Basic Fundamentals in Hearing Science

Tony L. Sahley, PhD, CCC-AFrank E. Musiek, PhD, CCC-A

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Contents

Foreword by James A. Kaltenbach, PhD xiiiPreface xvAcknowledgments xvii

Chapter 1. What Is Science? 1What Is Hearing Science? 2

The Roots of Science 2The Definition of Science 2The Structure and Philosophy of Science 3

The Scientific Method: Philosophy and Practice 41A. Asking a Scientific Question: The Doctrine of 5

Empiricism2A. Formulating a Hypothesis: Identifying Relevant 7

Variables3A. Designing an Experimental Method: Operationally 9

Defining Variables1B. Asking Scientific Questions: Formulating 15

Predictions Based on a Theoretical Model and the Role of Deductive Logic (Deduction)

2B. Formulating Theory-Driven Hypotheses 163B. Designing Experimental Methods: Operationally 17

Defining Theory Constructs4. Reporting the Results: Hypothesis Testing 175A. Discussing and Interpreting the Results: 18

Evaluating Single Hypothesis-Driven Research5B. Discussing and Interpreting the Results: 18

Evaluating Theory-Driven ResearchThe Scientific Method: Structure of a Scientific 23

ManuscriptChapter Summary 31Chapter 1 Questions 32References 33

Chapter 2. Measurement 35Measurement 36Measurement Levels (Scales of Measurement) 36

Categorical Versus Continuous Variables 36Nominal-Level Measurement 37Ordinal-Level Measurement 39Interval-Level Measurement 40Ratio-Level Measurement 43

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Exponential Notation and Scientific Notation 45Exponents 45Scientific Notation 48Logarithms (Logs) 49Exponents/Logarithms of Whole Number 51

Integers of 10Nonwhole Number Exponents/Logarithms 52

Measurement Systems 53The Importance of Standard Units of Measurement 53

Proportionality 58Direct Proportionality 58Inverse Proportionality 59

Chapter Summary 59Chapter 2 Questions 60References 60

Chapter 3. Basic Terminology for Hearing Science 63The Importance and Relevance of Physics to Hearing 64

SciencePhysics and Energy 65Physics and Motion: An Overview 71

Physics and Motion: Length, Mass, and Time 75Derivatives of Length 76Displacement (Motion) of a Pendulum 78Elasticity and the Restorative Force of Elasticity 85

Chapter Summary 104Chapter 3 Questions 106References 106

Chapter 4. Application of the Basic Principles in 109 Hearing ScienceA Brief Historical Account of Motion 110

Galileo Galilei (1564–1642) 110Isaac Newton (1642–1727) 112

Kinematics and Dynamics 114Inertia 114

Mass, Inertia, and Newton’s First Law of Motion 115Force 116

Mass, Acceleration, and Newton’s Second Law 117 of Motion

A Closer Examination of Force — I 118A Closer Examination of Force — II 122MKS and CGS Metric Units Compared: Force 123MKS and CGS Metric Units Compared: Work 124

Contents vii

Force and Area: Pressure 125Power 128

Making Sense of Power 128Work and Energy Revisited: Types of Energy 130

Potential Energy 131Kinetic Energy 138

Momentum 142Collisions 143

Changes in Energy, Force, and Momentum During 148 Harmonic Motion

Scalar and Vector Quantities 152Chapter Summary 152Chapter 4 Questions 154References 154

Chapter 5. Harmonic Motion 157What Is Harmonic Motion? 159What Is Sinusoidal Motion? 159

Simplified Trigonometry 159Simplified Trigonometry and the Unit Circle 161

Phase Relations Between Displacement, Velocity, and 173Acceleration During Harmonic Motion

Peak Amplitude of a Sine Wave 174Peak-to-Peak Amplitude of a Sine Wave 175Compression and Rarefaction of a Sine Wave 176Compression, Rarefaction, and Equilibrium 177Root-Mean-Square (RMS) Amplitude 178What Are Radians? 187

Mass and Stiffness in Opposition 193The Role of Mass 193The Role of Stiffness 193Relation to Sound 194

