The propagation of sounds and vibrations in fluids and solids is at the basis of most of the phenomena related to musical instruments, building and environmental acoustics, noise and vibration from machinery and industrial products. In this course, we will cover the fundamentals of acoustics, starting from the basic description of oscillations and wave motion, the normal modes of strings and membranes, to the propagation of sound in gas media and the description of reflection, transmission, absorption, and scattering phenomena during sound propagation.

The course will provide students with:

1. The knowledge and tools for the analysis of the generation, propagation, reception and perception of sound in various human activities (Dublin Descriptor 1, Knowledge and understanding);
2. the ability to approach and solve analytically simple problems related to the generation and propagation of sound (Dublin Descriptor 2, Applying knowledge and understanding);
3. the ability to critically assess (at least qualitatively) the basic acoustic phenomena related to the specific features of certain musical instruments, acoustic environments and vibration dynamics (Dublin Descriptor 2, Applying knowledge and understanding, and Dublin Descriptor 3, Making judgements);
4. the ability to independently apply the knowledge and tools acquired during the course to a specific advanced problem/topic of choice (Dublin Descriptor 5, Learning skills).

1. Introduction and basic tools

Introduction to Sound and Vibrations; Complex numbers, harmonic Functions and Phasors; RMS value of a time dependent quantity; Harmonic Analysis: Fourier series and Fourier Transform; Vector and Tensor Algebra and differential operators; Superficial forces in a continuum medium: stress tensor.

2. Fundamentals of Oscillations and Wave Motion

Mechanical Simple Oscillator: 1 degree of freedom; Equivalent Electrical Circuit; Impedance and Admittance; Natural frequency and resonance; Inextensible Flexible String Vibration: Waves Equation; Standing Wave and Normal Modes in String; Waves in String Driven from One End.

3. Wave Equation for Sound Propagation in Gas media

Derivation of Wave Equation: Conservation Principles; Vibration in standing fluids; Thermodynamic constitutive low for an isentropic fluid; Linearized Wave Equation for an Isentropic Fluid; Speed of Sound; Acoustic Energy Quantities: Intensity and Energy density; Plane Waves; Acoustic specific impedance; Spherical wave equation; Intensity and Energy density in near and far field; Acoustic Point Source; Sound Levels; the Doppler effect.

4. Sound reflection, refraction, diffraction, scattering, and absorption

Fluid-to-fluid Normal Incidence; Fluid-to-fluid Oblique Incidence; Evanescent Waves; Reflection at a Solid Rigid Surface; Reflection at a Solid Flexible Surface: normal specific impedance.; Apparent absorption; Absorption and Attenuation of Sound; Effect of Viscosity; Effect of Heat Conduction; Molecular Thermal Relaxation; Sound Absorbing Materials; elements and qualitative description of sound diffraction and scattering; standing waves and normal modes in closed spaces.

5. Elements of musical instruments

Sound radiation from a vibrating plate; sound transmission in pipes and horns; qualitative description of turbulent flow phenomena.

This course requires a solid background in general physics (classical mechanics as well as thermal physics).

In addition to traditional lectures, the course includes tutorial lectures aimed at applying the knowledge acquired to the solution of analytical problems and to the understanding of the basic principles of musical instruments.

The examination will consist of two distinct parts:

• A written examination with exercises (intended to verify the learning outcomes number 1 and 2);
• An oral examination including a brief presentation of a specific topic chosen by the student (intended to verify the learning outcomes number 3 and 4).