Sound and Its Measurement

Sound is produced by a disturbance in particle density (whereby a particle is made up of many molecules of the sound-propagating medium) triggered by a sound-producing body, or sound source. If this disturbance in particle density travels through an elastic medium, such as air or fluid, sound propagation occurs. As a tuning fork (a sound source) is struck, it causes the air particles adjacent to it to vibrate. The vibration of these air particles causes other nearby air particles to vibrate, enabling sound propagation. The velocity of sound propagation in dry air is about 340 m/sec at room temperature, whereas in water, sound travels at around 1500 m/sec.

Simple harmonic motion provides the framework for understanding acoustic energy (Fig. 129-1). Simple harmonic motion is a periodic motion that undulates around a null point with equal amplitudes, similar to a sine function. The frequency of a simple harmonic motion is the number of cycles per second and is measured in Hertz (Hz). The period of a cycle is the inverse of its frequency (1/f), and represents the duration of a single cycle. The amplitude is the maximum amount of displacement from the null point in one direction. The sound produced by simple harmonic motion is called a pure tone. In the everyday environment, most sound sources do not produce sounds that follow simple harmonic motion. Any vibration that does not follow simple harmonic motion is said to be complex. If there is a repetitive periodic pattern to the complex vibration, it produces tones. If the complex vibration has no repetitive pattern, it results in noise.

Figure 129-1. Simple harmonic motion. Simple harmonic motion is a periodic motion that undulates around a null point with equal amplitudes. The amplitude is the maximum amount of displacement from the null point in one direction. The frequency of a simple harmonic motion is the number of cycles per second, and is measured in Hertz (Hz). The period of a cycle is the inverse of its frequency (1/f), and represents the duration of a single cycle.

One way to quantify sound is by its intensity, which is cumbersome to measure directly. Sound pressure, which is related to the square root of intensity, is relatively easy to measure, however, and is the most common way of quantifying sound. Sound pressure, which has units of pascal (Pa) (which is Newton per meter squared [N/m²]), represents the amount of force that vibrating sound particles exert on a surface area.

Because the human ear is capable of perceiving a huge dynamic range of sound intensity (about 10¹²-fold), a convenient way of expressing sound intensity is by taking the logarithmic ratio of two sound intensities (the numerator being the sound intensity of interest, and the denominator being a reference sound intensity) and multiplying by 10. This is called the decibel scale. The formula for determining decibels for sound intensity is: dB = 10 log₁₀ J/Jr, where J is the intensity of the sound of interest, and Jr is the intensity of reference.

Because pressure varies as the square root of intensity, it is necessary to square the pressures in the decibel formula when sound pressure is being used. The formula for determining decibels for sound pressure is dB = 10 log₁₀ P²/Pr² = 10 log₁₀ (P/Pr)² = 20 log₁₀ P/Pr, where P is the sound pressure of interest, and Pr is the reference sound pressure. If the sound of interest has 10 times more pressure than the reference sound pressure, the sound of interest is 20 dB louder than the reference. If the sound of interest has 100 times more pressure, it is 40 dB louder than the reference. The most commonly used reference sound pressure is 20 µPa, which is referred to as sound pressure level (SPL). Another reference sound pressure that is occasionally used is hearing level (HL), which is the threshold sound pressure at a specific frequency (as measured in normal subjects); this threshold sound pressure varies across the frequency range.

Impedance

Impedance generally can be thought of as the impediment to movement. In the study of acoustics, impedance is defined as the ratio of the acoustic pressure over the volume velocity generated by the acoustic pressure. Imagine an acoustic stimulus striking an elastic membrane (e.g., the tympanic membrane); the greater the sound pressure of the acoustic stimulus, the larger the motion of the membrane, and the higher the velocities achieved by that motion. The exact relationship between the pressure of the acoustic stimulus and the membrane volume velocity is governed by acoustic impedance.

There are three components to acoustic impedance: stiffness, resistance (damping), and mass. If the membrane were stiffer than normal, the volume velocity generated by the acoustic stimulus would be decreased. Similarly, if the mass of the membrane were increased, one would also expect the volume velocity generated by the acoustic stimulus to decrease. In addition, a small amount of sound energy is lost because of the damping effect of the system. In a simple acoustic resonator, stiffness varies inversely with frequency and dominates the acoustic impedance at low frequencies, whereas the impedance of a mass increases with frequency and dominates at high frequencies. When the acoustic impedance is at its lowest point (i.e., at the frequency where the stiffness and mass components of the acoustic impedance cancel each other out), it is said that the system is in resonance.