Frequency and Period Revisited 194Hertz 194Mass, Stiffness, Frequency, and Period 199

Free Vibration and Resonance 200Angular Velocity/Angular Frequency 201Fundamental Frequency 201Friction, Damping, and Resistance 202Forced Vibration 205Impedance: Frictional Resistance and Reactance 209

Chapter Summary 217Chapter 5 Questions 219References 222

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Chapter 6. The Measurement of Sound 223Sound Defined 226Work, Power, and the Watt Revisited 230

Acoustic Intensity (I) 231Inverse Square Law 233Quantifying Acoustic Intensity 236

Newtons (N), Dynes, and Pressure Revisited 237Quantifying Pressure 237

The Relationship Between Intensity (I) and Pressure (P) 239Threshold and Upper Limit Values for Intensity 239

and PressureAcoustic Intensity Level (IL) and Sound Pressure 239

Level (SPL)Historical Overview: The Bel 240

Bel-Intensity Level (IL) 242Evaluation of the Bel 245

The Decibel (dB) 245Decibels of Intensity Level (dB IL) 246Bel-Sound Pressure Level (SPL) 247Relationship Between Intensity (I) and Pressure (P) 250

RevisitedDecibels of Sound Pressure Level (dB SPL) 251The Concept of Zero Decibels (0 dB) 256The Doubling or Halving of Signal Power or Pressure 257

Decibel Problems 259Sound Level Meters (SLMs) 262

SLM Weighting Networks (Filters) 263Octave-Band Analyses 265Determining Cut-Off Frequencies for Octave and 267 Third-Octave-Band FiltersSLM Calibration 269Types of SLMs 269

Microphones 270Types of Microphones 271Pressure Types of Microphones 272The Velocity Type of Microphone 277Microphone Directionality 278

The Sound-Field 279Types of Sound-Fields 280

Types of Sounds I: Periodic Waveforms 286Simple Periodic Sinusoidal Waveforms: Pure Tones 286Complex Waveforms 294

Types of Sounds II: (Complex) Aperiodic Waveforms 307(Complex) Aperiodic Transient Signals 308(Complex) Aperiodic Continuous Signals 321

Contents ix

Modulated Signals 331Warble Tones 334

The Spectral Analysis and the Amplitude Spectrum 334The Line Spectrum 335The Continuous Spectrum 340The Phase Spectrum 341

Spectral Shaping: Filters 343Types of Filters I: Ideal Filters 344Types of Filters II: Real Filters 346Filters in Personal Amplification 356

Linear Systems 360Linear Distortion 362

Nonlinear Distortion 363Amplitude Distortion 363Nonlinear Transient and Imaging Distortion 366Intermodulation Distortion: Combination Tones 366

Chapter Summary 369Chapter 6 Questions 372References 373

Chapter 7. Acoustics 375Acoustics Defined 376Wavelength 377

Sound Transmission and Wavelength 380Types of Waveform Motion 381

Transverse Wave Motion 381Longitudinal Wave Motion 384

The Behavior of Sound in a Sound-Field 386Sound Transmission and/or Reflection 386Sound Transmission and/or Absorption 389Sound Transmission and Diffraction 390Sound Transmission and Sound-Shadow Effects 397The Doppler-Effect 399Sound Transmission and Shock Waves 404Sound Transmission and Refraction 406Sound Transmission and Interference 410Sound-Field Calibration 422

Resonators 424Resonances of Air-Filled Tubes 426

Chapter Summary 442Chapter 7 Questions 446References 446

Chapter 8. Psychoacoustics 449Psychophysics 451

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Psychoacoustics 451Threshold Revisited 452Absolute Threshold Revisited 453The Threshold of Audibility 454

The Minimum Audibility Curve (MAC) 456The Threshold of Audibility: Relationship to the Pure 460

Tone AudiogramThe Audiometer 461The Pure Tone Audiogram 463

Loudness Scaling 467The Phon: Phons of Loudness Level 469Differential Threshold 472The Loudness of Complex Signals 480

