina. Three groups of the four groups of students that conform the class decided to design, implement and test sound diffusers between a pool of suggested topics. One group of students designed a one-dimensional quadratic residue diffuser, the second group an MLS and the third group a two-dimensional quadratic residue diffuser. The article is not organized by group of students but following a fundamentals section, an implementation section and finally the conclusions. 2 Fundamentals The acoustical design of rooms, once its volume and dimensions fixed, consist in choosing the more convenient materials to use as cladding, aiming to get optimal reverberation times and other acoustic parameters. Each one of the different types of materials and elements used, produce one or a combination of the next effects on sound energy: - Sound absorption: due to the presence of absorbent materials in the room, resonant elements, the audience and the seats. - Sound reflection: due to the presence of reflective materials used to generate useful reflections to the audience area. - Sound diffusion: due to the presence of diffusers elements and irregular surfaces used to disperse in multiple directions the incident sound energy. The existence of sound diffusion in a room means that the energy of reverberant field will arrive to the audience ears with similar probability from every direction. This will contribute to the spatial impression and in turn to improve the acoustic quality of the room. There are several types of diffusers and the correct choice depends on the room characteristics and the use intended for the room. The students chose and developed the following kind of diffusers: QRD Diffusers (Quadratic residue diffuser)! One-dimensional! Two-dimensional MLS (Maximum length sequence) Diffusers are arrays of elements that reflect the incident sound energy in several directions. 2

3 One of the principles that makes it possible is the interference of the portion of the sound energy reflected in each element of the array. Another phenomenon that contributes to reflect energy in several directions is diffraction. The diffraction takes place in the boundaries of the elements of the array. Diffraction happens for high frequencies, or short wavelengths compared with the dimensions of the elements of the array. How diffraction contributes to diffusers can be interpreted as the diffraction of the sound waves going through a hole or slot in a wall or screen. If the slot is big compared to the wavelength of the sound, the wave fronts go through the slot with almost no distortion. However, when the slot is smaller than the wavelength, hemispheric wave fronts spread inside the shadow zone. Figure 1. (α) A big slot compared to the wavelength allow the wave front go through with almost no distortion shadow zone. (β) Wave fronts behaviour when the slot is smaller than the wavelength. 2.1 MLS Diffuser This is the more simple design but the frequency range for which the diffuser is optimal, is only about an octave. Furthermore, this type of diffusers has less absorption at low frequencies than PRD and QRD diffusers. The design of this kind of diffusers is based in pseudorandom periodic sequences called maximum length sequences (MLS). This sequences are binary. The diffuser is created starting with a smooth and reflective surface, which is subdivided into sections of equal width. Each section has assigned a value of the pseudorandom sequence, according to the following procedure: - If the value is 0, the section remains unchanged. - If the value is 1, a slot is created in the space occupied by the stretch. W = λ 2 d = λ 4 Where λ corresponds to the wavelength of the design frequency of the diffuser. (1) (2) To design an MLS diffuser, we must initialize the registers at any state different from zero vector. We initialised the vector at 1 0 1, and proceed as follows: 3

4 Figure 2. Procedure to obtain the seed 2.2 One-dimensional QRD This design is based in the next formula: h n = c[n2 mod(n )] 2N. fd Where: h n : slot height c: sound speed N: slots quantity in prime numbers f d : design frequency mod: modulo (remainder after integer division) (3) fmax = fd( N 1) (4) d = 1 4 λ f max λ f max = maximum frequency wavelength χn = n N 2 2 π[ mod( )] (5) (6) Which: h n = χ n (2k) f d = ck (2π ) (7) (8) 4

5 2.3 Two-dimensional QRD Figure 3. One-dimensional QRD 3D view In this case the slots are replaced by wells and its dimension will affect the maximum diffusion frequency. W = C T 2f!"# (9) Where: W: width and length of the well C: speed of sound (344 m/s) f!"# : maximum diffusion frequency T: wells septum thick d!,! = (( h! + k! )mod N) N C f! (10) Where: d: well depth h and k: coordinate axis position. Values from 0 to N-1 N: number of wells in prime numbers C: speed of sound (344 m/s) f! : design frequency Figure 4. Two-dimensional QRD photograph 3 Implementation In this section we show the implementation and tests performed by each group in the class. 5

6 3.1 MLS This experience took place in a piano study classroom of the Instituto Superior de Música from Universidad Nacional del Litoral. Figure 5. ISM piano classroom We set the design frequency at 1300 Hz because of space considerations. Then we calculate the width and the depth of each section based on the wavelength at the design frequency. λ = c f λ =!""!/!!"##!" = 0,26 m (11) The width is half a wavelength: W= 0,26/2 = 0,13 m The depth is also half a wavelength: d= 0,26/2 = 0,065 m The starting vector was: and following the procedure shown in section 2.1 we got the next sequence: Figure 6. MLS sequence In Fig. 7 we show a render of the designed diffuser. 6

