Mechanics and Acoustics

Language of Instruction:Czech
Completion:classified credit
Type of
Guarantor:Koktavý Pavel, prof. Ing., CSc. Ph.D. (DPHYS)
Deputy guarantor:Grmela Lubomír, prof. Ing., CSc. (DPHYS)
Lecturer:Koktavý Pavel, prof. Ing., CSc. Ph.D. (DPHYS)
Faculty:Faculty of Electrical Engineering and Communication BUT
Department:Department of Physics FEEC BUT
Learning objectives:
  Understand the basic physical phenomena of mechanics and acoustics with emphasis on mastering the description and finding solutions to the basic problems of these areas so that the acquired skills can be later used in some computer applications, eg in signal processing or in modeling and simulation.
  The course gives an overview of basic concepts and laws in the field of mechanics. Students are acquainted with the procedures for compiling equations of motion and using software tools for their solution, with problems of choice of initial conditions, displaying and interpreting the obtained solution. There are presented basic quantities and principles of acoustics, especially physics, musical and physiological acoustics. Basic information on ultrasound and infrasound is also provided to the students.
Knowledge and skills required for the course:
  Vector operations. Fundamentals of differential calculus and integral calculus. For students of the first year, it is sufficient to obtain knowledge of differential and integral calculus in the parallel course of Mathematical analysis (IMA).
Learning outcomes and competencies:
  Students understand the basic physical processes of mechanics and acoustics, they are able to formulate relevant laws both verbally and mathematically, they can solve the basic problems related to these processes using suitable software support and can present and interpret the obtained results. They are able to describe and explain the laboratory experiments.
Why is the course taught:

It is very important to be able to analyze, describe and solve technical problems and situations around them for students of this school.

In addition to these general skills, the students will acquire a great deal of specific knowledge in mechanics and acoustics, which they will use advantageously in a number of other courses for example in signal processing or modeling and simulation.

Syllabus of lectures:
  1. Kinematics of the mass point. Position, velocity and acceleration, linear and curvilinear motion, superposition principle, circular motion.
  2. Dynamics of the mass point. Newton's laws, equation of motion, inertial and noninertial systems, work and impulse of force, energy and momentum, moment of force and angular momentum.
  3. Gravitational field. Newton's law of gravity, intensity and potential, planetary and satellite movements.
  4. A set of mass points and a rigid body. Center of gravity, momentum theorem, angular momentum theorem, equilibrium and motion, kinetic energy, moment of inertia, friction, pendulums, gyroscope.
  5. Impact of bodies. Impact forces, perfectly elastic impact and inelastic impact, direct and oblique impact, rotating impact, ball, wall reflection, billiards, Newton's cradle.
  6. Deterministic chaos in mechanical systems. Conditions for chaotic behavior, attractor, strange attractor, double pendulum.
  7. Fundamentals of analytical mechanics. Generalized coordinates and forces, Lagrange equations of the 2nd type, mathematical pendulum, particles in a central force field, two-body and three-body problems.
  8. Oscillations. Oscillatory motion, oscillator, harmonic oscillations, superposition and decomposition of oscillations, free, damped and forced oscillations, coupled oscillators.
  9. Waves. Travelling wave, phase velocity, wave reflection, refraction, diffraction, superposition and interference, standing wave, resonance vibrations in a string and in a tube, wave equation.
  10. Physical acoustics. Acoustic displacement and pressure, sound propagation velocity, acoustic impedance, specific power and intensity, sound pressure and intensity levels, sound field, Doppler effect.
  11. Music acoustics. Tone and noise, musical interval, consonance and dissonance, musical scale, natural and equal temperament tuning, tone color, musical instruments, noise.
  12. Physiological acoustics. Sound perception, spectral composition, sum and difference tones, volume, sound masking, sound measurement, noise.
  13. Ultrasound and infrasound. Properties, sources and detectors, propagation, effects, utilization, ultrasound diagnostics and defectoscopy.
Syllabus of laboratory exercises:
 Laboratory exercises  lasting 2 hours take place once every 2 weeks.
  1. Movement of the body on an inclined plane, impact forces.
  2. Moment of inertia, gyroscope.
  3. Study of oscillatory motion.
  4. Composition and decomposition of periodic signals, sum and difference tones, sound masking.
  5. Resonance vibrations of string.
  6. Sound/noise measurement, Doppler Phenomenon, ultrasound diagnostics.
Syllabus of computer exercises:
 Computer exercises lasting 2 hours take place once every 2 weeks.
  1. Mass point mechanics - projectile motion, inclined plane, equation of motion, software tools for its solution, choice of initial conditions, display and interpretation of the solution.
  2. Gravitational Field - solving body motion in a central-force field.
  3. Rigid body - equations of motion for translational and rotational motion, gyroscope, impact of bodies.
  4. Pendulums - linear and nonlinear description, chaotic behavior of the double pendulum.
  5. Oscillations - free, dumped and forced oscillations, coupled oscillators, Lissajous figures.
  6. Acoustics - superposition and interference of waves, creation of sum and difference tones.
Syllabus - others, projects and individual work of students:
 Each student solves two projects, each of them contains selected problems from the given area. For each problem, the student makes the description and then, with appropriate software support, performs the solution with a graphical representation and discussion of the results or simulates the course of the specified process.
  1. Individual project No. 1 (20 points): Mechanics
  2. Individual project No. 2 (20 points): Acoustics
Fundamental literature:
  • Halliday, D.; Resnick, R.; Walker, J. Fyzika. Vysoké učení technické v Brně, VUTIUM, Prometheus Praha, 2000, 2003, 2006, 2013.
  • Feynman, R; Leighton, R; Sands, M. Feynmanovy přednášky z fyziky 1-3, Fragment 2001, 2007, 2013.
Study literature:
  • Halliday, D.; Resnick, R.; Walker, J. Fyzika. Vysoké učení technické v Brně, VUTIUM, Prometheus Praha, 2000, 2003, 2006, 2013.
  • Support Electronic texts
Controlled instruction:
  Attendance at lectures is not compulsory. Knowledge of students is verified by two individual projects and a final individual work (written work using software support).

Compulsory lessons are laboratory exercises and computer exercises. Well-excused exercises can be compensated. In the laboratory exercises the students do not elaborate the reports, the evaluation of the measurements is made during the lesson.

Progress assessment:
  • Laboratory exercise: 30 points. Points are obtained for work and activity in exercises. No laboratory reports.
  • Two individual projects: a total of 40 points.
  • Final individual work (written work using software support): 30 points.
Exam prerequisites:
  To take the credit it is necessary to take part in all laboratory and computer exercises. Well-excused exercises can be replaced.

During the semester it is possible to get a point assessment for final independent work (written work using software support), two projects and work in laboratory exercises. It is necessary to obtain at least 50 points to obtain a credit. Classification is performed according to the standard scale.


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