15745 - Wave-Motion Phenomena (A-L)

Learning outcomes

At the end of the course, the student has acquired education to wave phenomena, their generic properties and some essential mathematical tools. He knows mechanical and electromagnetic waves and is able to solve simple problems.

Course contents

Linear oscillations:

Free oscillations. Examples of pendulum, mass and springs systems, and of RLC circuits. Damped and forced harmonic oscillator. The phenomenon of resonance. Oscillation analysis with rotary vectors (phasors); Complex field analysis. Elastic and absorbing amplitudes. Linearity of equations of motion and superposition principle.

Fourier Analysis:

Mathematical tools for analyzing oscillatory phenomena. Fourier series and trigonometric series for periodic signal. Continuous Fourier transformation for non-periodic signals. Fourier series and transform calculations for simple signals.

Mechanical waves:

Introduction to wave phenomena. Propagation of physical perturbations. Progressive and stationary waves, scalar and vector waves, longitudinal and transverse waves, plane and spherical waves. Elastic waves in ropes and solids. D'Alembert's equation. Solution of D'Alembert's equation: progressive and regressive waves. Harmonic waves. Wavelength and frequency. Dispersion relation. Study of a progressive wave. Energy and power in a wave. Wave intensity. Impedance of a medium. Energy, reflection and transmission. Wave superposition. Beats. Phase and group speeds. Stationary waves. Rope with two constrained extremes. Ventrals and knots. Normal and harmonic oscillations. Harmonic frequencies. Stationary waves as harmonic series. Musical notes.

Sound propagation in the air. Sound speed. Power, intensity and energy delivered by sound waves. Decibels and human ear. Stationary waves in a gas column. Superposition principle and beats. Harmonic waves in 3 dimensions. Plane waves. D'Alembert's equation in space. Spherical and cylindrical waves. Group and phase velocity in dispersive media. Sound Doppler Effect.

Electromagnetic waves:

From Maxwell equations to the equation of the electromagnetic waves. Transversal character of electromagnetic waves. Speed of light in the vacuum and in media. Impedance. Representation of an electromagnetic wave. Linear, elliptical and circular polarization. Energy, intensity and impulse: Poynting vector, radiation pressure. Accelerated charges. Irradiation from oscillating charges. Spectrum of electromagnetic waves and visible light. Propagation in a dielectric: dispersion and absorption. Light propagation in transparent media. Reflection and refraction. Complex refractive index. Snell's Law. Total reflection and limit angle, evanescent wave. Fresnel formulas. Brewster's angle. Fermat's Principle and Snell's Law. Dispersion in a prism. Propagation of electromagnetic waves in a metal. Wave equation in a metal and corresponding solution.

Interference and diffraction:


Principle of Huygens-Fresnel. Introduction to interference. Interference of light and electromagnetic waves: Young's experience. Distribution of light intensity on the screen. Optical path. Polarization Conditions. Interference with lenses. Interference on thin glasses and on thin wedges. Interference from N coherent light sources. Primary and Secondary amplitudes. Diffraction phenomena: Fraunhofer and Fresnel diffraction. Intensity on a screen. Diffraction from circular holes and objects. Resolution power. Diffraction pattern. Resolution and dispersion power of a grid. Spectroscopy with diffraction pattern.

Optics:

Introduction to geometric optics. Light rays and laws of Descartes. Mirrors and diopters. Cromatism. Objects and images. Paraxial approximation. Properties of concave and convex mirrors: equation of the spherical diopter. Focus and focal distance. Transverse magnification. Flat mirror. Thin lenses and their properties. Lens Equation. Converging and diverging lenses. Magnification. Aberrations. Optical instruments. The human eye.

Readings/Bibliography

Any book at the university level covering the subjects of the course. As an example:

Halliday and Resnick (+Walker), Fundamental of Physics, Wiley

Young and Freedman, Universitary Physics (latest edition), Pearson, Addison Wesley.

Teaching methods

The course consists of:

• lectures devoted to the presentation of the theoretical foundations;
• classroom problem-solving sessions aimed at applying physical models and solving quantitative problems;
• guided discussion of examples and applications connecting theoretical concepts with observable physical phenomena.

Teaching activities are designed to develop both a conceptual understanding of wave phenomena and the ability to use mathematical tools and physical models in problem solving.

Assessment methods

Assessment consists of a written examination followed by an oral examination.

Written Examination

The written examination is designed to assess:

• the ability to apply physical laws to problem solving;
• quantitative understanding of the phenomena covered in the course;
• mastery of the mathematical tools introduced during the lectures.

The written examination includes:

• three open-ended numerical problems;
• two open-ended theoretical questions concerning theorems, derivations, physical phenomena, and concepts discussed during the course.

Each question is assigned a specific score, evaluated according to the correctness, completeness, and clarity of the answer.

Students must obtain a minimum score of 18/30 in the written examination to be admitted to the oral examination.

Written examination results are published through AlmaEsami. A passing grade remains valid for the current examination session and for the first examination date of the following session.

Oral Examination

The oral examination is aimed at assessing:

• in-depth understanding of the course topics;
• ability to connect different physical concepts and models;
• correct use of scientific terminology;
• communication and reasoning skills.

The examination may include theoretical questions, discussion of derivations, and simple applications.

Final Grade

The final grade is determined by averaging the marks obtained in the written and oral examinations.

Assessment Criteria

• 18–21/30: basic knowledge of the topics, understanding of fundamental concepts, and ability to solve only the simplest problems.
• 22–25/30: good knowledge of the main topics, adequate problem-solving skills, and correct use of disciplinary language.
• 26–29/30: broad and in-depth knowledge, ability to connect different topics, and independent analysis of physical phenomena.
• 30–30 cum laude: comprehensive mastery of the subject, excellent critical thinking and reasoning skills, rigorous use of mathematical formalism and scientific terminology.

Examination Registration

Registration through AlmaEsami is mandatory and must be completed no later than three working days before the examination date.

Use of Artificial Intelligence

With regard to assessment activities, the use of Artificial Intelligence tools is not permitted during examinations. Any unauthorized use constitutes a violation of academic integrity.

Students with Disabilities or Specific Learning Disorders (SLD)

Students with temporary or permanent disabilities or specific learning disorders are encouraged to contact the University support services in due time (https://site.unibo.it/studenti-con-disabilita-e-dsa/en ). Any accommodations must be agreed upon according to University procedures and submitted to the instructor for approval at least 15 days before the examination.

Teaching tools

Teaching materials will be made available through the University's Virtuale platform and will include:

• lecture slides;
• collections of solved and proposed exercises;
• supplementary learning materials;
• information concerning course organization.

Generative Artificial Intelligence tools may be used to support individual study activities, such as summarization, conceptual clarification, and self-assessment, provided that they do not replace independent study of the recommended textbooks and course materials.

Office hours

See the website of Lorenzo Rinaldi

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