Essentials of Audiology E-Book

Stanley A. Gelfand

• Herausgeber: Thieme Medical Publishers
• Kategorie: Fachliteratur
• Sprache: Englisch

Veröffentlichungsjahr: 2022

Beschreibung

The quintessential core textbook for audiology and speech-language pathology students

Essentials of Audiology, Fifth Edition by renowned audiology and hearing science experts Stanley A. Gelfand and Lauren Calandruccio has been updated to incorporate advances and changes in the field of audiology that have occurred since the publication of the prior edition. These include advances in audiological diagnosis and intervention in such areas as electrophysiological assessment, pediatric evaluation, cochlear implants, speech perception, hearing aids, and related technologies. The text has also been updated to reflect revised clinical guidelines, expert position papers, current systematic reviews, and standards and regulations that affect clinical practice. In addition to the reader-friendly text for which the book is well-known, the new edition actively embraces diversity with features such as non-gendered language (e.g., singular they) and more inclusive photographs and drawings.

This textbook provides a comprehensive overview of audiology at the introductory level with discussions on acoustics, anatomy and physiology, sound perception, auditory disorders and the nature of hearing impairment, methods of measurement, screening, clinical assessment, and clinical management. The book includes 17 chapters, starting with Acoustics and Sound Measurement and concluding with Effects of Noise and Hearing Conservation. As with the prior editions, the text is highly relevant and conducive to learning, thanks to the input of a distinguished group of audiologists involved in clinical practice, research, teaching, and student supervision, along with insightful advice from recent audiology students.

Key Highlights

• Co-authored by renowned clinician-scientists, educators, and Fellows of the American Speech-Language-Hearing Association and the American Academy of Audiology
• Extensively updated and expanded content encompasses current standards and clinical guidelines
• State-of-the-art hearing science, audiology, and related disciplines provide a firm foundation for evidence-based audiological best practices
• Clear and informative classroom-tested illustrations, figures, tables, explanations, and examples enhance understanding

This comprehensive introductory text is essential reading for undergraduate students of speech, language, and hearing and will also benefit first-level graduate students who need to learn or review fundamentals.

This print book includes complimentary access to a digital copy on https://medone.thieme.com.

Leseprobe

Essentials of Audiology

5th Edition

Stanley A. Gelfand, PhD, CCC-A/SLPProfessorDepartment of Linguistics & Communication DisordersQueens College of the City University of New York (CUNY)Flushing, New York; AuD Program & PhD Program in Speech-Language-Hearing Sciences CUNY Graduate CenterNew York, New York, USA

Lauren Calandruccio, PhD, CCC-ALouis D. Beaumont University ProfessorDepartment of Psychological Sciences Case Western Reserve University Cleveland, Ohio, USA

448 illustrations

ThiemeNew York • Stuttgart • Delhi • Rio de Janeiro

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To Janice

In loving memory

Stanley A. Gelfand, PhD, CCC-A/SLP

To my students

Past, present, and future

Lauren Calandruccio, PhD, CCC-A

Contents

Preface

1.Acoustics and Sound Measurement

2.Anatomy and Physiology of the Auditory System

3.Measurement Principles and the Nature of Hearing

4.The Audiometer and Test Environment

5.Pure Tone Audiometry

6.Auditory System and Related Disorders

7.Acoustic Immittance Assessment

8.Speech Audiometry

9.Clinical Masking

10.Behavioral Tests for Audiological Diagnosis

11.Physiological Methods in Audiology

12.Assessment of Infants and Children

13.Audiological Screening

14.Nonorganic Hearing Loss

15.Audiological Management I

16.Audiological Management II

17.Effects of Noise and Hearing Conservation

Appendices

Subject Index

Author Index

Preface

What is audiology? Audiology is the clinical profession that deals with hearing and balance disorders. It is also the scientific study of normal and abnormal audition and related areas in the broadest sense.

What is an audiologist? An audiologist is a practitioner of audiology as a clinical profession. Audiologists are principally concerned with the identification, evaluation, and management of patients with auditory and balance disorders, as well as with the prevention of hearing impairment. The scope of audiological practice also includes such diverse areas as the evaluation of the vestibular system, noise assessment, and hearing conservation, as well as the physiological monitoring of various neurological functions during surgical procedures. As a result, audiologists possess a broad scope of knowledge and skills, and often have interests in common with a variety of other disciplines such as speech-language pathology, speech and hearing science, education of the deaf and hard-of-hearing, engineering, acoustics, industrial hygiene, musicology, medicine, physiology, psychology, linguistics, and vocational counseling.

Much like many other scholarly professions, pursuing a career in audiology involves a rigorous course of doctoral-level education and training. Most audiologists earn the Doctor of Audiology (AuD) degree, while others with research and academic as well as clinical interests obtain a PhD. Some pursue both. In addition, those qualified to practice audiology must possess professional licenses from the states in which they practice, and are usually certificated by the American Speech-Language-Hearing Association (ASHA) and/or the American Academy of Audiology (AAA).

So who is this book for? Introductory audiology is an essential and fundamental aspect of the education of all students who are interested in the two related professions of speech-language pathology and audiology. This book is primarily intended to serve as a comprehensive introductory text for students who are preparing to enter both of these fields. As such, it tries to address the needs of at least two rather different groups of students. Those planning a career in audiology need a broad overview of the field and a firm understanding of its many basic principles so that they have a solid foundation for the future as doctors of audiology in clinical practice.

The audiological needs of future and practicing speech-language pathologists are just as important, and go well beyond knowing the auditory implications of speech, language, and related disorders, and being able to understand audiological reports. Speech-language pathologists often find themselves working hand-in-hand with their audiological colleagues. They also need to perform certain audiological procedures themselves when these fall within the speech-language pathology scope of practice, especially when screening is involved; and they regularly make interpretations and referrals that are of audiological relevance. Moreover, speech-language pathologists often work with patients with a broad range of hearing and related disorders directly and on an ongoing basis. They frequently must explain the nature and management of auditory disorders to family members, teachers, and other professionals. This is especially true in school settings and long-term care facilities. What is more, cochlear implant and other multidisciplinary programs are enhancing the scope and depth of interactions among speech-language pathologists and audiologists, and are making knowledge and understanding of audiology all the more important for budding speech-language pathologists. With considerations like these in mind, we hope that students who become speech-language pathologists will find this text useful as a reference source long after their audiology courses have been completed. (Of course, we do admit hoping that at least a few speech-language pathology students will be attracted to a career in audiology by what they read here.)