External Ear

The external ear is composed of the pinna and the external auditory canal. The external ear funnels sound from the external environment into the ear. The peculiar shape of the pinna and the external auditory canal gives rise to specific resonant frequencies as these structures are struck by sound: the concha has a resonant frequency of around 5300 Hz, and the external auditory canal has a resonant frequency of around 3000 Hz. The external ear plays an important role in sound localization.

Sound localization is achieved by two major mechanisms: interaural time difference and interaural amplitude difference. Because the left and the right ears are located on opposite sides of the head, the amount of time it takes for a sound stimulus to arrive at each individual ear is governed by the distance of the sound source to that particular ear: the farther the distance, the longer it takes for the sound stimulus to arrive. The differences in the time arrival of the sound stimulus between the two ears can be used as a cue for sound localization. The differences in amplitude perceived by the two ears can also be used as a cue for sound localization.^1,2 This difference in amplitude is increased further by the “head shadow” effect: sound coming from one side is attenuated by the head as it travels to the contralateral ear. The head shadow effect in binaural hearing helps to improve the signal-to-noise ratio in adverse listening environments; one ear can be closer to the source of sound or speech, whereas the contralateral ear is exposed to the background noise. It has been shown that the interaural time difference is important for low-frequency sound localization, whereas the interaural amplitude difference is important for higher frequency sound localization.³

Middle Ear Mechanics

The middle ear is composed of the tympanic membrane, the ossicles (malleus, incus, and stapes), and the stapedius and tensor tympani muscles. As a sound stimulus enters the external auditory canal, it causes the tympanic membrane to vibrate. The malleus, which is coupled to the tympanic membrane, vibrates in response to the motion of the tympanic membrane. This causes the entire ossicular chain to vibrate, resulting in sound transmission to the inner ear via the stapes footplate. This pathway of sound transmission is referred to as ossicular coupling.⁴ The ossicular chain has two synovial joints that are mobile: the incudomalleal and the incudostapedial joints.⁵ The ossicular chain vibrates along an axis that projects through the head of the malleus and the body of the incus in an anterior-to-posterior direction (Fig. 129-2). The stapes, the smallest bone in the body, transmits the output of the middle ear into the inner ear through the oval window.

Figure 129-2. Schematic of the middle ear system. A, Motion of the ossicular chain along its axis of rotation. B, Concept of area ratio (ATM/AFP) and lever ratio (lm/li). AFP, area of the footplate; ATM, area of the tympanic membrane; li, length of the incus long process; lm, length of the manubrium; PEC, external canal sound pressure; Pv, sound pressure of the vestibule.

(From Merchant SN, Rosowski JJ. Auditory physiology. In: Glasscock ME, Gulya AJ, eds. Glasscock-Shambaugh Surgery of the Ear. 5th ed. Ontario: Decker; 2003:64.)

Because the inner ear is fluid-filled, if the sound stimulus strikes the inner ear fluid directly, most of the acoustic energy is deflected, as the impedance of fluid is much greater than the impedance of air. The pathway of sound transmission to the inner ear in the absence of the ossicular system is referred to as acoustic coupling.⁴ It has been shown that the difference between ossicular coupling and acoustic coupling is about 60 dB, which is the maximal amount of hearing loss expected in patients with ossicular discontinuity.⁶ The middle ear plays an important role in the process of “impedance matching” between the air-filled middle ear and the fluid-filled inner ear, allowing for efficient sound transmission. The most important factor in the middle ear’s impedance matching capability comes from the “area ratio” between the tympanic membrane and the stapes footplate (see Fig. 129-2). The human tympanic membrane has a surface area approximately 20 times larger than the stapes footplate (69 vs. 3.4 mm²).⁷ If all the force applied to the tympanic membrane were to be transferred to the stapes footplate, the force per unit area would be 20 times larger (26 dB) on the footplate than on the tympanic membrane.

A second mechanism for impedance matching is called the lever ratio, which refers to the difference in length of the manubrium of the malleus and the long process of the incus. Because the manubrium is slightly longer than the long process of the incus, a small force applied to the long arm of the lever (manubrium) results in a larger force on the short arm of the lever (incus long process). In humans, the lever ratio is about 1.31 : 1 (2.3 dB).⁸ The combined effects of the area ratio and the lever ratio give the middle ear output a 28-dB gain theoretically. In reality, the middle ear sound pressure gain is only about 20 dB⁹; this is mostly due to the fact that the tympanic membrane does not move as a rigid diaphragm. At higher frequencies, it vibrates in a complex manner, with multiple areas that vibrate differently.¹⁰ The effective area of the tympanic membrane involved with impedance matching is smaller than its total area. Nevertheless, the 20-dB middle ear sound pressure gain assists sound transmission from the air-filled middle ear into the fluid-filled inner ear.

