Waves and oscillations

A.Y. 2021/2022
7
Max ECTS
64
Overall hours
SSD
FIS/01
Language
Italian
Learning objectives
The aim of the course is to introduce the students to the physics of oscillation and waves. Whenever possible the introduction of the topics of the course will involve an experimental demonstration of the investigated phenomenon in the classroom. The phenomenological introduction will be sided by the formulation of simple descriptive models, with the aim of showing how oscillations and waves of different nature can be dealt with by means of a unitary theoretical description.
Expected learning outcomes
At the end of the course, the student will have acquired the following abilities:
- Ability to describe the basic phenomenology of oscillations and wave propagation
- Ability to describe oscillations and waves with simple linearized models
- Ability to solve quantitatively problems on oscillations and waves
Course syllabus and organization

CORSO A

Responsible
Lesson period
Second semester
In case of travel restrictions due to Covid-19, the lectures could be delivered in remote mode. In this case, lectures will be pre-recorded and made available through a dedicated web site. Interaction with the teachers will be provided through the Forum application on the Ariel web site, by email or through dedicated Zoom sessions.
Course syllabus
Course Syllabus
1 - Oscillations
- Harmonic oscillator
- Elements of differential equations
- Damped oscillator
- Introduction to complex numbers
- Forced-damped oscillator

2 - Mechanical waves: vibrating string
- Free string
- Derivation of D'Alembert equation and its properties
- Properties of the solutions, harmonic waves
- Bounded string and standing waves, normal modes
- Power transferred by a wave
- Transmission and reflection of waves

3 - Mechanical waves: acoustics
- Pressure, density and temperature of a gas
- Equation of state and thermodynamic transformations for an ideal gas
- Acoustic waves in an ideal gas; equation of motion
- Speed of sound; isothermal and adiabatic models
- Standing waves in pipes; normal modes
- Power transferred by an acoustic wave
- Plane waves and spherical waves; wave function
- Phonometry; sound level
- Geometrical attenuation and absorption
- Sound perception, music instruments
- Doppler effect

4 - Introduction to Fourier analysis
- Normal modes and the Fourier series of sines and cosines
- Fourier coefficients, spectrum and examples
- Complex definition, the Fourier Transform
- Duality of configuration and Fourier spaces: principle of uncertainty
- Dispersion relation and beats
- De Broglie waves and Fourier packets
- Nature of "matter waves"
- The quantum wave equation

5 - Reflection and refraction of waves
- Snell-Descartes law
- Fermat's principle
- Total internal reflection
- Reflection and transmission coefficients
- Chromatic dispersion

6 - Interference and diffraction of light and sound waves
- Spectrum of electromagnetic waves; wave-particle duality
- Interference and beatings
- Huygens-Fresnel principle
- Fraunhofer diffraction by an aperture
- Double slit interference
- Rayleigh criterion
- Diffraction grating
- Interference by a thin film
- Michelson interferometer

7 - Geometrical optics
- Paraxial approximation; imaging
- Plane and curved mirror; diopters; thin lenses; lensmaker equation
- Systems of mirrors and lenses and optical instruments
Prerequisites for admission
- calculus
- trigonometry
- elements of mechanics
Teaching methods
The course includes classroom lectures. The introduction to the different topics starts typically from the observed phenomenology, followed by the derivation of simple linear descriptive models. The phenomenological introduction is often accompanied by experimental demonstrations, as to visualize the phenomenon under study. Lectures are complemented by sets of class exercises, during which quantitative problems are solved using the formulas and methods developed in the lectures.
Teaching Resources
- Video-lectures, L. Guzzo
- Fleisch, Kinnaman, Guida allo Studio delle Onde, Ed. Riuniti
- Mazzoldi-Nigro-Voci, Fisica 2, Edises
Additional textbooks:
- Halliday-Resnick-Krane, Fisica vol 1 e 2, CEA
- Jewett & Serway, Principi di Fisica, vol 1, Edises
- Bettini, Le onde e la luce, Zanichelli
Assessment methods and Criteria
The exam consists in a written test, followed by an oral test. The former includes a series of exercises at the same level of those proposed by the teacher during class exercises. The written exam has to be completed within two hours. Students attending the lectures can decide to split the final written test with two partial tests, respectively half-way and at the end of the course. The tests consist of exercises analogous to those of the global final test, but involving only topics of the corresponding part of the program. To access the oral exam, students must have obtained a mark above the minimum threshold (18/30) in both partial tests. The mark obtained in the written test(s) is valid for one calendar year. A collection of previous exam tests is made available on the course website. In case of a reprise of the Covid emergency, the procedures of the written exam may be modified, as happened during the past two academic years. This will be notified and explained during the course, if the need for that emerges.