This textbook attempts to provide a comprehensive overview of audiology at the introductory level, including such topics as acoustics, anatomy and physiology, sound perception, auditory disorders and the nature of hearing impairment, methods of measurement, screening, clinical assessment, and clinical management. It is intended to serve as the core text for undergraduate students in speech, language, and hearing, as well as to serve the needs of graduate students who need to learn or review the fundamentals of audiology. It is anticipated that the material will be covered in a one-, two-, or three-term undergraduate sequence, depending on the organization of the communication sciences and disorders curriculum at a given college or university. For example, the first three chapters are often used in the text for an undergraduate hearing science course, while selections from the other chapters might be used in one or two audiology courses.

With these considerations in mind, we have tried to prepare a textbook that is extensive enough for professors to pick and choose material that provides the right depth and scope of coverage for a particular course. For example, text readings can be assigned to cover clinical masking at almost any level from simple to complex by selecting various sections of Chapter 9. It is unlikely that all of that chapter will be assigned in a single undergraduate class. However, the material is there, if needed, for further study to provide the groundwork for a term paper or independent study report, or for future reference. We also have tried to provide relatively extensive and up-to-date reference lists for similar reasons.

This fifth edition was undertaken to provide the student with an up-to-date coverage of a field that is steadily developing, as well as to take advantage of accumulating experience to improve upon what is included and how it is presented. Many developments and changes have taken place since the prior edition was published. Some of them are in areas of rapidly unfolding development like cochlear implants, hearing aids and related technologies, as well as in electrophysiological assessment. But most of them are the slow, methodical, and often subtle—albeit important—advances that unfold over time in an active clinical science. Other changes reflect the influence of systematic reviews, changes in guidelines, expert position papers, standards and regulations which affect clinical practices, and technical matters. Of course, there are always a few developments that surface the day after the textbook is printed—a frustration to the textbook authors, but the kind of thing that makes audiology such an exciting and interesting field.

As with the prior editions, this one was influenced by the input graciously provided by many audiologists involved in clinical practice, research, and teaching and student supervision. In addition, considerable attention was given to the comments and insights of students who were taking or recently completed audiology courses, including those who used the prior edition of this textbook as well as other books. The content and especially the style of the text were substantially influenced by their advice. As a result of their insights, the current edition retains a writing style that has been kept as conversational and informal as possible, and only classroom-proven examples and drawings are included. Similarly, clinical masking, acoustic immittance, and screening have been kept in separate chapters; the material on audiological management continues to be spread over two chapters; and the history of audiology has been omitted.

Many old figures have been updated or replaced and others have been added to keep the material up-to-date. In addition, many older and dated photographs have been replaced to keep the book contemporary and fresh for the reader. More importantly, we have attempted to use figures that reflect and encourage diversity and inclusiveness.

All four prior editions used gender-specific pronouns (he, she, him, her, etc.) to maximize clarity for the benefit of the reader, which was well-received although originally undertaken with great trepidation. However, we strongly believe that non-gendered language (e.g., singular they) is more appropriate and inclusive, and that it can be incorporated into the text while keeping the material maximally reader-friendly (or at least minimally unfriendly). As a result, we have changed the previously used gender-specific pronouns to gender-neutral wording whenever possible throughout the text.

This book would not exist without the influence of many very special people, with our sincerest apologies to anyone inadvertently omitted.

From Stanley A. Gelfand: I would like to extend my heartfelt thanks to the following very special individuals for their influence, insights, advice, encouragement, assistance, support, devotion, and friendship over the years: Marilyn Agin, Matthew Bakke, Moe Bergman, Arthur Boothroyd, Lauren Calandruccio, Tong Chun, Joseph Danto, Lillian and Sol Gelfand, Judy Gravel, Irving Hochberg, Gertrude and Oscar Katzen, Renee Kaufman, Barbara Kruger, Fred Kruger, Harry Levitt, John Lutolf, Maurice Miller, Edward O'Connor, Sharon O'Connor, Neil Piper, Leslie Ross, Mark Ross, Adrienne Rubenstein, Brian Scanlan, Teresa Schwander, Gerald Studebaker, Shlomo Silman, Carol Silverman, Helen and Harris Topel, Ellen and Glenn Unger, Barbara Weinstein, Mark Weiss, and Joyce West. I am particularly grateful to my current and former colleagues and students in the Department of Linguistics and Communication Disorders at Queens College, the AuD Program and the PhD Program in Speech Language and Hearing Sciences at the City University of New York Graduate Center, and the East Orange VA Medical Center.

From Lauren Calandruccio: To all my amazing mentors, collaborators, and my go-to audiology peeps, thank you! A special thanks to Harvey Abrams, Gin Best, Karen Beverly-Ducker, Kristina Bowdrie, Ann Bradlow, Emily Buss, Laurel Carney, Angela Ciccia, Nicole Corbin, Sumit Dhar, Karen Doherty, Ann Clock Eddins, Andy Faulkner, Erick Gallun, Stan Gelfand, Tucker Gleason, Larry Humes, Lisa Hunter, David Kemp, Wei Wei Lee, Lori Leibold, Nancy Nelson, Gayla Poling, Nia Potier, Stuart Rosen, Sharon Sandridge, Jessica Sullivan, Lee Thompson, Kathy Vander Werff, Peter Wasiuk, and Sharon Williams, and in memory of Judy Gravel and Lu Feng Shi. To Dr. H (Nick Hipskind), thank you for being the first to show me the (cone of) light.

We would also like to express our appreciation to the extraordinary, talented, and dedicated professionals at Thieme Medical Publishers, who have been so helpful, cooperative, and supportive throughout the process of preparing this book.

Finally, our greatest appreciation is expressed to our families.