Inner Ear Physiology

The inner ear is enclosed in a bony cavity called the otic capsule. It has two mobile windows: the oval and the round windows. The two important functions of the inner ear are hearing and balance. The portion of the inner ear that deals with hearing is the cochlea, and the portion of the inner ear that deals with balance is collectively known as the vestibular organs (semicircular canals, utricle, and saccule). The cochlea is shaped like a snail, and has a spiral configuration with two and a half turns (Fig. 129-3A). The center portion of the spiral is called the modiolus. The portion of the cochlea that is closest to the oval window is referred to as the base, whereas the portion of the cochlea that is farthest away from the oval window is referred to as the apex. The cochlea is a fluid-filled space with three compartments: scala tympani, scala media, and scala vestibuli (Fig. 129-3B). The scala tympani and the scala media are separated by the basilar membrane, and the scala media and the scala vestibuli are separated by Reissner’s membrane. The scala tympani and the scala vestibuli join together at the apex of the cochlea to form the helicotrema.

Figure 129-3. A, Histologic section showing normal human cochlea. The cochlea is shaped like a snail, and has a spiral configuration with two and a half turns. The center portion of the spiral is called the modiolus. The portion of the cochlea that is closest to the oval window is referred to as the base, and the portion of the cochlea that is farthest away from the oval window is referred to as the apex. (H&E stain.) B, Higher magnification of the histologic section in A showing the organ of Corti. The cochlea is a fluid-filled space with three compartments: scala tympani, scala media, and scala vestibuli. The scala tympani and the scala media are separated by the basilar membrane, whereas the scala media and the scala vestibuli are separated by Reissner’s membrane. The scala tympani and the scala vestibuli join together at the apex of the cochlea to form the helicotrema. The scala media contains the organ of Corti, which rests on the basilar membrane. The organ of Corti and the basilar membrane together are sometimes referred to as the cochlear partition. The stria vascularis plays an important role in maintaining the electrochemical environment of the cochlea. (H&E stain.)

(Modified from www.temporalboneconsortium.org.)

The scala media contains the organ of Corti, which rests on the basilar membrane. Taken together, organ of Corti and the basilar membrane are also referred to as the cochlear partition. The organ of Corti has an arch at its center, called the arch of Corti, which is formed by the inner and the outer pillar cells. The inner hair cells are flask-shaped cells that rest on the side of the inner pillar cells, whereas the outer hair cells are cylindrical-shaped cells that rest on the side of the outer pillar cells. The human cochlea contains about 3000 inner hair cells that extend in a single row from the base to the apex; there are about 12,000 outer hair cells arranged in three or four rows. The hair cells derive their names from having hairlike projections on their apical surface. These hairlike projections are stereocilia, which play an important role in the signal transduction properties of the hair cells.

The scala vestibuli and the scala tympani are filled with perilymph, which has a similar composition to the extracellular fluid (high in sodium, low in potassium) (Fig. 129-4A). The scala media is filled with endolymph, which has a similar composition to the intracellular fluid (low in sodium, high in potassium).¹¹ The unique electrolyte composition of the scala media sets up a large electrochemical gradient, called the endocochlear potential, which is +60 to +100 mV relative to the perilymph (Fig. 129-5).¹² The maintenance of such a large electrochemical gradient is performed by the stria vascularis, which resides on the outer wall (away from the modiolus) of the scala media. The stria vascularis contains multiple active ion channels, and maintains the chemical composition of the endolymph and its positive electrical potential.¹³

Figure 129-4. Mechanoelectrical transduction of the auditory signal depends on the recycling of potassium ions in the organ of Corti. A, Schematic cross-sectional view of the human cochlea. The scala media (cochlear duct) is filled with endolymph, and the scala vestibuli and tympani are filled with perilymph. The endolymph of the scala media bathes the organ of Corti, located between the basilar and tectorial membranes and containing the inner and outer hair cells. A high concentration of potassium in the endolymph of the scala media relative to the hair cell creates a cation gradient that is maintained by the activity of the epithelial supporting cells, spiral ligament, and stria vascularis. B, Hair cells contain stereocilia along the apical surface and are connected by tip links. The potassium gradient shown in A is essential to enable depolarization of the hair cell in B after influx of potassium ions in response to mechanical vibration of the basilar membrane, deflection of stereocilia, displacement of tip links, and opening of gated potassium channels. Depolarization results in calcium influx through channels along the basolateral membrane of the hair cell, causing degranulation of neurotransmitter vesicles into the synaptic terminal and propagation of an action potential along the auditory nerve, shown in blue. Gap junction proteins between the hair cells (potassium channel, yellow) and epithelial supporting cells (connexin channels, red) allow for the flow of potassium ions back to the stria vascularis where they are pumped back into the endolymph.