The oral exam lasts approximately twenty minutes and involves questions about oscillatory phenomena and their theoretical description, as explained during the lectures. Particularly relevant is the ability to properly describe the phenomenology of the physical processes under discussion, correctly deriving the corresponding theoretical description. The ability to elaborate upon the concepts introduced in the lectures, applying them to new situations is also particularly important.
FIS/01 - EXPERIMENTAL PHYSICS - University credits: 7
Practicals: 24 hours
Lessons: 40 hours
Professor: Guzzo Luigi

CORSO B

Responsible
Lesson period
Second semester
The course will be delivered entirely remotely in case of
restrictions due to Covid-19. In this case, the lectures will be offered in synchronous form.
Course syllabus
1 - Oscillations
- harmonic oscillator
- Damped oscillator
- Forced-damped oscillator

2 - Mechanical waves: vibrating string
- Free string; wave equation
- Bounded string; normal modes;
- Interference and standing waves
- Harmonic waves
- Power transferred by a wave
- Transmission and reflection of waves

3 - Mechanical waves: acoustics
- Pressure, density and temperature of a gas
- Equation of state and thermodynamic transformations for an ideal gas
- Acoustic waves in an ideal gas; equation of motion
- Speed of sound; isothermal and adiabatic models
- Standing waves in pipes; normal modes
- Power transferred by an acoustic wave
- Plane waves and spherical waves; wave function
- Phonometry; sound level; geometrical attenuation and absorption
- Doppler effect

4- Reflection and refraction of waves
- Snell-Descartes law
- Fermat's principle
- Total internal reflection
- Reflection and transmission coefficients
- Chromatic dispersion

5- Interference and diffraction of light and sound waves
- Spectrum of electromagnetic waves; wave-particle duality
- Interference and beatings
- Huygens-Fresnel principle
- Fraunhofer diffraction by an aperture
- Double slit interference
- Rayleigh criterion
- Diffraction grating
- Interference by a thin film
- Michelson interferometer

6 - Geometrical optics
- Paraxial approximation; imaging
- Plane and curved mirror; diopters; thin lenses; lensmaker equation
- Systems of mirrors and lenses and optical instruments
- Polarization of light
Prerequisites for admission
- integral and differential calculus
- trigonometry
- elements of mechanics
Teaching methods
The course includes classroom lectures. The arguments are introduced starting from phenomenology, to arrive at formulating simple linear descriptive models. The phenomenological introduction is accompanied by experimental demonstrations, in order to allow students to visualize the phenomena illustrated. The lectures are supported by a part of exercises, during which quantitative problems are solved using the theoretical models formulated during the lectures.
Teaching Resources
Mazzoldi-Nigro-Voci, Fisica 2, Edises
Additional texts:
- Halliday-Resnick-Krane, Fisica vol 1 e 2, CEA
- Jewett & Serway, Principi di Fisica, vol 1, Edises
- Bettini, Le onde e la luce, Zanichelli
Assessment methods and Criteria
The exam includes a written test followed by an oral test. The written test includes some exercises of difficulty similar to that of the problems proposed during the exercises. The written test is valid for one calendar year. On the website of the teaching a collection of exam topics is available. The oral exam lasts approximately thirty minutes and consists of answering questions about oscillations, mechanical and light waves. The ability to describe the phenomenology of the physical processes under discussion and the ability to correctly reproduce the related descriptive models are assessed. The critical reasoning ability to deal with new problems is also assessed.
FIS/01 - EXPERIMENTAL PHYSICS - University credits: 7
Practicals: 24 hours
Lessons: 40 hours
Professor: Vailati Alberto
Professor(s)
Reception:
Upon email appointment
To be defined (either at the Department or via Zoom teleconference)