Pitch 481Signal Duration and Pitch 481Differential Thresholds for Pitch 482Intensity Level and Pitch 483The Mel: Mels of Pitch Perception 485The Pitch of Complex Signals 487

The Critical Band 490Loudness Summation and the Critical Band 492Pitch and the Critical Band 494Masking 495Masking and the Critical Band 497The Equivalent Rectangular Bandwidth (ERB) 498The Critical Ratio 500Beats, Flutter, Roughness, and the Critical Band 502

The Temporal Aspects of Hearing 503Temporal Summation 504Temporal Masking 504Auditory Adaptation and Auditory Fatigue 506

Binaural Hearing 510Binaural Summation 511Binaural Fusion 511Binaural Sound Localization 512Monaural Sound Localization 518Binaural Sound Lateralization 519

Chapter Summary 520Chapter 8 Questions 527References 530

Chapter 9. Nervous System Terminology: The Structure and 535 Function of Neurons and the Cranial NervesThe Neuron 537

Structure and Function of the Neuron 539

Contents xi

Generation of the Action Potential 545Types of Neurons 551

The Peripheral Nervous System (PNS) 554The Cranial Nerves 554

Chapter Summary 590Bibliography 593

Chapter 10. Anatomy and Physiology of Hearing 595Introduction 595The Peripheral Auditory System 596

The Temporal Bone 596The Outer Ear 598The Middle Ear (Tympanum) 600The Cochlea 606The Auditory Nerve 615

The Central Auditory Nervous System 617The Cochlear Nucleus 619The Superior Olivary Complex 620The Lateral Lemniscus 621Inferior Colliculus 621The Medial Geniculate Body 622Auditory Cortex and Subcortex 623The Corpus Callosum 626

The Efferent System 628Structure 628Function 628

Vascular Supply for the Auditory System 629The Peripheral System 629The Central System 630

Chapter Summary 630References 631

Appendix A. Exponential and Scientific Notation 635Section A1. Conversion From Conventional to 635

Exponential Notation Numbers That Are Exact Multiples of Ten 635

Section A2. Operating Principles in the Use of 636 Exponents

I. Multiplication 636II. Exponentiation 637III. Division 637IV. Combining Multiple Exponents 638

Section A3. Conversion From Conventional to 638 Scientific Notation

Section A4. Working With Scientific Notation 640

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I. Multiplication With Scientific Notation 640II. Division With Scientific Notation 641

References 642

Appendix B. Logarithms 643Section B1. The Characteristic and the Mantissa 643Section B2. Working With Logarithms 644

Rules in the Use of Logarithms 644Section B3. Antilogarithms (Antilogs) 647

Rules for Computations With Logarithms 650References 651

Appendix C. Exponents With Metric Prefixes 653

Index 655

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Foreword

Hearing science is a multidisciplinary subject that is rooted in a diverse array of fields, including physics, engineer-ing, anatomy, physiology, cell biology, and psychology. Bringing together the vast reservoir of knowledge from all these disciplines into a single text-book that does justice to the field’s complexity without alienating its read-ers is not a simple task and few have done so effectively. Sahley and Musiek are among the exceptions. Drawing on their many years of combined teach-ing and research experience/expertise in clinical audiology, hearing science, and auditory neuropharmacology, as well as their combined expertise in gen-eral medical physiology, neuroanatomy, and neurophysiology, they have done a masterful job of making this com-plex body of knowledge approachable and straightforward. The book is orga-nized into 10 chapters, each describ-ing a different core aspect of hearing science. The book’s first two chapters are introductory to students new to sci-ence, providing an overview of what science is and summarizing basic con-cepts, quantities, and measurement systems that are used to describe and characterize the physical world. These chapters set the stage for Chapters 3 and 4, focusing on the terminology of hearing science and the application of its basic principles. Chapters 5 and 6 describe harmonic motion and all the properties of sound waves and how they are measured, while Chapter 7 journeys into the domain of acoustics, examining the propagation of sound

