Course details

# Mechanics and Acoustics

IMK Acad. year 2019/2020 Summer semester 6 credits

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Assessment points

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Subject specific learning outcomes and competences

Learning objectives

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 modelling and simulation.

Prerequisite kwnowledge and skills

Study literature

- Halliday, D.; Resnick, R.; Walker, J. Fyzika. Vysoké učení technické v Brně, VUTIUM, Prometheus Praha, 2000, 2003, 2006, 2013.
- Support Electronic texts

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.

Syllabus of lectures

- Kinematics of the mass point. Position, velocity and acceleration, linear and curvilinear motion, superposition principle, circular motion.
- 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.
- Gravitational field. Newton's law of gravity, intensity and potential, planetary and satellite movements.
- 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.
- Impact of bodies. Impact forces, perfectly elastic impact and inelastic impact, direct and oblique impact, rotating impact, ball, wall reflection, billiards, Newton's cradle.
- Deterministic chaos in mechanical systems. Conditions for chaotic behaviour, attractor, strange attractor, double pendulum.
- 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.
- Oscillations. Oscillatory motion, oscillator, harmonic oscillations, superposition and decomposition of oscillations, free, damped and forced oscillations, coupled oscillators.
- 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.
- Physical Acoustics. Acoustic displacement and pressure, sound propagation velocity, acoustic impedance, specific power and intensity, sound pressure and intensity levels, sound field, Doppler effect.
- Music Acoustics. Tone and noise, musical interval, consonance and dissonance, musical scale, natural and equal temperament tuning, tone colour, musical instruments, noise.
- Physiological Acoustics. Sound perception, spectral composition, sum and difference tones, volume, sound masking, sound measurement, noise.
- Ultrasound and infrasound. Properties, sources and detectors, propagation, effects, utilization, ultrasound diagnostics and defectoscopy.

Syllabus of laboratory exercises

- Movement of the body on an inclined plane, impact forces.
- Moment of inertia, gyroscope.
- Study of oscillatory motion.
- Composition and decomposition of periodic signals, sum and difference tones, sound masking.
- Resonance vibrations of string.
- Sound/noise measurement, Doppler Phenomenon, ultrasound diagnostics.

Syllabus of computer exercises

- Mass point mechanics - projectile motion, inclined plane, the equation of motion, software tools for its solution, choice of initial conditions, display and interpretation of the solution.
- Gravitational Field - solving body motion in a central-force field.
- Rigid body - equations of motion for translational and rotational motion, gyroscope, the impact of bodies.
- Pendulums - linear and nonlinear description, chaotic behaviour of the double pendulum.
- Oscillations - free, dumped and forced oscillations, coupled oscillators, Lissajous figures.
- Acoustics - superposition and interference of waves, the creation of sum and difference tones.

Syllabus - others, projects and individual work of students

- Individual project No. 1 (20 points): Mechanics
- Individual project No. 2 (20 points): Acoustics

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.

Controlled instruction

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.

Exam prerequisites

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.

Schedule

Course inclusion in study plans