• 051487 - MODULE 1: FUNDAMENTALS OF ROOM ACOUSTICS

The course aims to provide the base knowledge and tools for the analysis of the generation, propagation, reception and perception of sound in various human activities. This course will introduce to the comprehension of  acoustics phenomena in buildings and, in particular,  the understanding of definitions and physical concepts of various involved acoustical features will be emphasized. Physical modelling and mathematical formulation for analysing the sound will be also covered. 

Knowledge:

- Knowledge of basic theory on sound generation and propagation;

- Knowledge of sound propagation in rooms, sound perception, acoustic regulation and sound absorbents

Skills:

- Be able to understand and analyse acoustic phenomena in buildings

- Have developed the ability to understand their physical base and to adopt new theory that will be needed in the future.

types

Vibrational motions in fluids: continuity equation, momentum and energy, small oscillations and isentropic fluid: wave equation. Sound as pressure wave phenomena. Acoustic intensity and energy density: definition. General solution of the sound wave equation: Decomposition in Fourier series and Helmholtz equation. 1D solution. Plane wave: speed-pressure relationship, specific acoustic impedance; relationships between periodic average values of intensity, energy density and effective pressure (RMS).

Spherical waves: differential equation of motion, isotropic acoustic wave propagation equation, sound pressure equation, vibration speed, phase angle, specific acoustic impedance, intensity and energy density instantaneous and average values over the period, relationships between intensity, average energy density and effective pressure. Directivity of an acoustic source: directivity index.  Acoustic propagation law for spherical waves in non-dissipative medium (free field propagation), extended to the real case by directivity and empirical correction coefficients. The acoustic sound pressure levels, intensity and power: units in decibels. Combining decibel levels: incoherent sources, coherent sources. From spectral to total levels. Equivalent levels.

Reflectivity, and transmissivity, reflectance and transmittance, Snell's law and critical angle, evanescent waves at the interface between two fluids.

Normal specific acoustics impedance for oblique wave, reflection and absorption coeff.: reflection of an incident planar wave on a perfectly rigid surface.

Room acoustics

Oblique planar wave in a finite volume limited by perfectly rigid surfaces: vibrations in the cavity, frequencies and natural modes of the room (axial, tangential, oblique).

Absorption influence on the vibration modes of the room, damped vibration and resonance peaks. Research of natural frequencies for a free damped vibrational motion. Forced vibration: the reverberant field as a linear combination of the dumped natural motions. Reverberant field: the transient attack, steady state, the sound tail.

Diffuse sound field: hypothesis, sound intensity on the boundary as function on energy density, mean free path e time between two reflections. Sound energy balance equation: spit contribution of direct and reverberant fields

Steady state solution: total energy density function of equivalent absorption area; reverberant field energy density function of room index. Energy density decay, assumption of continuity of the reflections, the Sabine equation for T₆₀. The energy density of the hypothesis of discontinuity reflections: Eyring equation for T60. SPL Difference, normalized vale. Acoustic human perception: phone diagram and A-scale correction for dBA.

Calculus knowledge is required with reference to complex numbers, derivatives, integrals, ordinary and partial derivatives equations. Knowledge of continuum mechanics basic principia and constitutive laws is advised.

Final written and oral examination on the main course topics.  In the written examination, the student has to answer to four open questions aiming to assess the ability of:

• understanding and analysing acoustic phenomena;
• understanding and analysing basic acoustic phenomena in buildings;

Correction and discussion on the written answers constitute the oral examination.