University of St Andrews

Key information

SCOTCAT credits : 15

ECTS credits : 7

Level : SCQF level 10

Semester: 1

Availability restrictions: Not automatically available to General Degree students

Musical instruments function according to the laws of physics contained in the wave equation. Wind instruments, the human voice and the acoustics of concert halls can be explained largely by considering waves in the air, but understanding drums, percussion, string instruments and even the ear itself involves studying the coupling of waves in various media. The concepts of pitch, loudness and tone are all readily explained in quantitative terms as are the techniques that musicians and instrument makers use to control them. The module includes a look at how digital audio of musical instrument sounds can be analysed and synthesised using a programming language such a Python.

Relationship to other modules

Pre-requisite(s): Before taking this module you must pass PH3081 or pass PH3082

Learning and teaching methods and delivery

Weekly contact: 3 lectures or tutorials.

Scheduled learning hours: 30

Guided independent study hours: 120

Assessment pattern

As used by St Andrews: Written examinations :80%. Continual assessment: 20%


Re-assessment: Oral Re-assessment, capped at grade 7

Personnel

Additional information from school

PH4036 - Physics of Music

Aims & Objectives

To provide a detailed overview of the physics involved in the production, analysing and synthesizing of musical sounds.

Learning Outcomes

By the end of this module, students are expected to be able to:

• Derive the wave equation in one, two and three dimensions.

• Know expressions for acoustic pressure and volume velocity for acoustic plane waves in free space and in cylindrical pipes.

• Derive the specific acoustic impedance in free space and the acoustic impedance in cylindrical pipes and the effect of boundary conditions such as side holes, branches and open or closed ends.

• Derive the Fourier series for sine waves, pulse waves, square waves and triangle waves and relate these to sound synthesis and the harmonic series and sound generation in real musical instruments.

• Describe beats, perception of roughness, pitch differences in cents and standard musical intervals from the perspective of the relationship between harmonic series, equal temperament and just intonation for standard musical intervals.

• Derive approximate frequencies of the formants of the vocal tract and describe the separate roles of the harmonic series and of the formants in forming vowel sounds.

• Derive the decibel values associated with spherical waves in free space, absorption of plane waves and diffuse sound fields in rooms.

• Develop skills in using computer programming in a language such as Python on digital audio and in report writing.

Synopsis

Beats, Fourier series. Discrete Fourier transform and using Python. Plucked, struck and bowed strings. Air damping. Vibrating membranes and plates. Wave equation in air. Transmission and reflection, losses and radiation. Standing waves, pipes, cross-section changes, side holes. The ear and perception of musical sound. Scales and temperament. Reverberation and architectural acoustics. Case studies on strings, drums, woodwind, brass, and voice. Synthesizing musical sound (additive, subtractive, FM, wave-table and physical modelling).

Accreditation Matters

This module may not contain material that is part of the IOP “Core of Physics”, but does contribute to the wider and deeper learning expected in an accredited degree programme.  The skills developed in this module, and others, contribute towards the requirements of the IOP “Graduate Skill Base”.

Recommended Books

Please view University online record:

http://resourcelists.st-andrews.ac.uk/modules/ph4036.html

General Information

Please also read the general information in the School's honours handbook that is available via st-andrews.ac.uk/physics/staff_students/timetables.php