Section 12.3
Hearing and the Ear
169
FIGURE 12.5 A semidiagrammatic drawing of the ear with various structures cut away and simplified to show the basic relationships more clearly. The middle earmuscles have been omitted.
The ear canal of an average adult is about 0.75 cm in diameter and 2.5 cm long, a configuration that is resonant for sound waves at frequencies around3000 Hz. This accounts in part for the high sensitivity of the ear to soundwaves in this frequency range.
For an animal to perceive sound, the sound has to be coupled from air to the sensory cells that are in the fluid environment of the inner ear. We showedearlier that direct coupling of sound waves into a fluid is inefficient becausemost of the sound energy is reflected at the interface. The middle ear providesan efficient conduction path for the sound waves from air into the fluid of theinner ear.
The middle ear is an air-filled cavity that contains a linkage of three bones called ossicles that connect the eardrum to the inner ear. The three bones arecalled the hammer, the anvil, and the stirrup. The hammer is attached to theinner surface of the eardrum, and the stirrup is connected to the oval window,which is a membrane-covered opening in the inner ear.
Chapter 12 Waves and Sound
The middle ear serves yet another purpose. It isolates the inner ear from the disturbances produced by movements of the head, chewing, and the internal vibrations produced by the person’s own voice. To be sure, some of thevibrations of the vocal cords are transmitted through the bones into the innerear, but the sound is greatly attenuated. We hear ourselves talk mostly bythe sound reaching our eardrums from the outside. This can be illustrated bytalking with the ears plugged.
The Eustachian tube connects the middle ear to the upper part of the throat.
Air seeps in through this tube to maintain the middle ear at atmospheric pressure. The movement of air through the Eustachian tube is aided by swallowing. A rapid change in the external air pressure such as may occur during anairplane flight causes a pressure imbalance on the two sides of the eardrum.
The resulting force on the eardrum produces a painful sensation that lasts untilthe pressure in the middle ear is adjusted to the external pressure. The pain isespecially severe and prolonged if the Eustachian tube is blocked by swellingor infection.
The conversion of sound waves into nerve impulses occurs in the cochlea, which is located in the inner ear. The cochlea is a spiral cavity shaped likea snail shell. The wide end of the cochlea, which contains the oval and theround windows, has an area of about 4 mm2. The cochlea is formed into aspiral with about 2 3 turns. If the cochlea were uncoiled, its length would be
4
about 35 mm.
Inside the cochlea there are three parallel ducts; these are shown in the highly simplified drawing of the uncoiled cochlea in Fig. 12.6. All three ductsare filled with a fluid. The vestibular and tympanic canals are joined at theapex of the cochlea by a narrow opening called the helicotrema. The cochlearduct is isolated from the two canals by membranes. One of these membranes,called the basilar membrane, supports the auditory nerves.
The vibrations of the oval window set up a sound wave in the fluid filling the vestibular canal. The sound wave, which travels along the vestibular canaland through the helicotrema into the tympanic canal, produces vibrations inthe basilar membrane which stimulate the auditory nerves to transmit electrical pulses to the brain (see Chapter 13). The excess energy in the sound waveis dissipated by the motion of the round window at the end of the tympaniccanal.
Section 12.3 Hearing and the Ear
171
FIGURE 12.6 An uncoiled view of the cochlea.
12.3.1 Performance of the Ear
Loudness, pitch, and quality are some of the terms we use to describe thesounds we hear. It is a great challenge for physiologists to relate these subjective responses with the physical properties of sound such as intensity andfrequency. Some of these relationships are now well understood; others arestill subjects for research.
In most cases, the sound wave patterns produced by instruments and voices are highly complex. Each sound has its own characteristic pattern. It wouldbe impossible to evaluate the effect of sound waves on the human auditorysystem if the response to each sound pattern had to be analyzed separately.
Fortunately the problem is not that complicated. About 150 years ago, J. B.
J. Fourier, a French mathematician, showed that complex wave shapes canbe analyzed into simple sinusoidal waves of different frequencies. In otherwords, a complex wave pattern can be constructed by adding together a sufficient number of sinusoidal waves at appropriate frequencies and amplitudes.
Therefore, if we know the response of the ear to sinusoidal waves over a broadrange of frequencies, we can evaluate the response of the ear to a wave patternof any complexity.
An analysis of a wave shape into its sinusoidal components is shown in Fig. 12.7. The lowest frequency in the wave form is called the fundamental, and the higher frequencies are called harmonics. Figure 12.8, shows thesound pattern for a specific note played by various instruments. It is the harmonic content of the sound that differentiates one sound source from another.
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Chapter 12 Waves and Sound
FIGURE 12.7 The analysis of a complex wave shape (a), into its sine components (b). The point-by-point addition of the fundamental frequency sine wave and theharmonic frequency sine waves yields the wave shape shown in (a).