(From Willems PJ. Genetic causes of hearing loss. N Engl J Med. 2000;342:1101-1109.

Figure 129-5. Schematic showing the electrochemical environment of the cochlea. The scala vestibuli and the scala tympani are filled with perilymph, which has a low potassium concentration. The scala media is filled with endolymph, which has a high potassium concentration. The unique electrolyte composition of the scala media sets up a large electrochemical gradient, called the endocochlear potential, which is about +80 mV relative to perilymph. The maintenance of such a large electrochemical gradient is performed by the stria vascularis.

(From Geisler CD. From Sound to Synapse: Physiology of the Mammalian Ear. New York: Oxford University Press; 1998:85.)

As sound energy travels through the external and middle ears, it causes the stapes footplate to vibrate. The vibration of the stapes footplate results in a compressional wave in the inner ear fluid, which travels across the scala vestibuli, around the helicotrema, and out across the scala tympani toward the round window. An inward motion of the stapes causes an outward motion of the round window. As this compression wave travels across the scala vestibuli, however, the pressure in the scala vestibuli is higher than the pressure in the scala tympani. This sets up a pressure gradient, which causes the cochlear partition to vibrate.

von Bekesy¹² first described the vibration of the cochlear partition in cadaveric human cochleas. He showed that as the cochlear partition is deflected by the compressional wave created by the stapes footplate vibration, it sets up a traveling wave on the basilar membrane, which travels from the base of the cochlea to its apex (Fig. 129-6). von Bekesy¹² also found that the basilar membrane varied in its stiffness along its length, with higher stiffness near the base and lower stiffness near the apex. This property of the basilar membrane allows it to respond to various frequencies differently (i.e., the amplitude of the traveling wave peaks [resonates] at a specific place along the basilar membrane), with the higher frequencies at the base and the lower frequencies toward the apex. The basilar membrane is able to act as a series of filters, responding to specific sound frequencies at specific locations along its length. In other words, the basilar membrane is tonotopically tuned to different frequencies along its length. von Bekesy’s seminal work on cochlear mechanics earned him the Nobel Prize in Physiology or Medicine in 1961.

Figure 129-6. Schematic showing sound propagation in the cochlea. As sound energy travels through the external and middle ears, it causes the stapes footplate to vibrate. The vibration of the stapes footplate results in a compressional wave on the inner ear fluid. Because the pressure in the scala vestibuli is higher than the pressure in the scala tympani, this sets up a pressure gradient that causes the cochlear partition to vibrate as a traveling wave. Because the basilar membrane varies in its stiffness and mass along its length, it is able to act as a series of filters, responding to specific sound frequencies at specific locations along its length.

(From Geisler CD. From Sound to Synapse: Physiology of the Mammalian Ear. New York: Oxford University Press; 1998:51.)

Although the cochlea is usually thought of as having two mobile windows (the oval and round windows), the possibility of a third mobile window has been proposed.¹⁴ More recently, a select group of patients with an air-bone gap on audiologic testing (which is typically associated with middle ear pathology) who do not have any middle ear pathology on intraoperative exploration has been described.^15–17 It has been shown that the air-bone gap in this group of patients can be explained by a pathologic “third window” in the inner ear.¹⁸ Perhaps the most well-studied example of this phenomenon is seen in superior semicircular canal dehiscence (Fig. 129-7; video clip available on website).

Figure 129-7. Inner ear impedance changes resulting from superior semicircular canal dehiscence (SSCD) are associated with an air-bone gap on audiometric testing. A-F, Clinical images from a 28-year-old woman with autophony, hearing loss, and sound-induced and pressure-induced oscillopsia and dizziness. Left-sided SSCD syndrome was diagnosed. A and B, Temporal bone CT scans reformatted to Stenver (A, perpendicular to the superior canal) and Pöschl (B, parallel to the superior canal) of the left ear showing a 4-mm SSCD (arrowheads). C and D, Intraoperative photos of left SSCD during middle fossa craniotomy and dural retraction. Note the exposed membranous labyrinth of the superior canal and surrounding dehiscent tegmen in C that correlates with radiologic images in A and B. D shows plugging of left SSCD with bone wax. Temporalis fascia and a split-calvarial bone graft were also used to reconstruct the dehiscent middle fossa floor. E (preoperative audiogram) and F (post-SSCD plugging audiogram) show closure of air-bone gap associated with SSCD. SSC, superior semicircular canal.