waves through space and the com-plex interactions that shape the sound field. This provides a perfect segue into Chapter 8, summarizing the principles and concepts of psychoacoustics, the science of auditory perception. This chapter deals with what we hear and how the psychophysical attributes of sound vary with changes in the physi-cal parameters of auditory stimulation. The last two chapters focus on the biol-ogy of hearing, beginning with a sum-mary of terminology used to describe the various components and principles of nervous system organization (Chap-ter 9) and ending with a review of the anatomy and physiology of the three subdivisions of the ear (Chapter 10). Each of these chapters is characterized by a well-organized text that is pref-aced by an inspiring quote and a list of terms to be defined, and each ends with a clear and succinct summary of concepts and principles introduced. Those chapters with a more quantitative bent also include numerous questions and/or problems to encourage stu-dents to put their knowledge to work or think beyond the boundaries of the book’s pages. The text is written with meticulous and thorough attention to detail and accuracy. This is especially apparent with regard to the formulas and tables provided for the compu-tations of the Bel, decibel, and RMS amplitude. An additional feature that adds to the attractiveness and flair of the book is the frequent reference to historic discoveries and to those who made them. Concepts presented in the

xiv Basic Fundamentals in Hearing Science

text are beautifully complemented by illustrations, graphs, and equations. This is a book I wish I had had when I was a student, and I believe it will become a first choice textbook among undergraduate and graduate students.

It will provide quick answers to ques-tions, both simple and complex, and will provide ever-deepening insights into hearing science when knowledge of details is the goal.

— James A. Kaltenbach, PhD Director of Otology Research The Cleveland Clinic

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Chapter 4

Application of the Basic Principles in Hearing Science

In a letter to Robert Hooke dated February 5, 1675, Newton wrote, “If I have seen further than others it is by standing upon the shoulders of

giants” (Gianopoulos, 2006, p. 49; Hawking, 2002, p. 725). Perhaps Newton should have said, “I used the shoulders of giants as a springboard.”

Hawking, 2002, p. XIII

Alphabetized Listing of Key Terms Discussed in Chapter 4

acceleration

action

atmospheric pressure

bar

CGS metric system

collisions

compliance

cycle

displacement

dynamics

dyne

Einstein, Albert

elastic collision

energy

erg

first law of motion, Newton’s

force

friction

frictional resistance

Galilei, Galileo

geocentric

gravitational potential energy

gravity

Halley, Edmond

heliocentric

Hooke’s law

horsepower

Huygens, Christiaan

inertia

inertia, law of

Inquisition

interactive forces

joule

Joule, James Prescott

kinematics

kinetic energy

law of inertia

laws of motion, Newton’s

Leibniz, Gottfried Wilhelm

mass

mechanics

Medicean stars

microbar

MKS metric system

momentum

motion

natural motion

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A Brief Historical Account of Motion

The connection between vibratory motion and sound was introduced in the previous chapter. Historically, the study of motion, known also in physics as mechanics, has occupied the inter-ests of scholars that have originated from the time of the ancient philoso-pher Aristotle (384–322 BC), up to and beyond the era of the eminent Albert Einstein (1879–1955). Today, a thorough understanding of motion remains an essential component within the study of contemporary hearing science. What follows is a brief historical account of Galileo Galilei (1564–1642) and Isaac Newton (1642–1727), both of whom

made significant contributions that advanced the study of motion, and of hearing science.

Galileo Galilei (1564–1642)

Recall the image of Galileo (see Por-trait 1–1) that was presented in Chapter 1. Galileo was born in Pisa, Italy, and became the foremost scientist of the early 17th century. He studied medicine and the philosophy of Aristotle at the University of Pisa from 1581 to 1584. At the age of 20, Galileo discovered the properties of the pendulum. As indi-cated in the previous chapter, Galileo demonstrated that the rate of harmonic motion of a pendulum is inversely dependent on its length. This discovery

net force

newton (of force)

Newton, Isaac

one atmosphere of pressure

pascal (Pa)

Pascal, Blaise

pendulum

peripatetics

Pope, Alexander

potential energy

pounds per square inch (psi)

power

pressure

Principia

rate

reaction

recoil

reflecting telescope

refracting telescope

restorative force

Rome, Holy Office of

Rules of Reasoning, Newton’s

scalar quantity

scalars

second law of motion, Newton’s

Slinky

spring-mass system

stretching force (tension)

support force

telescope, Newtonian

third law of motion, Newton’s

time

vector quantity

vectors

velocity

violent motion

watt

Watt, James

weight

work

Wren, Christopher

Application of the Basic Principles in Hearing Science 111

made accurate time-keeping possible. It is not known whether Galileo actually built a pendulum clock, though Chris-tiaan Huygens (1629–1695) did build one more than ten years after Galileo’s death (Giancoli, 2005).