For a given note played by the various instruments shown in Fig. 12.8, thefundamental frequency is the same but the harmonic content of the wave isdifferent for each instrument.
12.3.2 Frequency and Pitch
There are wide variations in the frequency response of individuals. Somepeople cannot hear sounds above 8000 Hz, whereas a few people can hearsounds above 20,000 Hz. Furthermore, the hearing of most people deteriorateswith age.
The sensation of pitch is related to the frequency of the sound. The pitch increases with frequency. Thus, the frequency of middle C is 256 Hz, and the
Section 12.3 Hearing and the Ear
173
FIGURE 12.8 Wave forms of sound from different musical instruments sounding the same note.
frequency of the A above is 440 Hz. There is, however, no simple mathematical relationship between pitch and frequency.
12.3.3 Intensity and Loudness threshold of hearing and the , respectively. Sound intensities above the threshold of pain may causepermanent damage to the eardrum and the ossicles.
The ear does not respond linearly to sound intensity; that is, a sound which is a million times more powerful than another does not evoke a million timeshigher sensation of loudness. The response of the ear to intensity is closer tobeing logarithmic than linear.
Because of the nonlinear response of the ear and the large range of inten sities involved in the process of hearing, it is convenient to express soundintensity on a logarithmic scale. On this scale, the sound intensity is measured relative to a reference level of 10−16 W/cm2 (which is approximately the Chapter 12 Waves and Sound TABLE 12.1 Sound Levels Due to Various Sources (representative values) Sound level Sound level Source of sound (dB)
(W/cm2)
Threshold of pain
120
10−4
Riveter
90
10−7
Busy street traffic
70
10−9
Ordinary conversation
60
10−10
Quiet automobile
50
10−11
Quiet radio at home
40
10−12
Average whisper
20
10−14
Rustle of leaves 10
10−15
Threshold of hearing
0
10−16 lowest audible sound intensity). The logarithmic intensity is measured in unitsof decibel (dB) and is defined as Sound intensity in W/cm2 Logarithmic intensity 10 log
(12.5)
10−16 W/cm2 Thus, for example, the logarithmic intensity of a sound wave with a power of 10−12 W/cm2 is
10−12
Logarithmic intensity 10 log 40 dB 10−16 Intensities of some common sounds are listed in Table 12.1.
At one time, it was believed that the ear responded logarithmically to sound intensity. Referring to Table 12.1, a logarithmic response would implythat, for example, a busy street sounds only six times louder than the rustle ofleaves even though the power of the street sounds is a million times greater.
Although it has been shown that the intensity response of the ear is not exactlylogarithmic, the assumption of a logarithmic response still provides a usefulguide for assessing the sensation of loudness produced by sounds at differentintensities (see Exercises 12-1 and 12-2).
The sensitivity of the ear is remarkable. At the threshold of hearing, in the range of 2000–3000 Hz, the ear can detect a sound intensity of 10−16 W/cm2.
This corresponds to a pressure variation in the sound wave of only about2.9 × 10−4 dyn/cm2 (see Exercise 12-3). Compare this to the backgroundatmospheric pressure, which is 1.013 × 106 dyn/cm2. This sensitivity appears
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even more remarkable when we realize that the random pressure variationsin air due to the thermal motion of molecules are about 0.5 × 10−4 dyn/cm2.
Thus, the sensitivity of the ear is close to the ultimate limit at which it wouldbegin to detect the noise fluctuations in the air. The displacement of themolecules corresponding to the power at the threshold of hearing is less thanthe size of the molecules themselves.
The sensitivity of the ear is partly due to the mechanical construction of the ear, which amplifies the sound pressure. Most of the mechanical amplification is produced by the middle ear. The area of the eardrum is about 30times larger than the oval window. Therefore, the pressure on the oval windowis increased by the same factor (see Exercise 12-4). Furthermore, the ossiclesact as a lever with a mechanical advantage of about 2. Finally, in the frequencyrange around 3000 Hz, there is an increase in the pressure at the eardrum dueto the resonance of the ear canal. In this frequency range, the pressure isincreased by another factor of 2. Thus, the total mechanical amplificationof the sound pressure in the 3000-Hz range is about 2 × 30 × 2 120.
Because the intensity is proportional to pressure squared (see Eq. 12.3), theintensity at the oval window is amplified by a factor of about 14,400.
The process of hearing cannot be fully explained by the mechanical con struction of the ear. The brain itself plays an important role in our perceptionof sound. For example, the brain can effectively filter out ambient noise andallow us to separate meaningful sounds from a relatively loud background din.
