The University of Southampton
Courses

# ISVR6136 Fundamentals of Acoustics

## Module Overview

This module provides an introduction to the basic elements of acoustics for the purpose of meeting the fundamental needs of practising engineers. This module provides the knowledge and tools to understand and predict the behaviour of complex acoustical systems, including the behaviour of sound propagation in free field and simple bounded environments, and the characteristics of source radiation. It provides the fundamental knowledge required in order to study a range of other modules on more specialist aspects of acoustics. A knowledge of mathematics equivalent to that obtained from a 1st year undergraduate engineering degree is required.

### Aims and Objectives

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• The propagation of longitudinal acoustic disturbances in the form of plane waves and waves in a free environment (SM7M).
• The derivation of the wave equation and Helmholtz Equation from linearised conservation equations (SM7M).
• The behaviour of sound in enclosures including analytical descriptions of sound propagation at both low and high frequencies (SM7M, contributes to SM9M).
• The limitations and characteristics of acoustic sources (SM7M).
• Methods of estimating source sound power from measurements of sound pressure level and sound intensity under different conditions, and the international standards for the measurement of sound power (SM7M, P6, contributes to EL12M).
• The use of a sound level meter and intensity probe, and the use of standard bandwidths and frequency weightings (contributes to P2m).
##### Disciplinary Specific Learning Outcomes

Having successfully completed this module you will be able to:

• Read, understand and interpret the literature relating to basic topics in acoustics (contributes to G1).
• Model simple acoustical problems involving sources of sound in simple geometries (contributes to G1).
• Undertake acoustic measurements and provide critical analysis and conclusions (contributes to P2m, P3 and P6).
• Manipulate complex numbers in the solution of problems associated with wave motion (contributes to SM5m).
• Produce a formal technical report (contributes to G1).

### Syllabus

1. Introduction to Acoustics: Acoustic pressure. rms and mean square pressures. Definition and use of the decibel, and the reasons for its use. Addition of quantities (coherent and incoherent) in decibels. Third-octave bands. Human hearing. A-weighting. Sound level meters. Other acoustic metrics. 2. Introduction to the propagation of acoustic disturbances: Longitudinal wave motion, introduction to plane acoustic waves. Speed of sound, frequency, wavelength, wavenumber, particle velocity, characteristic acoustic impedance. Thermodynamics of acoustic compressions. Linear relationships between basic acoustic quantities. Variation of speed of sound with temperature and pressure. 3. One-dimensional acoustic wave motion: Conservation equations in one dimension; linearisation of governing equations; derivation of one-dimensional wave equation. Solutions to the one-dimensional wave equation. Complex exponential representation of wave motion. Helmholtz equation. Linearity and the superposition principle. Specific acoustic impedance. Acoustic energy density and intensity. Standing waves. Application to impedance tube measurements. Concepts of nonlinear propagation. 4. Waves in three dimensions: Conservation equations in three dimensions; derivation of the three-dimensional wave equation. Solutions to the three-dimensional wave equation. Spherical waves. Impedance of spherical waves. Sound radiation from a pulsating sphere. The point monopole source. Sound intensity due to a spherical wave. Sound power output of a pulsating sphere and its radiation efficiency. Sound Intensity measurement. International standards for sound power measurement. 5. Sound in enclosures: Solution to the three-dimensional wave equation in a room with rigid walled boundaries. Room modes and their natural frequencies. Modal statistics; modal density, modal overlap and the Schroeder frequency. The concepts of a diffuse field and average absorption coefficient; the energy balance equation and reverberation time. Basic auditorium requirements. 6. Sound radiation: The Rayleigh integral for the solution of sound radiation problems. Radiation from a plane vibrating piston. On axis radiation in near and far fields of a circular piston. Directivity and interference. Radiation impedance. 7. Multipole sources: The point monopole source. The point dipole source; vector dipole strength. Concept of quadrupoles. Acoustic source mechanisms. 8. Sound reflection, transmission, refraction and attenuation: Reflection and transmission at a fluid-fluid interface. The transmission and reflection coefficients. Normal and oblique incidence. Refraction in the atmosphere and underwater: Snell’s law. Sound attenuation. 9. Laboratory sessions: Use of sound level meters. Sound power measurement.

### Learning and Teaching

#### Teaching and learning methods

This is a one-semester course, three lectures per week with two laboratory sessions. Lecture notes and tutorial sheets are provided and one-to-one assistance and verbal feedback is facilitated through six tutorial classes with short tests in some. Past exam papers are supplied to aid personal study, feedback and revision. Blackboard is used to allow the lecture materials and additional material to be disseminated (including solutions to past exam papers and recordings of lectures). The students have to write-up two laboratory reports. Students are encouraged to read supporting texts and a booklist is provided.

TypeHours
Revision30
Tutorial6
Lecture30
Practical classes and workshops6
Total study time150

Laboratory space and equipment required. The practical sessions will be held in teaching laboratory 13/4061 using existing experimental designs.

### Assessment

#### Summative

MethodPercentage contribution
Continuous Assessment 30%
Final Assessment  70%

#### Repeat

MethodPercentage contribution

#### Referral

MethodPercentage contribution