From Stanley A. Gelfand: To Janice, whose memory will always be a blessing and inspiration; and to my wonderful children, Michael and Hillary, Joshua and Erin, and Jessica and Bobby for their love, encouragement, support, insight, and unimaginable patience; as well as to my amazing grandchildren, Jacob, Alexander, Jackson, Benjamin, and Joey for the special love and joy that only they can bring.

From Lauren Calandruccio: To Jamie and Aunt Sis, you are the "fun" to my "serious," thank you for the balance. To my parents, thank you for teaching me how to work hard. That work ethic allowed me to complete this project. To my two Ks, thank you for always cheering me on and for your love and patience (especially when mom has to work). Eric, 20 years and you are still my rock. Your support is the foundation to all my successes. Thank you for everything.

Stanley A. Gelfand, PhD, CCC-A/SLP

Lauren Calandruccio, PhD, CCC-A

1Acoustics and Sound Measurement

We begin our study of audiology by reviewing the nature of sound because, after all, sound is what we hear. The science of sound is called acoustics, which is a branch of physics, and relies on several basic physical principles. Many useful sources are available for students wishing to pursue the areas covered in this chapter in greater detail (e.g., Peterson & Gross 1972; Hewitt 1974; Kinsler, Frey, Coppens, & Sanders 1982; Sears, Zemansky, & Young 1982; Beranek 1986; Gelfand 2018).

■ Physical Quantities

The basic physical quantities are mass, time, and length (or distance). All other physical quantities are derived by combining these three basic ones, as well as other derived quantities, in a variety of ways. The principal basic and derived quantities are summarized in Table 1.1. These basic quantities are expressed in terms of conventional units that are measurable and repeatable. The unit of mass (M) is the kilogram (kg) or the gram (g); the unit of length (L) is the meter (m) or the centimeter (cm); and the unit of time (t) is the second (s). Mass is not really synonymous with weight even though we express its magnitude in kilograms. The mass of a body is related to its density, but its weight is related to the force of gravity. If two objects are the same size, the one with greater density will weigh more. However, even though an object’s mass would be identical on the earth and the moon, it would weigh less on the moon, where there is less gravity.

Table 1.1 Principal physical quantities

When we express mass in kilograms and length in meters, we are using the meter-kilogram-second or MKS system. Expressing mass in grams and length in centimeters constitutes the centimeter-gram-second or cgs system. These two systems also have different derived quantities. For example, the units of force and work are called newtons and joules in the MKS system and dynes and ergs in the cgs system, respectively. We will emphasize the use of MKS units because this is the internationally accepted standard in the scientific community, known as the Système International d’Unites (SI). Equivalent cgs values will often be given as well because the audiology profession has traditionally worked in cgs units, and the death of old habits is slow and labored. These quantities are summarized with equivalent values in MKS and cgs units in Table 1.1. In addition, the correspondence between scientific notation and conventional numbers, and the meanings of prefixes used to describe the sizes of metric units are shown for convenience and ready reference in Table 1.2 and Table 1.3.

Table 1.2 Expressing numbers in standard notation and scientific notation

Standard notation

Scientific notation

0.000001

10−6

0.00001

10−5

0.0001

10−4

0.001

10–3

0.01

10–2

0.1

10–1

1

100

10

101

100

102

1000

103

10,000

104

100,000

105

1,000,000

106

3600

3.6 × 103

0.036

3.6 × 10−2

0.0002

2 × 10−4

0.00002

2 × 10–5

Table 1.3 Examples of prefixes used to express metric units

Prefix

Symbol

Definition

Multiply by

Standard notation

Scientific notation

micro

μ

millionths

1/1,000,000 or 0.000001

10−6

milli

m

thousandths

1/1000 or 0.001

10–3

centi

c

hundredths

1/100 or 0.01

10−2

deci

d

tenths

1/10 or 0.1

10–1

deka

da

tens

10

101

hecto

h

hundreds

100

102

kilo

k

thousands

1000

103

mega

M

millions

1,000,000

106

Quantities may be scalars or vectors. A scalar can be fully described by its magnitude (amount or size), but a vector has both direction and magnitude. For example, length is a scalar because an object that is one meter long is always one meter long. However, we are dealing with a vector when we measure the distance between two coins that are one meter apart because their relationship has both magnitude and direction (from point x1 to point x2). This quantity is called displacement (x). Derived quantities will be vectors if they have one or more components that are vectors; for example, velocity is a vector because it is derived from displacement, and acceleration is a vector because it involves velocity. We distinguish between scalars and vectors because they are handled differently when calculations are being made.

Velocity Everyone knows that “55 miles per hour” refers to the speed of a car that causes it to travel a distance of 55 miles in a one-hour period of time. This is an example of velocity (v), which is equal to the amount of displacement (x) that occurs over time (t):

Displacement is measured in meters and time is measured in seconds (s); thus, velocity is expressed in meters per second (m/s). Velocity is the vector equivalent of speed because it is based on displacement, which has both magnitude and direction. When we take a trip we usually figure out the distance traveled by making a mental note of the starting odometer reading and then subtracting it from the odometer reading at the destination (e.g., if we start at 10,422 miles and arrive at 10,443 miles, then the distance must have been 10,443 – 10,422 = 21 miles). We do the same thing to calculate the time it took to make the trip (e.g., if we left at 1:30 and arrived at 2:10, then the trip must have taken 2:10 – 1:30 = 40 minutes). Physical calculations involve the same straightforward approach. When an object is displaced, it starts at point x1 and time t1 and arrives at point x2 and time t2. Its average velocity is simply the distance traveled (x2 – x1) divided by the time it took to make the trip (t2 – t1):

The term instantaneous velocity describes the velocity of a body at a particular moment in time. For the math-minded, it refers to the velocity when the displacement and time between one point and the next one approach zero, that is, the derivative of displacement with respect to time:

Acceleration Driving experience has taught us all that a car increases its speed to get onto a highway, slows down when exiting, and also slows down while making a turn. “Speeding up” and “slowing down” mean that the velocity is changing over time. The change of velocity over time is acceleration (a). Suppose a body is moving between two points. Its velocity at the first point is v1, and the time at that point is t1. Similarly, its velocity at the second point is v2 and the time at that point is t2. Average acceleration is the difference between the two velocities (v2 – v1) divided by the time interval by the time interval (t2 – t1):

In more general terms, acceleration is written simply as

Because velocity is the same as displacement divided by time, we can replace v with x/t, so that

which can be simplified to

Consequently, acceleration is expressed in units of meters per second squared (m/s2) in the MKS system. When measurements are made in cgs units, acceleration is expressed in centimeters per second squared (cm/s2).