(This feature of the brain permits us to have a private conversation in the midstof a loud party.) The brain can also completely suppress sounds that appear tobe meaningless. Thus, we may lose awareness of a sound even though it stillproduces vibrations in our ear. The exact mechanism of interaction betweenthe brain and the sensory organs is not yet fully understood.
12.4
Bats and Echoes Vespertilionidae family of bats emitshort chirps as they fly. The chirps last about 3 × 10−3 sec (3 msec) with atime interval between chirps of about 70 msec. Each chirp starts at a frequencyof about 100 × 103 Hz and falls to about 30 × 103 Hz at the end. (The earsof bats, of course, respond to these high frequencies.) The silent interval Chapter 12 Waves and Sound
Experiments have shown that with echo location bats can avoid wire obsta cles with diameters down to about 0.1 mm, but they fail to avoid finer wires.
This is in accord with our discussion of wave diffraction (see Exercise 12-7).
Other animals, such as porpoises, whales, and some birds, also use echoes tolocate objects, but they are not able to do so as well as bats.
12.5 Sounds Produced by Animals vocal cords are the primarysource of sound. These are two reeds, shaped like lips, attached to the upperpart of the trachea. During normal breathing the cords are wide open. To produce a sound the edges of the cords are brought together. Air from the lungspasses through the space between the edges and sets the cords into vibration.
The frequency of the sounds is determined by the tension on the vocal cords.
The fundamental frequency of the average voice is about 140 Hz for males andabout 230 Hz for females. The sound produced by the vocal cords is substantially modified as it travels through the passages of the mouth and throat. Thetongue also plays an important role in the final sound. Many voice sounds areproduced outside the vocal cords (for example, the consonant s). The soundsin a whispering talk are also produced outside the vocal cords.
12.6
Acoustic Traps
Electronically generated sounds that mimic those of animals and insects areincreasingly being used as lures to trap the creatures. Electronic fishing luresare now commercially available. One such device mimics the distress call ofa mackerel and attracts marlin and other larger fish to the fishhook.
Ultrasonic Waves
177
To obtain baseline data on bat populations, often the bats have to be captured and examined. In one such study, the social call of a rare Bechstein’sbat that inhabits the woodlands of southeast England was synthesized luringthe bats into the net. (The bats were released after examination.)
The Mediterranean fruit fly commonly called medfly is a pest that infests fruits and other crops causing on the order of $1 billion damage worldwide.
At present, spraying of pesticides is the most common way of controlling themedfly. An environmentally more friendly way of controlling the pest hasbeen sought for many years. Sound traps under development may provide aviable alternative. The male medfly produces with its wings a vibration at afundamental frequency of about 350 Hz accompanied by complex harmonics.
The female medflys are attracted to this courtship call and can be lured intoa trap.
12.7 Clinical Uses of Sound
A modified version of the stethoscope consists of two bells that are placed ondifferent parts of the body. The sound picked up by one bell is conducted toone ear, and the sound from the other bell is conducted to the other ear. Thetwo sounds are then compared. With this device, it is possible, for example, tolisten simultaneously to the heartbeats of the fetus and of the pregnant mother.
12.8 Ultrasonic Waves ultrasonic waves. Because of their short wavelength, ultrasonic waves can befocused onto small areas and can be imaged much as visible light (see Exercise 12-8).
Ultrasonic waves penetrate tissue and are scattered and absorbed within it.
Using specialized techniques called ultrasound imaging, it is possible to formvisible images of ultrasonic reflections and absorptions. Therefore, structureswithin living organisms can be examined with ultrasound, as with X-rays.
Ultrasonic examinations are safer than X-rays and often can provide as much Chapter 12 Waves and Sound
The frequency of sound detected by an observer depends on the relative motion between the source and the observer. This phenomenon is called theDoppler effect. It can be shown (see Exercise 12-9) that if the observer isstationary and the source is in motion, the frequency of the sound f detectedby the observer is given by
v
f f
(12.6)
v ∓ vs f is the frequency in the absence of motion, v is the speed of sound, and vs is the speed of the source. The minus sign in the denominator is to beused when the source is approaching the observer, and the plus sign when thesource is receding.
Using the Doppler effect, it is possible to measure motions within a body.
One device for obtaining such measurements is the ultrasonic flow meter,which produces ultrasonic waves that are scattered by blood cells flowingin the blood vessels. The frequency of the scattered sound is altered by theDoppler effect. The velocity of blood flow is obtained by comparing the incident frequency with the frequency of the scattered ultrasound.
Within the tissue, the mechanical energy in the ultrasonic wave is con verted to heat. With a sufficient amount of ultrasonic energy, it is possible toheat selected parts of a patient’s body more efficiently and evenly than can bedone with conventional heat lamps. This type of treatment, called diathermy,is used to relieve pain and promote the healing of injuries. It is actually possible to destroy tissue with very high-intensity ultrasound. Ultrasound is nowroutinely used to destroy kidney and gall stones (lithotripsy).
