Speech and Audio Signal Processing: Processing and Perception of Speech and Music, Second Edition

CHAPTER 10

WAVE BASICS

10.1 INTRODUCTION

Many pleasing sounds are produced by carefully designed and carefully controlled acoustic tubes or vibrating strings).¹ A brief categorization of some of these sounds follows: (a) plucked string instruments such as guitars, banjos, mandolins, and harps are set into vibration by the musician directly (i.e., with fingers); (b) bowed string instruments such as violins, violas, and cellos are set into vibration by the frictional force between the bow and string. (c) Struck string instruments like the piano are set into vibration by a complicated mechanism following the depression of the piano keys by the performer. (d) Acoustic tube resonances in the human vocal tract help produce the sounds of speech or music. (e) Acoustic tube resonances in brass instruments such as trumpets, cornets, flugelhorns, and trombones are excited by the player's lip vibrations. (f) Acoustic tube resonances in the clarinet and oboe produce sound stimulated by a vibrating reed that is set into vibration by the player's breath stream.

Many instruments can be mathematically characterized by the wave equation, a partial differential equation in both time and space. For example, the vibration of a plucked guitar string is described by knowing the motions of every point along the string. We will see that the solutions to the simplest wave equation consist of traveling ...