Fundamentals of Acoustics

Learning Outcomes

Disciplinary Specific Learning Outcomes

Having successfully completed this module you will be able to:

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

Knowledge and Understanding

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

• The derivation of the wave equation and Helmholtz Equation from linearised conservation equations (SM7M).
• The use of a sound level meter and intensity probe, and the use of standard bandwidths and frequency weightings (contributes to P2m).
• 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 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).
• The propagation of longitudinal acoustic disturbances in the form of plane waves and waves in a free environment (SM7M).

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. 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.

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.

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.

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 and directivity.

7. Sound reflection, transmission, refraction and attenuation:

Reflection and transmission at a fluid-fluid interface. The transmission and reflection coefficients. Normal and oblique incidence, evanescent waves and Snell’s law. Transmission loss of a finite layer at normal incidence, and of a reactive silencer.

8. Laboratory sessions:

Use of sound level meters for noise measurement (BS4142). Sound power measurement (BS EN ISO 3740:2019).

This is a one-semester course, taught in the 'flipped classroom' mode with two in-person tutorials per week. There are also two laboratory sessions. Regular formative problem sheets are set and marked via Teams to give students practice at solving acoustics problems.

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.