Acceleration at a given moment is called instantaneous acceleration, and quantitatively oriented readers should note it is equal to the derivative of velocity with respect to time, or

Because velocity is the first derivative of displacement, we find that acceleration is the second derivative of displacement:

Force An object that is sitting still will not move unless some outside influence causes it to do so, and an object that is moving will continue moving at the same speed unless some outside influence does something to change it. This commonsense statement is Newton’s first law of motion. It describes the attribute of inertia, which is the property of mass to continue doing what it is already doing. The “outside influence” that makes a stationary object move, or causes a moving object to change its speed or direction, is called force (F). Notice that force causes the moving object to change velocity or the motionless object to move, which is also a change in velocity (from zero to some amount). Recall that a change of velocity is acceleration. Hence, force is that influence (conceptually a “push” or “pull”) that causes a mass to be accelerated. In effect, the amount of “push” or “pull” needed depends on how much mass you want to influence and the amount of acceleration you are trying to produce. In other words, force is equal to the product of mass times acceleration:

Since acceleration is velocity over time (v/t), we can also specify force in the form

The quantity Mv is called momentum, so we may also say that force equals momentum over time.

The amount of force is measured in kg · m/s2 because force is equal to the product of mass (measured in kg) and acceleration (measured in m/s2). The unit of force is the newton (N), where one newton is the amount of force needed to cause a 1 kg mass to be accelerated by 1 m/s2; hence, 1 N = 1 kg · 1 m/s2. (This might seem very technical, but it really simplifies matters; after all, it is easier to say “one newton” than “one kg · m/s2.”) It would take a 2 N force to cause a 1 kg mass to be accelerated by 2 m/s2, or a 2 kg mass to be accelerated by 1 m/s2. A 4 N force is needed to accelerate a 2 kg mass by 2 m/s2, and a 63 N force is needed to accelerate a 9 kg mass by 7 m/s2. In the cgs system, the unit of force is called the dyne, which is the force needed to accelerate a 1 g mass by 1 cm/s2; that is, 1 dyne = 1 g · cm/s2. It takes 105 dynes to equal 1 N.

Many different forces are usually acting upon an object at the same time. Hence, the force we have been referring to so far is actually the net or resultant force, that is, the “bottom line” effect of all the forces that act upon an object. If a force of 3 N is pushing an object toward the right and a second force of 8 N is also pushing that object toward the right, then the net force would be 3 + 8 = 11 N toward the right. In other words, if two forces push a body in the same direction, then the net force would be the sum of those two forces. Conversely, if a 4 N force pushes an object toward the right at the same time that a 9 N force pushes it toward the left, then the net force is 9 – 4 = 5 N toward the left. Thus, if two forces push an object in opposite directions, then the net force is the difference between the two opposing forces, and it causes the object to accelerate in the direction of the greater force. If two equal forces push in opposite directions, then the net force is zero. Because the net force is zero it will not cause the motion of the object to change. The situation in which net force is zero is called equilibrium. In this case, a moving object will continue moving and an object that is at rest (i.e., not moving) will continue to remain still.

Friction When an object is moving in the real world, it tends to slow down and eventually comes to a halt. This happens because anything that is moving in the real world is always in contact with other bodies or mediums. The sliding of one body on the other constitutes a force that opposes the motion, called resistance or friction.

The opposing force of friction or resistance depends on two parameters. The first factor is that the amount of friction depends on the nature of the materials that are sliding on one another. Simply stated, the amount of friction between two given objects is greater for “rough” materials than for “smooth” or “slick” ones, and is expressed as a quantity called the coefficient of friction. The second factor that determines how much friction occurs is easily appreciated by rubbing the palms of your hands back and forth on each other. First rub slowly and then more rapidly. The rubbing will produce heat, which occurs because friction causes some of the mechanical energy to be converted into heat. This notion will be revisited later, but for now we will use the amount of heat as an indicator of the amount of resistance. Your hands become hotter when they are rubbed together more quickly. This illustrates the notion that the amount of friction depends on the velocity of motion. In quantitative terms,

where Ff is the force of friction, R is the coefficient of friction between the materials, and v is the velocity of the motion.

Elasticity and restoring force It takes some effort (an outside force) to compress or expand a spring; and the compressed or expanded spring will bounce back to its original shape after it is released. Compressing or expanding the spring is an example of deforming an object. The spring bouncing back to its prior shape is an example of elasticity. More formally, we can say that elasticity is the property whereby a deformed object returns to its original form. Notice the distinction between deformation and elasticity. A rubber band and saltwater taffy can both be stretched (deformed), but only the rubber band bounces back. In other words, what makes a rubber band elastic is not that it stretches, but rather that it bounces back. The more readily a deformed object returns to its original form, the more elastic (or stiff) it is.

We know from common experiences, such as using simple exercise equipment, that it is relatively easy to begin compressing a spring (e.g., a “grip exerciser”), but that it gets progressively harder to continue compressing it. Similarly, it is easier to begin expanding a spring (e.g., pulling apart the springs on a “chest exerciser”) than it is to continue expanding it. In other words, the more a spring-like material (an elastic element) is deformed, the more it opposes the applied force. The force that opposes the deformation of an elastic or spring-like material is known as the restoring force. If we think of deformation in terms of how far the spring has been compressed or expanded from its original position, we could also say that the restoring force increases with displacement. Quantitatively, then, restoring force (FR) depends on the stiffness (S) of the material and the amount of its displacement as follows:

Pressure Very few people can push a straight pin into a piece of wood, yet almost anyone can push a thumbtack into the same piece of wood. This is possible because a thumbtack is really a simple machine that concentrates the amount of force being exerted over a larger area (the head) down to a very tiny area (the point). In other words, force is affected by the size of the area over which it is applied in a way that constitutes a new quantity. This quantity, which is equal to force divided by area (A), is called pressure (p), so

Because force is measured in newtons and area is measured in square meters in MKS units, pressure is measured in newtons per square meter (N/m2).