In 1585, Galileo abandoned the study of medicine for research in mathematics (Hawking, 2002). His approach to sci-ence included idealization and simpli-fication, the quantification of theories (operationism), the development of the-ories (induction) with testable hypoth-eses (deduction), and the completion of empirical investigations in order to test his predictions (or simply, hypoth-esis testing). For these reasons, Gali-leo is often called the “father of mod-ern experimental science” (Hawking, 2002). In 1589 at the age of 25, Galileo became a professor of mathematics at the University of Pisa. From his experi-ments with falling and rolling objects, he developed the concept of accelera-tion. He demonstrated that for a given location on the earth, solid objects with different amounts of mass would fall to the earth at roughly equivalent speeds or with constant acceleration, provided the air resistance was equivalent, or zero, as in a vacuum. Galileo, however, could not explain why. This explanation would require the genius of Isaac New-ton. Galileo additionally determined that objects forcibly set into motion by a push or a pull on a horizontal sur-face eventually come to rest due to a force, called “friction” and not “nature,” as Aristotle had originally asserted. He also reasoned that if friction were com-pletely removed, an object forcibly set into motion would continue to move indefinitely in a straight line with con-stant velocity, provided that no other

force acted to alter its motion. Galileo coined the term “inertia,” and inertia became central to Galileo’s laws of motion. Hence, according to Galileo, the constant horizontal motion of an object was no less natural than the condition of rest. This way of thinking was in direct contradiction to the popu-larly held metaphysical philosophies of Aristotle. Hence, Galileo discredited the contemporarily held Aristotelian con-cepts of nature and motion and this led to the creation of a new vision of the universe (Gianopoulos, 2006). From his prudent observations and experimen-tation, Galileo helped advance a new worldview in which the affairs of the mind were separate from the affairs of matter. In turn, advocates of Aristotelian thinking (called Peripatetics) eventually forced Galileo to leave the University of Pisa. In 1592, Galileo became profes-sor of mathematics at the University of Padua where he made significant dis-coveries in astronomy (Gianopoulos, 2006). Galileo built a refracting tele-scope that was an improvement on a design first proposed in 1610 by Hans Lipperhey (Hawking, 2002). His conclu-sions, based on his earlier observation in 1604 of a supernova, and his telescopic observations in 1610 of the moon, Jupi-ter, and the galaxy, were again in direct opposition to the prevailing philosophy of an unchanging universe, as put forth by Aristotle (Hawking, 2002).

In 1610 Galileo discovered and named the four brightest moons of Jupi-ter, which he called the Medicean stars (Hawking, 2002). Later he detected the phases of Venus, and the sunspots of the Sun. In total, Galileo’s scientific conclusions gave credence to a helio-centric Copernican view of the cosmos

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(Gianopoulos, 2006). By displacing the earth from the center of the universe, he was able to conclude that the earth and the heavens both operated under simi-lar laws (Hawking, 2002). He attacked, with empirical evidence, the belief that mechanics and cosmology were sepa-rate subject matters. In 1616, officials of the Church, together with other Peri-patetics, warned Galileo to abandon his belief in the Copernican view of the cosmos. In 1632, the Holy Office of Rome (The Inquisition) imprisoned Gal-ileo for his published writings and con-fined him for an indefinite time to his villa in Florence (Gianopoulos, 2006; Hawking, 2002). Galileo remained there under house arrest in Tuscany, where he later died in 1642 (Giancoli, 2005; Hewitt, 2010).

