Matematičko modeliranje puhačkih instrumenata

master's thesis

• Author: Melita Malezan Jurić
• Mentor: Eduard Marušić-Paloka (mentor)
• Committee member: Eduard Marušić-Paloka (predsjednik povjerenstva)
• Committee member: Ivica Nakić (član povjerenstva)
• Committee member: Vedran Krčadinac (član povjerenstva)
• Committee member: Juraj Šiftar (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-04-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U radu je dana klasifikacija puhačkih instrumenata i pripadne matematičke formulacije proizvodnje zvuka koji oni proizvode. Analiziran je rombos, slobodni aerofon i dane su jednadžbe koje opisuju njegovo gibanje prilikom njegovog sviranja. Izvedena je valna jednadžba za prave aerofone cjevastog oblika, te jednadžbe harmonika. Opisana su osnovna svojstva valova; princip superpozicije i stojni valovi. U ovisnosti o građi pravog aerofona, jesu li obje strane cijevi otvorene (u slučaju flaute) ili je jedna strana zatvorena (u slučaju klarineta) dobivamo pripadni skup harmonika. Od pravih aerofona analizirani su skandinavska frulica, okarina i rog.

Abstract (english)

In this paper the classification of wind instruments is given, alongside the mathematical formulation on making of the sound. The analysis of the bullroarer, the free aerophone and the equations that describe his motion while it’s being played is performed. Derivation of the wave equation is done for proper aerophones that are tube-shaped as well as harmonic equations. Basic wave properties are described such as superposition principle and standing waves. Depending on the structure of proper aerophone, weather the both sides of the tube are open (in case of the flute) or one side of the tube is closed (in case of the clarinet) we’re getting harmonics set accordingly. Proper aerophones that have been analysed are willow flute, ocarina and the horn.

• Keywords: klasifikacija puhačkih instrumenata; rombos; slobodni aerofon; osnovna svojstva valova; princip superpozicije; stojni valovi; skandinavska frulica; ocarina; rog
• Keywords (english): classification of wind instruments; bullroarer; free aerophone; basic wave properties; superposition principle; standing waves; willow flute; ocarina; horn
• Language: croatian
• URN:NBN: urn:nbn:hr:217:092332
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-06-09 09:18:45