Sound and Recording

Applications and Theory

Francis Rumsey

• Publisher: Routledge
• Year: 2021
• ISBN:
  9781000399356
• Edition: 8
• Topic: Media & Performing Arts
• Subtopic: Music Theory & Appreciation

Providing vital reading for audio students and trainee engineers, Sound and Recording is the essential guide for anyone who wants a solid grounding in both theory and industry practices in audio, sound, and recording. This updated and comprehensively restructured edition includes new content on DAW configuration, effects processing, 3D/immersive audio systems, object-based audio, and VR audio technology.

This bestselling book introduces you to the principles of sound, perception, audio technology, and systems. Sound and Recording is the ideal audio engineering text for students, an accessible reference for professionals, and a comprehensive introduction for hobbyists.

CHAPTER 1

Audio and Acoustics

CHAPTER CONTENTS

A Vibrating Source

Characteristics of a Sound Wave

How Sound Travels in Air

Simple and Complex Sounds

Frequency Spectra of Repetitive Sounds

Frequency Spectra of Non-Repetitive Sounds

Phase

Sound in Electrical Form

Displaying the Characteristics of a Sound Wave

The Decibel

Sound Power and Sound Pressure

Free and Reverberant Fields

Standing Waves

Recommended Further Reading

This chapter offers an introduction to some of the basic principles of audio and acoustics, such as the nature of sound in the air and in electrical form, and some units, measurements, and laws that are useful for understanding explanations in the rest of the book.

A Vibrating Source

Sound is produced when an object (the source) vibrates and causes the air around it to move. Consider the sphere shown in Figure 1.1. It is a pulsating sphere which could be imagined as something like a squash ball, and it is pulsating regularly so that its size oscillates between being slightly larger than normal and then slightly smaller than normal. As it pulsates, it will alternately compress and then rarefy the surrounding air, resulting in a series of compressions and rarefactions traveling away from the sphere, rather like a three-dimensional version of the ripples which travel away from a stone dropped into a pond. These are known as longitudinal waves since the air particles move in the same dimension as the direction of wave travel. The alternative to longitudinal wave motion is transverse wave motion (see Figure 1.2), as found in vibrating strings, where the motion of the string is at right angles to the direction of apparent wave travel.

FIGURE 1.1
a) A simple sound source can be imagined to be like a pulsating sphere radiating spherical waves. (b) The longitudinal wave thus created is a succession of compressions and rarefactions of the air.

FIGURE 1.2
In a transverse wave, the motion of any point on the wave is at right angles to the apparent direction of motion of the wave

Characteristics of a Sound Wave

The rate at which the source oscillates is the frequency of the sound wave it produces, and is quoted in hertz (Hz) or cycles per second (cps). 1000 Hz is termed 1 kilohertz (1 kHz). The amount of compression and rarefaction of the air which results from the sphere’s motion is the amplitude of the sound wave, and is related to the loudness of the sound when it is finally perceived by the ear (see Chapter 2). The distance between two adjacent peaks of compression or rarefaction as the wave travels through the air is the wavelength of the sound wave, and is often represented by the Greek letter lambda (λ). The wavelength depends on how fast the sound wave travels, since a fast-traveling wave would result in a greater distance between peaks than a slow-traveling wave, given a fixed time between compression peaks (i.e. a fixed frequency of oscillation of the source).

As shown in Figure 1.3, the sound wave’s characteristics can be represented on a graph, with amplitude plotted on the vertical axis and time plotted on the horizontal axis. It will be seen that both positive and negative ranges are shown on the vertical axis: these represent compressions (+) and rarefactions (−) of the air. This graph represents the waveform of the sound. For a moment, a source vibrating in a very simple and regular manner is assumed, in so-called simple harmonic motion, the result of which is a simple sound wave known as a sine wave. The simplest vibrating systems oscillate in this way, such as a mass suspended from a spring, or a swinging pendulum. It will be seen that the frequency (f) is the inverse of the time between peaks or troughs of the wave (f = 1/t). So, the shorter the time between oscillations of the source, the higher the frequency. The human ear is capable of perceiving sounds with frequencies between approximately 20 Hz and 20 kHz (see ‘Frequency Perception’, Chapter 2); this is known as the audio frequency range or audio spectrum.

FIGURE 1.3
A graphical representation of a sinusoidal sound waveform. The period of the wave is represented by t, and its frequency by 1/t.

How Sound Travels in Air

Air is made up of gas molecules and has an elastic property (imagine putting a thumb over the end of a bicycle pump and compressing the air inside — the air is springy). Longitudinal sound waves travel in air in somewhat the same fashion as a wave travels down a row of up-ended dominoes after the first one is pushed over. The half-cycle of compression created by the vibrating source causes successive air particles to be moved in a knock-on effect, and this is normally followed by a balancing rarefaction which causes a similar motion of particles in the opposite direction.

It may be appreciated that the net effect of this is that individual air particles do not actually travel — they oscillate about a fixed point — but the result is that a wave is formed which appears to move away from the source. The speed at which it moves away from the source depends on the density and elasticity of the substance through which it passes, and in air, the speed is relatively slow compared with the speed at which sound travels through most solids. In air, the speed of sound is approximately 340 meters per second (m s⁻¹), although this depends on the temperature of the air. At freezing point, the speed is reduced to just above 330 m s⁻¹. In steel, to give an example of a solid, the speed of sound is approximately 5100 m s⁻¹.

The frequency and wavelength of a sound wave are related very simply if the speed of the wave (usually denoted by the letter c) is known:

$$\begin{array}{ccc}c=f\lambda & \text{or}& \lambda =c/f\end{array}$$

To show some examples, the wavelength of sound in air at 20 Hz (the low-frequency or LF end of the audio spectrum), assuming normal room temperature, would be

$$\lambda =340/20=17\text{m}$$

whereas the wavelength of 20 kHz (at the high-frequency or HF end of the audio spectrum) would be 1.7 cm. Thus, it is apparent that the wavelength of sound ranges from being very long in relation to most natural objects at low frequencies, to quite short at high frequencies. This is important when considering how sound behaves when it encounters objects — whether the object acts as a barrier or whether the sound bends around it (see Fact File 1.5).

Simple and Complex Sounds

In the foregoing example, the sound had a simple waveform — it was a sine wave or sinusoidal waveform — the type which might result from a very simple vibrating system such as a weight suspended on a spring. Sine waves have a very pure sound because they consist of energy at only o...