(Modified from Watters KF, Rosowski JJ, Sauter T, Lee DJ. Superior semicircular canal dehiscence presenting as postpartum vertigo. Otol Neurotol. 2006;27:756-768.)

Patients with superior semicircular canal dehiscence often complain of autophony, aural fullness, sound-induced or pressure-induced vertigo, and hearing loss.^19–22 It is thought that the dehiscence in the superior semicircular canal acts as a third mobile window of the inner ear (in addition to the oval and round windows), shunting acoustic energy away from the cochlea, resulting in a decreased sensitivity to air-conducted sound and an air-bone gap seen on audiologic testing.^20,23–25 This third window is also theorized to decrease cochlear input impedance at the oval window, increasing the pressure gradient across the cochlear partition, and resulting in hypersensitivity to bone-conducted sound.²³ Repair, or plugging, of superior semicircular canal dehiscence in some cases results in improvement of the preoperative air-bone gap (see Fig. 129-7). The third window hypothesis has also been used to explain the air-bone gap associated with other temporal bone anomalies, such as large vestibular aqueduct syndrome and other inner ear malformations.^26–28

As the cochlear partition is deflected in response to the compressional wave initiated by the stapes, it causes a shearing force between the stereocilia of the hair cells and the tectorial membrane. This shearing force causes a deflection of the hair cell stereocilia. The hair cell stereocilia are arranged in rows, and the rows are arranged in an orderly fashion by height (see Fig. 129-4B). The tip of each stereocilia is connected from one row to another by an elastic filament called the tip link.²⁹ It is thought that as the stereocilia is deflected toward the direction of the tallest row, it causes the tip links to stretch. The stretch of the tip links causes the opening of stretch-sensitive cationic channels located on the stereocilia (Fig. 129-8).

Figure 129-8. Schematic showing the role of tip links in hair cell signal transduction. It is thought that as the stereocilia is deflected toward the direction of the tallest row, it causes the tip links to stretch. The stretch of the tip links causes the opening of stretch-sensitive cationic channels located on the stereocilia. The opening of these stretch-sensitive cationic channels on the stereocilia causes a large influx of cationic current, which leads to hair cell depolarization. As the stereocilia is deflected away from the tallest row, it causes a relaxation of the tip links, which decreases the probability of ion channel opening. This leads to hyperpolarization of the hair cell.

(From Gillespie PG. Molecular machinery of auditory and vestibular transduction. Curr Opin Neurobiol. 1995;5:449-455.)

Because there is a large electrochemical gradient across the apical surface of the hair cells (with a large positive endocochlear potential on one side, and a large negative intracellular potential on the other side), the opening of these stretch-sensitive cationic channels on the stereocilia causes a large influx of cationic current, which leads to hair cell depolarization. As the stereocilia is deflected away from the tallest row, the tip links relax, decreasing the probability of ion channel opening; this leads to hyperpolarization of the hair cell.^30–32 The relationship between the degree of stereocilia deflection and hair cell depolarization or hyperpolarization is not symmetric or linear. Stereocilia deflection in the depolarization direction produces a greater response than deflection in the hyperpolarization direction (Fig. 129-9).³⁰ The deflection of the hair cell stereocilia and the resulting hair cell depolarization or hyperpolarization represents an important step in the signal transduction process of the hair cell (i.e., by converting a mechanical signal [inner ear fluid wave] into an electrochemical signal).

Figure 129-9. Generation of receptor potentials in inner hair cells (IHC, upper panel) and outer hair cells (OHC, lower panel) in response to a sound stimulus of 84 dB sound pressure level (SPL). The sound stimulus changes the receptor potential according to each hair cell’s input-output curve (left). The input-output curves for both types of hair cells are nonlinear.

(From Russell IJ, Cody AR, Richardson GP. The responses of inner and outer hair cells in the basal turn of the guinea-pig cochlea and in the mouse cochlea grown in vitro. Hear Res. 1986;22:199-216.)

Because potassium is the major cation in the endolymph, it is believed that potassium current plays an important role in triggering the signal transduction process in hair cells. When inner hair cells are depolarized, voltage-gated calcium channels open.³³

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