# Tag Info

Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. Applications of acoustics are for instance the audio and noise control industries.

## When to Use this Tag

Use when asking questions about the generation, propagation, or absorption of elastic waves in solids, liquids, or gases. For similar problems of wave motion in the electro-magnetic field, use the tag .

## Introduction

Acoustic may exist in any elastic medium which is capable of experiencing compression and rarefaction. This is manifestly true in the case of liquids and gases. However even solids, which are often taken to be perfectly incompressible, can sustain small oscillations of their constituent atoms about some mean position which enables wave propagation throughout the material. Generally speaking, the higher the compressibility of a material, the lower its speed of sound.

## Equations of Motion

Wave motion in a variety of different contexts is governed by the classical acoustic wave equation

$$\frac{\partial^2\phi}{\partial t^2} - c^2\nabla^2\phi = 0$$

where $\phi$ may represent the local displacement of a solid structure, acoustic pressure in a fluid, etc., and $c$ is the speed of sound in the medium. This linear partial differential equation has been derived on the hypothesis that the perturbation quantity $\phi$ is small relative to a mean value. Generalizations to this equation may be obtained which incorporate more exotic physical effects such as dispersion, convection of acoustic energy, and nonlinear wave steepening.

## Prerequisites for Studying Acoustics

Phys: Some exposure to rigid body dynamics and fluid mechanics

Math: Ordinary Differential Equations (ODEs), Partial Differential Equations (PDEs)