The unit of pressure is the pascal (Pa), so that 1 Pa = 1 N/m2. In the cgs system, pressure is measured in dynes per square centimeter (dynes/cm2), occasionally referred to as microbars (μbars).

Work and energy As a physical concept, work (W) occurs when the force applied to a body results in its displacement, and the amount of work is equal to the product of the force and the displacement, or

Because force is measured in newtons and displacement is measured in meters, work itself is quantified in newton-meters (N · m). For example, if a force of 2 N displaces a body by 3 m, then the amount of work is 2 × 3 = 6 N. There can only be work if there is displacement. There cannot be work if there is no displacement (i.e., if x = 0) because work is the product of force and displacement, and zero times anything is zero. The MKS unit of work is the joule (J). One joule is the amount of work that occurs when one newton of force effects one meter of displacement, or 1 J = 1 N · m. In the cgs system, the unit of work is called the erg, where 1 erg = 1 dyne · cm. One joule corresponds to 107 erg.

Energy is usually defined as the capability to do work. The energy of a body at rest is potential energy and the energy of an object that is in motion is kinetic energy. The total energy of a body is the sum of its potential energy plus its kinetic energy, and work corresponds to the exchange between these two forms of energy. In other words, energy is not consumed when work is accomplished; it is converted from one form to the other. This principle is illustrated by the simple example of a swinging pendulum. The pendulum’s potential energy is greatest when it reaches the extreme of its swing, where its motion is momentarily zero. On the other hand, the pendulum’s kinetic energy is greatest when it passes through the midpoint of its swing because this is where it is moving the fastest. Between these two extremes, energy is being converted from potential to kinetic as the pendulum speeds up (on each down swing), and from kinetic to potential as the pendulum slows down (on each up swing).

Power The rate at which work is done is called power (P), so that power can be defined as work divided by time,

The unit of power is called the watt (W). One unit of power corresponds to one unit of work divided by one unit of time. Hence, one watt is equal to one joule divided by one second, or 1 W = 1 J/s. Power is also expressed in watts in the cgs system, where work is measured in ergs. Since 1 J = 107 erg, we can also say that 1 W = 107 erg/s.

Power can also be expressed in other terms. For example, because W = Fx, we can substitute Fx for W in the power formula, to arrive at

We know that v = x/t, so we can substitute v for x/t and rewrite this formula as

In other words, power is also equal to force times velocity.

Intensity Consider a hypothetical demonstration in which one tablespoonful of oil is placed on the surface of a still pond. At that instant the entire amount of oil will occupy the space of a tablespoon. As time passes, the oil spreads out over an expanding area on the surface of the pond, and it therefore also thins out so that much less than all the oil will occupy the space of a tablespoon. The wider the oil spreads the more it thins out, and the proportion of the oil covering any given area gets smaller and smaller, even though the total amount of oil is the same. Clearly, there is a difference between the amount of oil, per se, and the concentration of the oil as it is distributed across (i.e., divided by) the surface area of the pond.

An analogous phenomenon occurs with sound. It is common knowledge that sound radiates outward in every direction from its source, constituting a sphere that gets bigger and bigger with increasing distance from the source, as illustrated by the concentric circles in Fig. 1.1. Let us imagine that the sound source is a tiny pulsating object (at the center of the concentric circles in the figure) and that it produces a finite amount of power, analogous to the fixed amount of oil in the prior example. Consequently, the sound power will be divided over the ever-expanding surface as distance increases from the source, analogous to the thinning out of the widening oil slick. This notion is represented in the figure by the thinning of the lines at greater distances from the source. Suppose we measure how much power registers on a certain fixed amount of surface area (e.g., a square inch). As a result, a progressively smaller proportion of the original power falls onto a square inch as the distance from the source increases, represented in the figure by the lighter shading of the same-size ovals at increasing distances from the source.

Fig. 1.1 Intensity (power divided by area) decreases with distance from the sound source because a fixed amount of power is spread over an increasing area, represented by the thinning of the lines. Proportionately less power falls on the same unit area (represented by the lighter shading of the ovals) with increasing distance from the source.

The examples just described reveal that a new quantity, called intensity (I), develops when power is distributed over area. Specifically, intensity is equal to power per unit area, or power divided by area, or

Because power is measured in watts and area is measured in square meters in the MKS system, intensity is expressed in watts per square meter (W/m2). Intensity is expressed in watts per square centimeter (W/cm2) in the cgs system.

Intensity decreases with increasing distance from a sound source according to a rule called the inverse square law. It states that the amount of intensity drops by 1 over the square of the change in distance. Two examples are illustrated in Fig. 1.2. Fig. 1.2a shows that when the distance from a loudspeaker is doubled from 5 m to 10 m, the amount of intensity at 10 m will be one quarter of what it was at 5 m (because 1/22 = 1/4). Similarly, Fig. 1.2b shows that tripling the distance from 5 m to 15 m causes the intensity to fall to one-ninth of its value at the closer point because 1/32 = 1/9.

Fig. 1.2 Illustrations of the inverse square law. (a) Doubling of distance: The intensity at 10 m away from a loudspeaker is one quarter of its intensity at 5 m because 1/22 = 1/4. (b) Tripling of distance: The intensity at 15 m away from the sources is one-ninth of its intensity at 5 m because 1/32 = 1/9.

An important relationship to be aware of is that power is equal to pressure squared,

and pressure is equal to the square root of power,

In addition, intensity is proportional to pressure squared,

and pressure is proportional to the square root of intensity,

This simple relationship makes it easy to convert between sound intensity and sound pressure.