7 3.2 One-dimension QRD Figure 7. MLS diffusor 3D view We choose a design frequency of 300 Hz to diffuse as much lows as possible without getting the slots too deep but useful in the frequency range of human voice. Based on equations (3-8), we made the next table: Table 1 Obtained values from equations 3-8 N n n^2 n^2modn h n χ n C fd fmax Λ(fmax) d Thick ,082 6, ,191 0,048 0, ,328 25, ,164 12, ,164 12, ,328 25, ,082 6, ,000 0, With the depths obtained we rendered the following isometric view: Figure 8. One-dimensional QRD isometric view To keep the symmetric design, we split in a half the first slot (cero depth) and distributed to the extreme sides Test & measurement The test was made in moderately reverberant closed room. It consisted in placing a measurement microphone 1 meter from a reflecting surface (See Fig. 9), then excite the room with an impulsive sound source (snare drum). The audio was recorded for a later 7

8 spectral analysis. Then we repeated the experience placing the diffuser in front of that reflecting surface (See Fig. 10). Figure 9. Elements distribution for the experience without diffuser Figure 10. Elements distribution for the experience with diffuser We repeated the experience in the class using the recording studio facilities. The students of the class agreed in that the sound of the snare, when recorded using the diffuser, was perceived slightly more defined and with a less coloration. 3.3 Two-dimensional QRD In this case the design frequency chosen was 700 Hz with N=11. The construction material available were 45x45 mm wood strips. The highest diffused frequency is constraint by the dimensions of the section of the strips. Using equation (9), we calculated f max : f!"# = 3882 hz Then using the equation (10) we obtained the block positions with their corresponding height: 8

9 Table 2 Block positions with their corresponding height To keep a symmetric scheme we moved the design to maintain that symmetry in both axis. The final design is shown in Fig. 11. and Fig. 12. and a photograph of the diffuser constructed by the students is shown in Fig. 4. Figure 11. Two-dimensional QRD diffusor modelled with QR Dude free software 9

10 Figure 12. Two-dimensional QRD diffusor modelled with QR Dude free software (other) Test & measurement The measurement was made in a shoebox room (2,3mx5mx2, 5m) and consisted in an impulse generated by a speaker analysed by RTA microphone (75cm from the rear wall). As well as the one-dimensional case, the experience was repeated with the diffuser for further comparison. The impulse was a snare drum sample. Figure 13. Elements distribution for the experience Figure 14. Elements distribution for the experience (photograph) Once again the experience was repeated in the recording studio facilities with the class. The perceived difference was a slightly, but greater than the case of the one-dimensional QRD, better definition of the sound and a richer spectral timbre. 10

11 4 Conclusions Each group of students designed one kind of diffuser. A one-dimensional and a twodimensional quadratic residue diffusers examples were also constructed. They tested aurally for themselves and then repeated the experience in a practice class in the recording studio facilities. The students experienced how to build diffusors and how do they improve sound of a recorded material. The perceived result was an improve on the definition and armonic richness of the recorded signals. Acknowledgments We wish to thank our friends and colleagues Federico Galiano, Demian Gonzalez Petrich, Pablo Guillen and Andres Gordillo Pizarro for their contribution and collaboration. References [1] Antoni Carrión Isbert. Diseño acústico de espacios arquitectónicos. Primera edición [2] Cox, T.J., and D Antonio. Acoustic absorbers and diffusers: theory, design, and application. [3] Wikipedia, Online enciclopedia: [4] Bongiovanni Pablo, Cascino Marcelo, Sanso Marco. Análisis y diseño de difusores acústicos. Universidad Tecnológica Nacional [5] García Céspedes María de los Ángeles, Hernández Almazán Marisela. Tesis Diseño de un difusor acústico. Instituto Politécnico Nacional México [6] [7] Miyara, F. (1999) Control de Ruido 1ra edición, Rosario, Argentina. [8] Miyara, F. (2003) Acústica y Sistemas de sonido 4ta edición, Rosario, Argentina [9] Huizar, J. (2012) Acústica en los Recintos m2db.files.wordpress.com/2012/11/acustica-en-los-recintos-jesus-huizar.pdf [10] Burred Sendino, J. (1999) La Acústica del Piano, Conservatorio Profesional de Música Arturo Soria, Madrid. Versión revisada en Septiembre de