Acoustics I

Fundamental knowledge in Mathematics (12th grade).

The Acoustics I curriculum unit includes a wide range of activities and use tools that will facilitate the development of useful skills and a more complete view of how any digital signal acquisition and processing system works in the context of research. As an example, we should refer to the use of auditory stimulus simulation programs (e.g. E-System – version 1.65) and calculation tools (e.g. Excel) to be used in the quantification of acoustic quantities and understanding the applied concepts.

The curricular unit comprises:

– 1 theoretical-practical class of 1 hour per week, where the teacher briefly exposes the programmatic contents of the discipline and applies the physical and mathematical concepts to explain practical examples related to the field of Audiology;

– 1 theoretical-practical class of 1 hour per week, where the teacher helps the student to apply the concepts and mechanisms in problem solving, encouraging the student to achieve a greater autonomy;

– 1 practical-laboratory class of 1 hour per week, where students perform with laboratory activities, involving the acquisition and processing of experimental data, relating the thematic contents identified in these activities with the subjects addressed in the theoretical-practical component.

The discipline of Acoustics I aims to provide the Audiology students with a solid basis in the fundamental concepts of Acoustics necessary to achieve the general objectives inscribed in the training plan of the Audiology course of Coimbra Health School, with a special emphasis on general concepts necessary for the understanding of sound as a physical phenomenon, of acoustics applied to physiological systems , and the instrumentation found in Audiology, transmitting at the same time the fundamentals of mathematics and intellectual mechanisms of understanding and rigor underlying the scientific method.

1. Mathematics (12 h)

Differential Calculus

Definitions

Graphs of some elementary functions: trigonometric F., inverse trigonometric F., exponential and logarithmic F.

Derivatives: Definitions and interpretations, derivative rules, Applications of derivatives

Integrals of real valued functions of a real variable

Primitives: definition and operation

Integrals: definition and properties of defined integrals; fundamental theorem of calculus; Surface area determination.

2. Preliminary Review of concepts (3 hours)

Units and dimensions – physical quantities; systems of units; the S. I.

Mechanical material point – kinematic quantities and movement; dynamics: interactions, forces and Newton’s laws, kinetic, potential and mechanical energy, energy theorems

3. Free oscillations (6 hours)

Simple harmonic oscillator – simple harmonic motion (SHM); SHM and circular motion; SHM energy; Non-linearity and inharmonicity

Damped oscillator – mechanical resistance and quality factor; movement in the regime of small damping; dissipation of mechanical energy; regime for large damping

4. Forced oscillations (6 hours)

Forced oscillations – forced oscillation in steady state; resonance; transient

Mechanical impedance – definition; correlation with the transfer function of a mechanical system and its frequency response

5. General concepts of wave (3 hours)

Wave motion – concept of wave and its qualitative characterization; wavefronts; harmonic waves: amplitude, frequency, wavelength; not harmonic waves and impulses

Waves on a vibrating string – velocity of propagation; energy transport; reflection boundaries, principle of superposition, standing waves

6. Sound waves (9 hours)

Sound waves – definition and physical quantities underlying its description; transport of energy and loudness; sound propagation: speed of sound, the law of inverse square of the distance, absorption

Pure tones and complex sounds – distinction between pure tones and complex sounds; overlapping MHS beats and sound; principles of harmonic analysis and synthesis

Wave phenomena – Huygens’ principle; Diffraction and interference; spatial location in auditory perception; Doppler effect

The continuous evaluation scheme is optional and consists of:

1) periodic exercises/questions and reports of experimental activities (EA) to be resolved at each class (of practical-laboratory matrix).

2) two written evaluation tests (PE1 + PE2) to be scheduled in the first week of classes (theoretical-practical matrix).

The final score is given by the average of the classifications obtained at all evaluation moments, i.e.:

Final Grade = (EA + PE1 + PE2)/3, in which PE represents the average of the classification obtained in the various periodic exercises/questions/reports (EA), and PE1 and PE2 represents the evaluation obtained in the written evaluation tests.

Both the mean of the components of the theoretical-practical matrix evaluation or the mean of the components of the practical-laboratory matrix evaluation will have to be equal to or greater than 9.5 values.

NAO