■ The Nature of Sound

Sound is often defined as a form of vibration that propagates through the air in the form of a wave. Vibration is nothing more than the to-and-fro motion (oscillation) of an object. Some examples include a playground swing, a pendulum, the floorboards under a washing machine, a guitar string, a tuning fork prong, and air molecules. The vibration is usually called sound when it is transferred from air particle to air particle (we will see how this happens later). The vibration of air particles might have a simple pattern such as the tone produced by a tuning fork, or a very complex pattern such as the din heard in a school cafeteria. Most naturally occurring sounds are very complex, but the easiest way to understand sound is to concentrate on the simplest ones.

Simple Harmonic Motion

A vibrating tuning fork1 is illustrated in Fig. 1.3. The initial force that was applied by striking the tuning fork is represented by the green arrow in frame 1. The progression of the drawings represents the motion of the prongs at selected points in time after the fork has been activated. The two prongs vibrate as mirror images of each other, so that we can describe what is happening in terms of just one prong. The circular insert highlights the motion of the right prong. Here the center position is where the prong would be at rest. When the fork is struck the prong is forced inward as shown by arrow a. After reaching the leftmost position it bounces back (arrow b), accelerating along the way. The rapidly moving prong overshoots the center and continues rightward (arrow c). It slows down along the way until it stops for an instant at the extreme right, where it reverses direction again and starts moving toward the left (arrow d) at an ever-increasing speed. It overshoots the center again, and as before, the prong now follows arrow a, slowing down until it stops momentarily at the extreme left. Here it reverses direction again and repeats the same process over and over again. One complete round trip (or replication) of an oscillating motion is called a cycle. The number of cycles that occur in one second is called frequency.

Fig. 1.3 After being struck, a tuning fork vibrates or oscillates with a simple pattern that repeats itself over time. One replication (cycle) of this motion is illustrated going from frames 1 to 5. The arrows in the insert highlight the motion of one of the prongs.

This form of motion occurs when a force is applied to an object having the properties of inertia and elasticity. Due to its elasticity, the deformation of the fork caused by the applied force is opposed by a restoring force. In the figure the initial leftward force is opposed by a restoring force in the opposite direction, that is, toward the right. The rightward restoring force increases as the prong is pushed progressively toward the left. As a result, the movement of the prong slows down and eventually stops. Under the influence of its elasticity the prong now reverses direction and starts moving rightward. As the restoring force brings the prong back toward the center, we must also consider its mass. Because the prong has mass, inertia causes it to accelerate as it moves back toward its center resting position. In fact, the prong is moving at its maximum speed as it passes through the resting position. The force of inertia causes the prong to overshoot the center and continue moving rightward. The deformation process begins again once the prong overshoots its resting position. As a result, opposing elastic restoring forces start building up again, now in the leftward direction. Just as before, the increasing (leftward) restoring force eventually overcomes the rightward inertial force, thereby stopping the prong’s displacement at the rightmost point, and causing a reversal in the direction of its movement. Hence, the same course of events is repeated again, this time in the leftward direction; then rightward, then leftward, etc., over and over again. This kind of vibration is called simple harmonic motion because the oscillations repeat themselves at the same rate over and over again.

We know from experience that the oscillations just described do not continue forever. Instead, they dissipate over time and eventually die out completely. The dying out of vibrations over time is called damping, and it occurs due to resistance or friction. Resistance occurs because the vibrating prong is always in contact with the surrounding air. As a result, there will be friction between the oscillating metal and the surrounding air molecules. This friction causes some of the mechanical energy that has been supporting the motion of the tuning fork to be converted into heat. In turn, the energy that has been converted into heat is no longer available to maintain the vibration of the tuning fork. Consequently, the sizes of the oscillations dissipate and eventually die out altogether.

A diagram summarizing the concepts just described is shown in Fig. 1.4. The curve in the figure represents the tuning fork’s motion. The amount of displacement of the tuning fork prong around its resting (or center) position is represented by distance above and below the horizontal line. These events are occurring over time, which is represented by horizontal distance (from left to right). The initial displacement of the prong due to the original applied force is represented by the dotted segment of the curve. Inertial forces due to the prong’s mass and elastic restoring forces due to the elasticity of the prong are represented by labeled arrows. Damping of the oscillations due to friction is shown by the decline in the displacement of the curve as time goes on. The curve in this diagram is an example of a waveform, which is a graph that shows displacement (or another measure of magnitude) as a function of time.

Fig. 1.4 Diagrammatic representation of tuning fork oscillations over time. Vertical displacement represents the amount of the tuning fork prong displacement around its resting position. Distance from left to right represents the progression of time. (Adapted from Gelfand 2018, courtesy of CRC Press.)

Sound Waves

Tuning fork vibrations produce sound because the oscillations of the prongs are transmitted to the surrounding air particles. When the tuning fork prong moves to the right, it displaces air molecules to its right in the same direction. These molecules are thus displaced to the right of their own resting positions. Displacing air molecules toward the right pushes them closer to the air particles to their right. The pressure that exists among air molecules that are not being disturbed by a driving force (like the tuning fork) is known as ambient or atmospheric pressure. We can say that the rightward motion of the tuning fork prong exerts a force on the air molecules that pushes them together relative to their undisturbed, resting situation. In other words, forcing the air molecules together causes an increase in air pressure relative to the ambient pressure that existed among the undisturbed molecules. This state of positive air pressure is called compression. The amount of compression increases as the prong continues displacing the air molecules rightward. A maximum amount of positive pressure occurs when the prong and air molecules reach their greatest rightward displacement.

The tuning fork prong then reverses direction, overshoots its resting position, and proceeds to its leftmost position. The compressed air molecules reverse direction along with the prong. This occurs because air is an elastic medium, so the particles compressed to the right develop a leftward restoring force. Small as they are, air particles do have mass. Therefore, inertia causes the rebounding air particles to overshoot their resting positions and to continue toward their extreme leftward positions. As the particles move leftward, the amount of compression decreases and is momentarily zero as they pass through their resting positions. As they continue to move to the left of their resting positions, the particles are now becoming increasingly farther from the molecules to their right (compared with when they are in their resting positions). We now say that the air particles are rarefied compared with their resting states, so that the air pressure is now below atmospheric pressure. This state of lower than ambient pressure is called rarefaction. When the air particles reach the leftmost position they are maximally rarefied, which means that the pressure is maximally negative. At this point, the restoring force instigates a rightward movement of the air molecules. This movement is enhanced by the push of the tuning fork prongs that have also reversed direction. The air molecules now accelerate rightward (so that the amount of rarefaction decreases), overshoot their resting positions, and continue to the right, and so on. The tuning fork vibrations have now been transmitted to the surrounding particles, which are now also oscillating in simple harmonic motion. Sounds that are associated with simple harmonic motion are called pure tones.

