Waves and Continuous Media

Code:

F201

Acronym:

F201

Keywords
Classification	Keyword
OFICIAL	Physics

Instance: 2013/2014 - 1S

Active?	Yes
Responsible unit:	Department of Physics and Astronomy
Course/CS Responsible:	Bachelor in Physics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:AST	17	Plano de Estudos a partir de 2008	2	-	7,5	-
L:B	0	Plano de estudos a partir de 2008	3	-	7,5	-
L:CC	0	Plano de estudos de 2008 até 2013/14	3	-	7,5	-
L:F	53	Plano de estudos a partir de 2008	2	-	7,5	-
L:G	0	P.E - estudantes com 1ª matricula anterior a 09/10	3	-	7,5	-
		P.E - estudantes com 1ª matricula em 09/10	3	-	7,5	-
L:M	0	Plano de estudos a partir de 2009	3	-	7,5	-
L:Q	0	Plano de estudos Oficial	3	-	7,5	-
MI:EF	28	Plano de Estudos a partir de 2007	2	-	7,5	-

Teaching language

Portuguese

Objectives

Train ideas and methods of wave mechanics, elasticity and hydrodynamics. • Understand the linear coupling between oscillators, the basic of normal modes. • Understand the concept of wave, and their description and their applications in various areas of applied physics. • Perform Fourier analysis, as well as understand its importance in the study of linear waves. • Understand the result of overlapping waves and the phenomenon of interference and diffraction. • Understand the concepts of phase velocity and group velocity and the concept of dispersion. • Understand and describe the state of deformation and the stresses applied in isotropic elastic body, as well as relate the two. • Analyze simple problems of fluid dynamics and fluid balance. • Connecting to technology issues.

Learning outcomes and competences

Train ideas and methods of wave mechanics, elasticity and hydrodynamics. • Understand the linear coupling between oscillators, the basic of normal modes. • Understand the concept of wave, and their description and their applications in various areas of applied physics. • Perform Fourier analysis, as well as understand its importance in the study of linear waves. • Understand the result of overlapping waves and the phenomenon of interference and diffraction. • Understand the concepts of phase velocity and group velocity and the concept of dispersion. • Understand and describe the state of deformation and the stresses applied in isotropic elastic body, as well as relate the two. • Analyze simple problems of fluid dynamics and fluid balance. • Connecting to technology issues.

 

Working method

Presencial

Program

Vibrations A mechanical harmonic oscillator 1 1.1 Mechanical Energy of the harmonic oscillator 1.2 Superposition of two harmonic simple oscillations (1D). Phasors. 1.2.1 Simple oscillations of different frequencies; beats. 1.2.2 Overlap of two oscillations with the same simple frequency and orthogonal directions 1.3 Overlap of n (n>> 1) simple harmonic oscillators the same amplitude and phase differences of consecutive equal. 1.4 Overlap of n (n>> 1) simple harmonic oscillators equal amplitudes and random phases. 2. Harmonic oscillator with damping 2.1 Energy of the oscillator with damping 2.1.1 Quality factor, Q [I]. 3 Forced oscillations. 3.1 Energy associated with the applied force. 3.1.1 Curve absorption. 3.1.2 Quality factor, Q [II]. 3.2 Applications. Problem I. 4 Coupled oscillators. 4.1 Normal modes. 4.2 Fourier series and integral. 4.2.1 Simple example. 4.2.2 Fourier Series expressed in the complex variable. 4.2.3 Fourier Integral. 4.3 Applications. Problems II. Waves 5 Transverse waves on strings. 5.1 Kinetic energy and potential. 5.2 Characteristic impedance of a rope. 5.3 Discontinuity in a rope, changes in linear density. 5.3.1 Standing waves on strings of finite length. 5.3.2 Energy of each mode of vibration. 5.4 Group Velocity. 5.4.1 Group Velocity of a wave of n (n> 2) compo- sinusoidal components. 5.5 Waves in two dimensions. 6 Longitudinal waves in bars homogeneous and isotropic. 6.1 Equation of motion. 6.2 Energy of vibration modes. 6.3 Sound waves in a gas. 6.3.1 Characteristic impedance. 6.3.2 Kinetic energy and potential of the sound wave. 6.3.3 Intensity of the wave. 7 Electromagnetic waves. 7.1 Waves in a vacuum. 7.2 Intensity of electromagnetic wave. 7.3 Diffraction. 7.3.1 Diffraction by a single slit of width L. 7.3.2 Diffraction by N slits of width L and spacing d, L <d. 7.3.3 The theory of diffraction and Fourier. 7.3.4 Diffraction by a wide slot and the uncertainty principle Heisenberg. 7.4 Transmission of electromagnetic energy in limited ways. 7.4.1 Transmission lines (parallel conductors and coaxial cables) 7.4.2 Waveguides. 7.5 Applications. Problems III. Elasticity 8 Elasticity 8.1 Hooke's Law. 8.2 Deformations uniform. And compression. 8.3 Twist. 8.3.1 Torsional waves. 8.4 Bending of a bar. 8.4.1 Buckling. 8.5 Applications. Problems IV. Fluid Fluids 9 9.1 Hydrostatic. 9.1.1 Equation of equilibrium. 9.2 Hydrodynamics. 9.2.1 Equation of continuity. 9.2.2 Equation of motion. 9.2.3 Euler equation. 9.2.4 Steady state. Bernoulli's equation. 9.2.5 Simple examples of application of the Bernoulli equation. 9.2.6 Viscosity. 9.2.7 Poiseuille's Law. 9.2.8 viscous fluid in a rotating motion between coaxial two-cylinders. 9.3 Applications. Problems V.

Mandatory literature

José Machado da Silva; Ondas e Meios Contínuos, U.Porto editorial, 2013
Young Donald F. 070; Introduction to fluid mechanics. ISBN: 9780470902158
French A. P.; Vibrations and waves
Pain H. J.; The physics of vibrations and waves. ISBN: 0-471-99407-3
Main Iain G.; Vibrations and waves in physics. ISBN: 0-521-21662-1

Teaching methods and learning activities

Classroom teaching with lectures, practical and theoretical computational practices.

Distribution by SIGARRA of notes (lectures support); classes of problems  and examples of programming in Python for solving problems (computational support for practical lessons).

Software

Linguagem de programação Python

keywords

Physical sciences
Physical sciences > Physics > Classical mechanics > Fluid dynamics
Physical sciences

Evaluation Type

Evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Frequência das aulas	0,00
Total:	0,00

Calculation formula of final grade

A final written test with problems. This includes an issue about computational application (mark 1.5/20).