ZDK_06 Math and Physics for Sound Design

Faculty of Arts
Autumn 2021
Extent and Intensity
2/2/2. 5 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. Ing. Bc. Vlasta Sedláková, Ph.D. (lecturer)
Mgr. Naděžda Bogatyreva, Ph.D. (lecturer)
prof. Ing. Jarmila Dědková, CSc. (assistant)
doc. Ing. Jiří Schimmel, Ph.D. (assistant)
Ing. Radim Číž, Ph.D. (assistant)
Guaranteed by
doc. Ing. Bc. Vlasta Sedláková, Ph.D.
Department of Musicology – Faculty of Arts
Contact Person: Mgr. Jan Karafiát
Supplier department: Department of Musicology – Faculty of Arts
Prerequisites
In general, the secondary-school level of knowledge from the area of mathematics and physics is required. It is assumed that student can transform and simplify expressions, solve basic equations and inequalities, modify equations with logarithms, complex numbers and trigonometric functions and know the basic definitions and laws of mechanics. A general knowledge of programming and computer skills are welcomed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main objective of the course is to explain basic concepts of mathematics and physics and introduce methods of differential and integral calculus, principles of oscillations and waves and their associations with a sound and musical instruments.
Learning outcomes
Student, who passed the course, is able:
- to add and multiply matrices, and compute the determinant and the inverse of a square matrix,
- to solve a system of linear equations,
- to differentiate and find the tangent to the graph of a function,
- to integrate using basic formulas including integration by parts,
- to evaluate a definite integral and to compute the area of a region using the definite integral,
- to work with the cumulative distribution function, the probability mass function and the probability density function,
- to characterize harmonic motion, damped and forced oscillations, to describe various harmonic oscillators,
- to explain properties of travelling and standing harmonic waves, illustrate the Doppler effect,
- to define basic quantities and to describe basic characteristics of acoustic waves,
- to describe physical principles of musical instruments.
Syllabus
  • 1. Vectors and matrices, trigonometric functions, coordinate systems, logarithmic quantities, logarithm theorems.
  • 2. Course of a function, limit and continuity of a function of one variable, derivation of a function of one variable.
  • 3. Integral calculus of functions of one variable, primitive functions, indefinite integral, definite integral and its applications, complex numbers.
  • 4. Kinematics and dynamics of a material point, uniform and uniformly accelerated motion, Newton's laws of motion, work, energy, power.
  • 5. Oscillating motion, mechanical oscillator, natural harmonics, kinematic and dynamic description.
  • 6. Energy of oscillating motion. Damped oscillations, forced oscillations, resonances.
  • 7. Mechanical waves, successive longitudinal and transverse waves, wave equation. Harmonic wave - basic description, phase velocity, transverse velocity. Waveform, diffraction, reflection and refraction. Energy and intensity of waves.
  • 8. Superposition and interference of waves, standing waves, echoes. Fourier series, Fourier transform, spectrum of periodic and non-periodic signals with continuous time. Doppler effect.
  • 9. Speed ​​of wave propagation on a string, natural oscillations on a string, principle of string instruments. Sound waves, speed of sound propagation, energy quantities, levels, natural oscillations in a tube, principle of wind instruments.
  • 10. Electric charge, electric field, intensity, potential, voltage. Conductor in electrostatic field, capacitance, capacitor, electric dipole, dielectric in electrostatic field, polarization of dielectric, piezoelectrics.
  • 11. Electric current, Ohm's law, electric resistance, resistor, work and power of electric current, electric source.
  • 12. Magnetic field, magnetic induction lines, magnetic induction, magnetic force action, coil and its magnetic field, magnetic properties of substances, ferromagnets, transformer.
  • 13. Natural, damped and forced electromagnetic oscillations, energies of electromagnetic oscillations. Comparison of mechanical and electromagnetic oscillations.
Literature
  • FONG Yuen, WANG Yuan: Calculus. Springer-Verlag, 2000, ISBN 9813083018
  • HALLIDAY, David, Robert RESNICK and Jearl WALKER. Fyzika. Translated by Petr Dub - Miroslav Černý - Jiří Komrska - Michal Lenc - Bohum. Druhé přepracované vydán. Brno: VUTIUM, 2013, x, 1248. ISBN 9788021441231. info
  • GASCHA, Heinz and Stefan PFLANZ. Kompendium fyziky : vzorce, zákony a pravidla, úlohy, příklady a jejich řešení, podrobná slovníková část. Vyd. 1. [Praha]: Universum, 2008, 488 s. ISBN 9788024220130. info
  • DELVENTHAL, Katka Maria, Alfred KISSNER and Malte KULICK. Kompendium matematiky : vzorce a pravidla : četné příklady včetně řešení : od základních operací po vyšší matematiku. Translated by Jiří Henzler. V Praze: Knižní klub, 2004, 714 s. ISBN 8024212277. info
Teaching methods
Self-study on the basis of teaching materials in IS with possible consultations.
Assessment methods
The final grade depends on total sum of points obtained during the computer exercises and for the written exam of the course. Student can obtain:
- up to 30 points for all computer exercises, during them student obtain points for correctly processed tasks and for the correctly answered questions of the final test.
- up to 70 points for compulsory exam, which has a written form and only students who passed ¾ of computer exercises, at least, and the final test can try to pass the exam. If the examiner has a problem with the evaluation of the written exam, he/she can put supplement oral questions to the student.
50 points is the minimum needed to successfully pass the course.
Language of instruction
Czech
Further comments (probably available only in Czech)
Information on completion of the course: 3 testy
The course is taught annually.
The course is taught: in blocks.
Listed among pre-requisites of other courses
Teacher's information
In the combined form of study there will be a continuous evaluation of acquired knowledge in the form of tests. Study preparation for the tests will take the form of self-study (see study materials) with the possibility of consultation.
The course is also listed under the following terms Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2021, recent)
  • Permalink: https://is.muni.cz/course/phil/autumn2021/ZDK_06