EXERCISES
12-1. The intensity of a sound produced by a point source decreases as the square of the distance from the source. Consider a riveter as a pointsource of sound and assume that the intensities listed in Table 12.1 aremeasured at a distance 1 m away from the source. What is the maximumdistance at which the riveter is still audible? (Neglect losses due toenergy absorption in the air.)
12-2. Referring to Table 12.1, approximately how much louder does busy street traffic sound than a quiet radio?
Exercises
179
12-3. Calculate the pressure variation corresponding to a sound intensity of 10−16 W/cm2. (The density of air at 0◦C and 1 atm pressure is 1.29 ×10−3 g/cm3; for the speed of sound use the value 3.3 × 104 cm/sec.)
12-4. Explain why the relative sizes of the eardrum and the oval window result in pressure magnification in the inner ear.
12-5. Explain how a bat might use the differences in the frequency content of its chirp and echo to estimate the size of an object.
12-6. With a 70-msec space between chirps, what is the farthest distance at which a bat can detect an object?
12-7. In terms of diffraction theory, discuss the limitations on the size of the object that a bat can detect with its echo location.
12-8. Estimate the lower limit on the size of objects that can be detected with ultrasound at a frequency of 2 × 106 Hz.
12-9. With the help of a basic physics textbook, explain the Doppler effect and derive Eq. 12.6.
The word electricity usually evokes the image of a man-made technologybecause we usually associate electricity with devices such as amplifiers, televisions, and computers. This technology has certainly played an important rolein our understanding of living systems, as it has provided the major tools forthe study of life processes. However, many life processes themselves involveelectrical phenomena. The nervous system of animals and the control of musclemovement, for example, are both governed by electrical interactions. Evenplants rely on electrical forces for some of their functions. In this chapter,we will describe some of the electrical phenomena in living organisms, and inChapter 14 we will discuss the applications of electrical technology in biologyand medicine. A brief review of electricity in Appendix B summarizes theconcepts, definitions, and equations used in the text.
13.1
The Nervous System
The most remarkable use of electrical phenomena in living organisms is foundin the nervous system of animals. Specialized cells called neurons form acomplex network within the body which receives, processes, and transmitsinformation from one part of the body to another. The center of this networkis located in the brain, which has the ability to store and analyze information.
Based on this information, the nervous system controls various parts of thebody. The nervous system is very complex. The human nervous system, forexample, consists of about 1010 interconnected neurons. It is, therefore, notsurprising that, although the nervous system has been studied for more than
180
a hundred years, its functioning as a whole is still poorly understood. It isnot known how information is stored and processed by the nervous system;nor is it known how the neurons grow into patterns specific to their functions.
Yet some aspects of the nervous system are now well known. Specifically,during the past 40 years, the method of signal propagation through the nervous system has been firmly established. The messages are electrical pulsestransmitted by the neurons. When a neuron receives an appropriate stimulus,it produces electrical pulses that are propagated along its cablelike structure.
The pulses are constant in magnitude and duration, independent of the intensity of the stimulus. The strength of the stimulus is conveyed by the number ofpulses produced. When the pulses reach the end of the “cable,” they activateother neurons or muscle cells.
13.1.1 The Neuron sensory neurons, motor neurons, and interneurons. Thesensory neurons receive stimuli from sensory organs that monitor the externaland internal environment of the body. Depending on their specialized functions, the sensory neurons convey messages about factors such as heat, light,pressure, muscle tension, and odor to higher centers in the nervous system forprocessing. The motor neurons carry messages that control the muscle cells.
These messages are based on information provided by the sensory neurons andby the central nervous system located in the brain. The interneurons transmitinformation between neurons.
Each neuron consists of a cell body to which are attached input ends called dendrites and a long tail called the axon which propagates the signal awayfrom the cell (see Fig. 13.1). The far end of the axon branches into nerveendings that transmit the signal across small gaps to other neurons or musclecells. A simple sensory-motor neuron circuit is shown in Fig. 13.2. A stimulusfrom a muscle produces nerve impulses that travel to the spine. Here the signalis transmitted to a motor neuron, which in turn sends impulses to control themuscle. Such simple circuits are often associated with reflex actions. Mostnervous connections are far more complex.
The axon, which is an extension of the neuron cell, conducts the electrical impulses away from the cell body. Some axons are long indeed—in people,for example, the axons connecting the spine with the fingers and toes are morethan a meter in length. Some of the axons are covered with a segmented sheathof fatty material called myelin. The segments are about 2 mm long, separatedby gaps called the Nodes of Ranvier. We will show later that the myelin sheathincreases the speed of pulse propagation along the axon.
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FIGURE 13.2 A simple neural circuit.
