An Introduction to Hearing

David M. Green

• Publisher: Routledge
• Year: 2021
• ISBN:
  9781000394764
• Edition: 1
• Topic: Psychologie
• Subtopic: Geschichte & Theorie in der Psychologie

Originally published in 1976, this introduction to hearing was intended to provide a sufficient introduction to each of several subareas of hearing so that the serious student can read the more advanced treatments with greater appreciation and understanding. It was intended for upper graduate and graduate students. It assumes some mathematical sophistication – calculus for example, but there is some review of more basic concepts, such as logarithms. There is also a brief treatment of the necessary material from the different disciplines – physics, physiology, psychology, anatomy and mathematics – that a student of hearing will need to know.

1

The Physical Nature of Sound

INTRODUCTION

The human senses are all remarkably acute. Under optimal conditions, the eye can detect a few photons. The skin can detect a vibratory stimulus that moves only a few microns. The ear can detect, at about 3,000 Hz (cycles per second), movements of the eardrum about a hundred times smaller than the diameter of a hydrogen molecule.

How is such sensitivity possible? How can the ear detect such minute vibrations? Why does the random vibration of the molecules in the air not obscure such faint sounds? These are some questions that arise in studying auditory perception. To understand in detail the answers to such questions, we must have a firm grasp of the physical nature of sound. Indeed, one of our goals is to understand the relation between what we hear and its physical properties.

We begin, then, by first considering what a sound wave is, how it is propagated, and what the rules are that govern its behavior. Answering these questions involves defining the units used to describe the intensity or energy of the sound wave. We review here several formulas specifying the intensity of the sound wave. We also discuss sinusoidal wave motion, in part because the absolute sensitivity of the ear depends strongly on the frequency of the signal. Finally, reflection of sound waves and resonance is discussed. This background material will permit us to answer some of our initial questions about absolute sensitivity. We begin by considering the nature of sound.

WHAT IS SOUND?

In ordinary usage the word “sound” refers to that which is heard. However, we want to understand the relation between what we hear and the physical aspects of sound. We therefore begin with a consideration of sound as a physical entity. From a physical viewpoint, sound is a mechanical disturbance that is propagated through an elastic medium. This physical disturbance alters certain properties of the medium, and the rapid variation of one of them, for example, the variation of pressure as a function of time, might be called the sound wave. We are primarily interested in this mechanical disturbance as it moves in air, but sound can also move in liquid or solid structures as well. Air is composed of a mixture of molecules, the majority being oxygen, nitrogen, and hydrogen. The molecules of a gas move about freely in space, colliding with other molecules or any surface containing the gas. The mass of the molecules and the velocity of their motion determine the temperature of the gas. These factors, along with the number of molecules per unit volume, also determine how far, on the average, molecules travel before colliding with other molecules. The gas molecules wander about at random in an undisturbed state. As a result of their collisions with other objects, they create a net static pressure on an object placed in the gas. Pressure is defined as a force per unit area, and static pressure is essentially the pressure measured by a barometer. The “barometric” pressure represents the force produced by the impact of the moving gas molecules, averaged over both time and space.

The magnitude of the static pressure is determined by the speed of the molecules, their mass, and the density of the gas, that is, the number of molecules per unit volume. Air at sea level contains about 2.7 × 10¹⁹ molecules per cubic centimeter and is a mixture of different molecules the velocities of which depend on their mass. Hydrogen molecules are light, and their velocity is nearly 200,000 cm/sec (about 6,000 ft/sec).¹ Oxygen molecules are heavier, and their velocity is only about 48,000 cm/sec (about 1,600 ft/sec). The mean free path, that is, the average distance between collisions, is about 2 × 10⁻⁵ cm. The mass of a single molecule is very slight, of course, so the force generated by a single collision is very small. A large number of collisions is needed to generate a total force per unit area, which is the static pressure.

Now if we introduce a change in the position of some large object in the air by vibrating the cone of a loudspeaker, for example, then a mechanical disturbance is created in the gas near the cone. On one side of the cone there is a temporary increase in pressure, an increase above the average or static pressure. Accompanying this increase in pressure is a temporary increase in density. The local increase in pressure and density causes a temporary increase in the number of collisions among the molecules in the gas near the cone. The temporary increase in collisions spreads via a number of other collisions to other, adjacent areas, and so the local disturbance eventually spreads throughout the neighboring space. Thus, the initially local increase in pressure and density is propagated throughout the entire medium. This moving mechanical disturbance is called the “sound wave.” Note that the mechanical disturbance can only be inferred by looking at the population characteristics of the gas. If we were to watch the movement of a single molecule, we would simply see it dancing about, striking the other molecules in the gas. An individual molecule would move unpredictably in different directions at different times. The direction of these motions only partially reflects external disturbance, such as the motion of the cone of the loudspeaker. “Sound,” therefore, refers to population characteristics or averages computed over a large set of molecules. Sound is a change in average values; it is an increase (or decrease) in the average pressure or in the average density or a change in the average displacement of the individual molecules.

If we could measure the average quantities at several points in this space, we would see that a particular disturbance moved systematically. Suppose, for example, that a speaker cone moved quickly forward and then returned to a resting position. If we could measure the average pressure or displacement at some distance from the speaker, we would see the same quick increase and subsequent return to the previous average values.

We must appreciate the molecular aspect of sound to understand many important acoustic phenomena, particularly the incredible sensitivity of the ear to small average displacements, and we return to this problem later in Chapter 2. For the most part, however, sound is described solely in terms of population or statistical averages that often ignore the molecular basis of sound. To understand this description of sound, we must know how the average values change as they travel through the gas. We must know the velocity at which the sound wave travels and how it is influenced when it strikes objects of dissimilar composition, such as walls, and other similar facts. Let us ...