This chapter provides a brief introduction to the physical nature of sound, the manner in which it is transmitted and transformed within the ear, and the nature of auditory neural responses.

THE NATURE OF AUDITORY STIMULI

Understanding hearing requires an understanding of sound. Sounds consist of fluctuations in pressure which are propagated through an elastic medium, and are associated with displacement of particles composing the medium. When the substance conducting sound is air at a temperature and pressure within the normal environmental ranges, compressions and rarefactions are transmitted at a velocity of about 335 meters per second, regardless of their amplitude (extent of pressure change) or waveform (pattern of pressure changes over time). Special interest is attached to periodic sounds, or sounds having a fixed waveform repeated at a fixed frequency. Frequency is measured in Hertz (Hz) or numbers of repetitions of a waveform per second (thus, 1,000 Hz corresponds to 1,000 repetitions of a particular waveform per second). The time required for one complete statement of an iterated waveform is its period. Periodic sounds from about 20 through 16,000 Hz can produce a sensation of pitch, and are called tones. For reasons to be discussed shortly, it is generally considered that the simplest type of periodic sound is a sine wave or pure tone (shown in Fig. 1.1A) which has a sinusoidal change in pressure over time. A limitless number of other periodic waveforms exist, including square waves (Fig. 1.1B) and pulse trains (Fig. 1.1C). Periodic sounds need not have simple, symmetrical waveforms: figure 1.1D shows a periodic sound produced by iteration of a randomly generated waveform.

The figure also depicts the waveforms of some nonperiodic sounds: white or Gaussian noise (Fig. 1.1E), a single pulse (Fig. 1.1F), and a short tone or tone burst (Fig. 1.1G).

The waveforms shown in figure 1.1 are time-domain representations in which both amplitude and time are depicted. Using a procedure developed by Joseph Fourier in the first half of the nineteenth century, it also is possible to represent any periodic sound in terms of a frequency-domain or spectral analysis in which a sound is described in terms of a harmonic sequence of sinusoidal components having appropriate frequency, amplitude, and phase relations. (Phase describes the portion of the period through which a waveform has advanced relative to an arbitrary reference.) A sinusoidal tone consists of a single spectral component as shown in figure 1.1A. The figure also shows the power spectra corresponding to the particular complex (nonsinusoidal) periodic sounds shown in figures 1.1B, 1.1C, and 1.1D. Each of these sounds has a period of 1 millisecond, a fundamental frequency of 1,000 Hz (corresponding to the waveform repetition frequency), and harmonic components corresponding to integral multiples of the 1,000 Hz fundamental as indicated.

Frequency analysis is not restricted to periodic sounds: nonperiodic sounds also have a spectral composition as defined through use of a Fourier integral or Fourier transform (for details see Leshowitz, 1978). Nonperiodic sounds have continuous rather than line spectra, as shown for the sounds depicted in figures 1.1E, 1.1F, and 1.1G.

As we shall see, frequency analysis of both periodic and nonperiodic sounds is of particular importance in hearing, chiefly because the ear performs a crude spectral analysis before the auditory receptors are stimulated.

While figure 1.1 shows how particular waveforms can be analyzed in terms of spectral components, it is also possible to synthesize waveforms by adding together sinusoidal components of appropriate phase and amplitude. Figure 1.2 shows how a sawtooth waveform may be approximated closely by the mixing of only six harmonics having appropriate amplitude and phase.

The range of audible amplitude changes is very large. A sound producing discomfort may be as much as 106 times the amplitude level at threshold. Sound level can be measured as power or intensity as well as amplitude or pressure: power usually can be considered as proportional to the square of the amplitude, so that discomfort occurs at a power level 1012 times the power threshold. In order to span the large range of values needed to describe the levels of sound normally encountered, a logarithmic scale has been devised. The logarithm to the base 10 of the ratio of a particular sound power level to a reference power level defines the level of the sound in Bels (named in honor of Alexander Graham Bell). However, the Bel is a rather large unit, and it is conventional to use a unit 1/10 this size, the deciBel (or dB) to express sound levels. The level in dB can be defined as:

dB = 10 log10 I1/I2

where I1 is the power level of the particular sound of interest, and I2 is the reference level expressed as sound power. DeciBels can also be calculated on the basis of amplitude or pressure units using the equation:

dB = 20 log10 P1/P2

where P1 is the relative pressure level being measured, and P2 is the reference pressure level. The standard reference pressure level is 0.0002 dyne/cm2 (which is sometimes expressed in different units of 20 microPascals), and the level in dB measured relative to this standard is called Sound Pressure Level (or SPL). Sound level meters are calibrated so that the numerical value of the SPL can be read out directly. There is another measure of sound level, also expressed in dB, called Sensation Level (SL), which is used occasionally in psychoacoustics. When measuring SL, the intensity corresponding to the threshold of a sound for an individual listener is used as the reference level rather than the standard physical value employed for SPL, so that dB SL represents the level above an individual’s threshold. Since SL is used relatively infrequently, dB will always refer to SPL unless otherwise specified.

To give some feeling for intensity levels in dB, the threshold of normal listeners for a 1,000 Hz sinusoidal tone is about 6 dB, the ambient level (background noise) in radio and TV studios is about 30 dB, conversational speech about 55 dB, and the level inside a bus about 90 dB.

Experimenters can vary the relative intensities of spectral components by use of acoustic filters which, in analogy with light filters, pass only desired frequency components of a sound. A high-pass filter transmits only frequency components above a lower limit, a low-pass filter only frequencies below an upper limit. Band-pass filters (which transmit frequencies within a specified range) and band-reject filters (which block frequencies within a specified range) are available. Filters are specified in terms of both cut-off frequency (the frequency at which the filter attenuation reaches 3 dB), and the slope, or roll-off, which is usually expressed as dB/octave beyond the cut-off frequency (an increase of one octave corresponds to doubling the frequency). Filter types are shown in figure 1.3.

OUR AUDITORY APPARATUS