ZD_06 Math and Physics for Sound Design

Faculty of Arts
Autumn 2022
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), doc. Ing. Jiří Schimmel, Ph.D. (deputy)
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
Timetable
Wed 13:00–17:40 VP
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 only offered to the students of the study fields 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 differentiate and find the tangent to the graph of a function,
- to integrate using basic formulas
- to evaluate a definite integral and to compute the area of a region using the definite integral,
- to characterize harmonic motion, damped and forced oscillations, to describe various harmonic oscillators, to compare mechanic and electromagnetic oscillations
- 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, trigonometric functions, coordinate systems, logarithmic quantities, logarithm theorems.
  • • 2. Course of a function, 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. Uniform and uniformly accelerated motion, Newton's laws of motion, work, energy, power.
  • • 5. Electric charge, electric field, potential, voltage. Capacitance, capacitor, electric dipole, piezoelectrics.
  • • 6. Electric current, Ohm's law, electric resistance, resistor, work and power of electric current, electric source.
  • • 7. Magnetic field, magnetic induction lines, magnetic induction, magnetic force action, coil and its magnetic field, magnetic properties of substances, ferromagnets, transformer. Properties of electrical circuits with DC and AC sources.
  • • 8. Oscillating motion, mechanical oscillator, natural harmonics, kinematic and dynamic description.
  • • 9. Energy of oscillating motion. Damped oscillations, forced oscillations, resonances.
  • • 10. Natural, damped and forced electromagnetic oscillations, energies of electromagnetic oscillations. Comparison of mechanical and electromagnetic oscillations.
  • • 11. 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.
  • • 12. Superposition and interference of waves, standing waves, echoes. Fourier series, Fourier transform. Doppler effect.
  • • 13. 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
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
Teaching methods comprehend lectures and computer exercises. During the lectures, the theory is explained with the aid of demonstrative solution of typical examples. The computer exercises are focused on solving practical problems from the field of mathematics and physics.
Assessment methods
The final grade depends on the total sum of the points obtained for the seminar work, interim tests and the credit test. Student can obtain:
- up to 10 points for presentation of the seminar work;
- up to 30 points for the correctly answered questions of 3 interim tests.
- up to 60 points for the credit test, which is compulsory, written and only students who have previously submitted/presented a seminar work are allowed to take it.
- Credit is awarded to those students who have completed at least ¾ of the total number of computer exercises, presented a seminar work, passed interim tests and a credit test.
- A minimum of 50 points is required to pass the course.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: 3 testy
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2021, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2022, recent)
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