Isaac Newton (1642–1727)

Newton was born in Woolsthorpe, Lin-colnshire, England, in the same year that Galileo died in Florence, while under house arrest (Gianopoulos, 2006; Hawk-ing, 2002) (Portrait 4–1). At the age of 11, while attending grammar school, Newton discovered his particular tal-ent for building clocks, sundials, and a working model of a windmill that was powered by a running mouse (Hawking, 2002). Newton led a rather solitary life (Gianopoulos, 2006), and much of New-ton’s adulthood was filled with episodes of harsh, vindictive attacks, not only against perceived enemies, but against friends and family as well. It has been speculated that Newton’s achievements were the result of his vindictive obses-sions and arrogance (Hawking, 2002). Beginning at the age of 19, and from 1661 to 1665, Newton attended Trinity

College, which was part of Cambridge University (Gianopoulos, 2006). While at Cambridge, Newton studied the phi-losophy of Aristotle and Descartes, the science of Thomas Hobbs and Robert Boyle, the mechanics of Copernicus, the astronomy of Galileo, and the optics of Kepler (Hawking, 2002). While New-tonian mechanics has guided astrono-mers and scientists in their search for knowledge for more than 200 years, it was Newton’s work with prisms and light (1704) (Portrait 4–2) that initially brought him fame (Gianopoulos, 2006). Newton was the first to use a prism to break a ray of light into a spectrum of colors. He then used a second prism to combine the colors back into white light (Stutz, 2006).

Portrait 4–1. Isaac Newton (1642–1727). “Nature and nature’s laws lay hid at night: God said, ‘Let Newton be! And all was light.’” Written by Alexander Pope to describe Newton’s gift to humanity (Hawking, 2002, p. 732). Printed with permission. Wikimedia Commons, public domain.

Application of the Basic Principles in Hearing Science 113

Newton was a rationalist whose em- phasis was often based on defining true mathematical notions, independent of observation (Gianopoulos, 2006). The British physicist Robert Hooke, the English astronomer Edmond Halley, the Dutch mathematician Christiaan Huygens, and the architect Christo-pher Wren were all contemporaries of Isaac Newton (Hawking, 2002). At the age of 23 (1665) Newton formu-lated his universal law of gravitation and later, from 1666 to 1667, developed the binomial theorem. The law of uni-versal gravitation stated that all mat-ter is mutually attracted with a force directly proportional to the product of their (individual) masses, and inversely proportional to the square of the dis-tance between them. He was also able to use his inverse square law theory of

gravity to explain the elliptical motions of the planets and the rising and fall-ing of the tides (Gianopoulos, 2006; Hawking, 2002). Newton invented the calculus (1666), though the differen-tial and integral calculus developed by Gottfried Wilhelm Leibniz (1646–1716) in roughly the same period, is more commonly used by mathematicians and engineers. Nevertheless, Newton is still considered to be the father of infinitesi-mal calculus, mechanics and planetary motion, and theories of light and color. He secured his place in history by for-mulating the law of gravitational force and defining his three laws of motion (Hawking, 2002).

Newton, like Galileo, adhered to the heliocentric-Copernican view of the cosmos, and he viewed changes in the motion of a mass as originating from sources external to the mass, rather than representing internal activity within the mass (Hawking, 2002). In 1668, Newton developed (Stutz, 2006), constructed, and later made revisions (1671–1672) to the first reflecting telescope (Gianopou-los, 2006). Newton’s original telescope was only 6 inches long and is still on display at the library of the Royal Soci-ety of London. His invention was the prototype for the design that later came to be called the “Newtonian telescope,” a term that is practically synonymous with the reflecting telescope (Stutz, 2006). Newton became a mathematics professor at Cambridge in 1669 and was appointed the Lucasian Professor of Mathematics at Trinity College (in Cambridge) which is the same posi-tion held today by the renowned phys-icist Stephen Hawking (Gianopoulos, 2006). Extending the work of Galileo, Newton formulated his three laws of motion in his great work, the Principia

Portrait 4–2. Newton’s mathematical principles of natural philosophy. Printed with permission. Wiki-media Commons, public domain.