Let us consider one of the air molecules that has already been set into harmonic motion by the tuning fork. This air particle now vibrates to-and-fro in the same direction that was originally imposed by the vibrating prong. When this particle moves toward its right it will cause a similar displacement of the particle that is located there. The subsequent leftward motion is also transmitted to the next particle, etc. Thus, the oscillations of one air particle are transmitted to the molecule next to it. The second particle is therefore set into oscillation, which in turn initiates oscillation of the next one, and so forth down the line. In other words, each particle vibrates back and forth around its own resting point, and causes successive molecules to vibrate back and forth around their own resting points, as shown schematically in Fig. 1.5. Notice that each molecule vibrates “in place” around its own average position; it is the vibratory pattern that is transmitted through the air.

Fig. 1.5 Sound is initiated by transmitting the vibratory pattern of the sound source to nearby air particles, and then the vibratory pattern is passed from particle to particle as a wave. Notice how it is the pattern of vibration that is being transmitted, whereas each particle oscillates around its own average location.

This propagation of vibratory motion from particle to particle constitutes the sound wave. This wave appears as alternating compressions and rarefactions radiating from the sound source in all directions, as already suggested in Fig. 1.1. The transmission of particle motion along with the resulting variations in air pressure with distance from the source are represented in Fig. 1.6. Most people are more familiar with the kinds of waves that develop on the surface of a pond when a pebble is dropped into the water. These are transverse waves because the particles are moving at right angles to the direction that the wave is propagating. That is, the water particles oscillate up and down (vertically) even though the wave moves out horizontally from the spot where the pebble hit the water. This principle can be demonstrated by floating a cork in a pool, and then dropping a pebble in the water to start a wave. The floating cork reflects the motions of the water particles. The wave will move out horizontally, but the floating cork bobs up and down (vertically) at right angles to the wave. In contrast, sound waves are longitudinal waves because each air particle oscillates in the same direction in which the wave is propagating (Fig. 1.6). Although sound waves are longitudinal, it is more convenient to draw them with a transverse representation, as in Fig. 1.6. In such a diagram, the vertical dimension represents some measure of the size of the signal (e.g., displacement, pressure, etc.), and left to right distance represents time (or distance). For example, the waveform in Fig. 1.6 shows the amount of positive pressure (compression) above the baseline, negative pressure (rarefaction) below the baseline, and distance horizontally going from left to right.

Fig. 1.6 Longitudinal and transverse representations of a sound wave. Wavelength (λ) is the distance covered by one replication (cycle) of a wave, and is most easily visualized as the distance from one peak to the next.

The Sinusoidal Function

Simple harmonic motion is also known as sinusoidal motion, and has a waveform that is called a sinusoidal wave or a sine wave. Let us see why. Fig. 1.7 shows one cycle of a sine wave in the center, surrounded by circles labeled to correspond to points on the wave. Each circle shows a horizontal line corresponding to the horizontal baseline on the sine wave, as well as a radius line (r) that will move around the circle at a fixed speed, much like a clock hand but in a counterclockwise direction.

Fig. 1.7 Sinusoidal motion (θ, phase angle; d, displacement). (Adapted from Gelfand 2018, courtesy of CRC Press.)

Point a on the waveform in the center of the figure can be viewed as the “starting point” of the cycle. The displacement here is zero because this point is on the horizontal line. The radius appears as shown in circle b when it reaches 45° of rotation, which corresponds to point b on the sine wave. The angle between the radius and the horizontal is called the phase angle (θ) and is a handy way to tell location going around the circle and on the sine wave. In other words, we consider one cycle (one “round trip” of oscillation) to be the same as going around a circle one time. Just as a circle has 360°, we also consider one cycle to have 360°. Since 45/360 = 1/8, a phase angle (θ) of 45° is the same as one-eighth of the way around a circle or one-eighth of the way into a sine wave. Returning to the circle, the vertical displacement from the horizontal to the point where r intersects the circle is represented by a vertical line labeled d. This vertical line corresponds to the displacement of point b on the sine wave, where the displacement of the air particle is represented by the height of the point above the baseline. Notice that we now have a right triangle in the circle, where r is the hypotenuse, θ is an angle, and d is the leg opposite that angle. Recall from high school math that the sine of an angle equals the length of the opposite leg over the length of the hypotenuse. Here, sin θ = d/r. If we conveniently assume that the length of r is 1, then displacement d becomes the sine of angle θ, which happens to be 0.707. In other words, displacement is determined by the sine of the phase angle, and displacement at any point on the sine wave corresponds to the sine of θ. This is why it is called a sine wave.

The peak labeled c on the sine wave corresponds to circle c, where the rotating radius has reached the straight-up position. We are now one-fourth of the way into the wave and one-fourth of the way around the circle. Here, θ = 90° and the displacement is the largest it can be (notice that d = r on the circle). Continuing the counterclockwise rotation of r causes the amount of displacement from the horizontal to decrease, exemplified by point d on the sine wave and circle d, where θ is 135°. The oscillating air particle has already reversed direction and is now moving back toward the resting position. When it reaches the resting position there is again no displacement, as shown by point e on the sine wave and by the fact that r is now superimposed on the horizontal at θ = 180° in circle e. Notice that 180° is one half of the 360° round trip, so we are now halfway around the circle and halfway into the cycle of simple harmonic motion. In addition, displacement is zero at this location (180°).

Continuing the rotation of r places it in the lower left quadrant of circle f, corresponding to point f on the wave, where θ = 225°. The oscillating particle has overshot its resting position and the displacement is now increasing in the other direction, so that we are in the rarefaction part of the wave. Hence, displacement is now drawn in the negative direction, indicating rarefaction. The largest negative displacement is reached at point g on the wave, where θ = 270°, corresponding to circle g, in which r points straight down.

