Course detail

# Mechanics and Acoustics

FIT-IMKAcad. year: 2018/2019

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.

Supervisor

Department

Learning outcomes of the course unit

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.

Prerequisites

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).

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

- Halliday, D.; Resnick, R.; Walker, J. Fyzika. Vysoké učení technické v Brně, VUTIUM, Prometheus Praha, 2000, 2003, 2006, 2013.
- Texty přednášek, návody k laboratorním a počítačovým cvičením ve formátu pdf.

- 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.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

- 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.

Language of instruction

Czech, English

Work placements

Not applicable.

Course curriculum

**Syllabus of lectures:**

**Syllabus of laboratory exercises:**

Aims

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.

Specification of controlled education, way of implementation and compensation for absences

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.

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

- 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 behavior, 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 color, 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.

Computer exercise

12 hours, compulsory

Teacher / Lecturer

Syllabus

Computer

exercises lasting 2 hours take place once every 2 weeks.

- 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. - Gravitational

Field - solving body motion in a central-force field. - Rigid body -

equations of motion for translational and rotational motion, gyroscope, impact

of bodies. - Pendulums - linear

and nonlinear description, chaotic behavior of the double pendulum. - Oscillations - free,

dumped and forced oscillations, coupled

oscillators, Lissajous figures. - Acoustics -

superposition and interference of waves, creation of sum and difference tones.

Laboratory exercise

12 hours, compulsory

Teacher / Lecturer

Syllabus

Laboratory

exercises lasting 2 hours take place

once every 2 weeks.

- 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.

Projects

12 hours, compulsory

Teacher / Lecturer

Syllabus

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.

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

eLearning

**eLearning:** currently opened course