The air particle now begins moving in the positive direction again on its way back toward the resting position. At point h and circle h, the displacement in the negative direction has become smaller as the rotating radius passes through the point where 0 = 315° (point h on the wave and circle h). The air particle is again passing through its resting position at point i, having completed one round trip or 360° of rotation. Here, displacement is again zero. Having completed exactly one cycle, 360° corresponds to 0°, and circle i is the same one previously used as circle a.

Recall that r rotates around the circle at a fixed speed. Hence, how fast r is moving will determine how many degrees are covered in a given amount of time. For example, if one complete cycle of rotation takes 1 second, then 360° is covered in 1 second; 180° is covered in 1/2 second; 90° takes 1/4 second; 270° takes 3/4 second, etc. Hence, the phase angle also reflects the elapsed time from the onset of rotation. This is why the horizontal axis in Fig. 1.8 can be labeled in terms of phase. As such, the phase of the wave at each of the points indicated in Fig. 1.7 is 0° at a, 45° at b, 90° at c, 135° at d, 180° at e, 225° at f, 270° at g, 315° at h, and 360° at i, which is also 0° for the next cycle.

Fig. 1.8 Each panel shows two waves that are identical in every way except they are displaced from one another in terms of phase, highlighted by the shaded areas and the dotted vertical guidelines. Analogous examples of two radii moving around a circle are shown to the left of the waveforms. Top panel: Two waves that are 45° out-of-phase, analogous to two radii that are always 45° apart as they move around a circle. Second panel: Waves that are 90° out-of-phase, analogous to two radii moving around a circle 90° apart. Third panel: Waves that are 180° out-of phase, analogous to two radii that are always 180° apart (pointing in opposite directions) moving around a circle. Bottom panel: Two waves (and analogous radii moving around a circle) that are 270° out-of-phase.

Phase is often used to express relationships between two waves that are displaced relative to each other, as in Fig. 1.8. Each frame in the figure shows two waves that are identical to each other except that they do not line up exactly along the horizontal (time) axis. The top panel shows two waves that are 45° apart. Here, the wave represented by the thicker line is at 45° at the same time that the other wave (shown by the thinner line) is at 0°. The phase displacement is highlighted by the shaded area and the dotted vertical guideline in the figure. This is analogous to two radii that are always 45° apart as they move around a circle. In other words, these two waves are 45° apart or out-of-phase. The second panel shows the two waves displaced from each another by 90°, so that one wave is at 90° when other one is at 0°. Hence, these waves are 90° out-of-phase, analogous to two radii that are always 90° apart as they move around a circle. The third panel shows two waves that are 180° out-of-phase. Here, one wave is at its 90° (positive) peak at the same time that the other one is at its 270° (negative) peak, which is analogous to two radii that are always 180° apart as they move around a circle. Notice that these two otherwise identical waves are exact mirror images of each other when they are 180° out-of-phase, just as the two radii are always pointing in opposite directions. The last example in the bottom panel shows the two waves 270° out-of-phase.

Parameters of Sound Waves

We already know that a cycle is one complete replication of a vibratory pattern. For example, two cycles are shown for each sine wave in the upper frame of Fig. 1.9, and four cycles are shown for each sine wave in the lower frame. Each of the sine waves in this figure is said to be periodic because it repeats itself exactly over time. Sine waves are the simplest kind of periodic wave because simple harmonic motion is the simplest form of vibration. Later we will address complex periodic waves.

Fig. 1.9 Each frame shows two sine waves that have the same frequency but different amplitudes. Compared with the upper frame, twice as many cycles occur in the same amount of time in the lower frame; thus, the period is half as long and the frequency is twice as high.

The duration of one cycle is called its period. The period is expressed in time (t) because it refers to the amount of time that it takes to complete one cycle (i.e., how long it takes for one round trip). For example, a periodic wave that repeats itself every one-hundredth of a second has a period of 1/100 seconds, or t = 0.01 seconds. One-hundredth of a second is also 10 thousandths of a second (milliseconds), so we could also say that the period of this wave is 10 milliseconds.

Similarly, a wave that repeats itself every one-thousandth of a second has a period of 1 millisecond or 0.001 seconds; and the period would be 2 milliseconds or 0.002 seconds if the duration of one cycle is two-thousandths of a second.

The number of times a waveform repeats itself in one second is its frequency (f), or the number of cycles per second (cps). We could say that frequency is the number of cycles that can fit into one second. Frequency is expressed in units called hertz (Hz), which means the same thing as cycles per second. For example, a wave that is repeated 100 times per second has a frequency of 100 Hz; the frequency of a wave that has 500 cycles per second is 500 Hz; and a 1000 Hz wave has 1000 cycles in one second.

If frequency is the number of cycles that occur each second, and period is how much time it takes to complete one cycle, then frequency and period must be related in a very straightforward way. Let us consider the three examples that were just used to illustrate the relationship of period and frequency:

●A period of 0.01 seconds corresponds to a frequency (f) of 100 Hz.

●A period of 0.002 seconds corresponds to a frequency of 500 Hz.

●A period of 0.001 seconds corresponds to a frequency of 1000 Hz.

Now, notice the following relationships among these numbers:

●1/100 = 0.01 and 1/0.01 = 100.

●1/500 = 0.002 and 1/0.002 = 500.

●1/1000 = 0.001 and 1/0.001 = 1000.

In each case, the period corresponds to 1 over the frequency, and the frequency corresponds to 1 over the period. In formal terms, frequency equals the reciprocal of period, and period equals the reciprocal of frequency,

Each wave in the upper frame of Fig. 1.9 contains two cycles in 4 milliseconds, and each wave in the lower frame contains four cycles in the 4 milliseconds. If two cycles in the upper frame last 4 milliseconds, then the duration of one cycle is 2 milliseconds. Hence, the period of each wave in the upper frame is 2 milliseconds (t = 0.002 s), and the frequency is 1/0.002, or 500 Hz. Similarly, if four cycles last 4 milliseconds in the lower frame, then one cycle has a period of 1 millisecond (t