La Place's Law

Imagine blood flowing through a blood vessel which has a certain radius and a

certain wall thickness. The blood vessel wall is stretched as a result of the difference

between the blood pressure inside the vessel and the surrounding pressure outside

the vessel. La Place's law describes the relationship between the transmural pressure

difference and the tension, radius, and thickness of the vessel wall. Obviously, the

higher the pressure difference the more tension there will be. On the other hand, the

thicker the wall the less tension there is. Also, the larger the radius the more tension

there is. These three rules culminate into one equation:

T = ( P * R ) / M

Where T is the tension in the walls, P is the pressure difference across the

wall, R is the radius of the cylinder, and M is the thickness of the wall. An example of

LaPlace Law is Dilated cardiomyopathy. In this condition heart becomes greatly

distended and the radius (R) of ventricle increases. Therefore to create the same

pressure (P) during ejection of the blood much larger wall tention (T) has be

developed by the cardiac muscle. Thus dilated heart requires more energy to pump

the same amount of blood as compared to the heart of normal size. The new surgical

procedure, called ventricular remodeling, uses LaPlace principle to improve the

function of dilated, failing hearts.

Imagine yourself blowing a balloon. The harder you blow the higher the air

pressure inside the balloon and the higher the pressure difference between the

outside and inside of the balloon become. Since the pressure difference rises, the

tension in the rubber walls of the balloon also rises, and this is what causes the

balloon to stretch. Now imagine you are blowing a balloon which is made of much

thicker rubber. Now you will notice that the balloon is harder to inflate because more

pressure difference is required to raise the tension in the walls of the balloon.

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Wall Tension Index

LaPlace's law

concepts

Pascal's principle requires that the pressure is everywhere the same inside the balloon at equilibrium. But examination immediately reveals that there are great differences in wall tension on different parts of the balloon. The variation is described by Laplace's Law.

Once you have established the geometry of the balloon, then the tension, pressure and radius have a definite relationship and could be used to measure tension or pressure. That is, if you have a gauge to measure pressure, then you can calculate the wall tension. In the interesting experiment of putting one end of a balloon into liquid nitrogen, you can collapse one end of it by cooling while the other end stays essentially at its previous radius. This can be taken to imply that the pressure is not diminishing significantly since for a given tension, the pressure is related to the radius.

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LaPlace's Law

The larger the vessel radius, the larger the wall tension required to withstand a given internal fluid

Index

LaPlace's law

concepts

pressure.

For a given vessel radius and internal pressure, a spherical vessel will have half the wall tension of a cylindrical vessel.

Why does the wall tension increase with radius?

Balloon example

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Why does wall tension increase with radius?

Index

LaPlace's law

concepts

Balloon example

If the upward part of the fluid pressure remains the same, then the downward component of the wall tension must remain the same. But if the curvature is less, then the total tension must be greater in order to get that same downward component of tension.

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Alveoli of the Lungs

The oxygen exchange in the lungs takes place across the membranes of small balloon-like structures called alveoli attached to the branches of the bronchial passages. These alveoli inflate and deflate with inhalation and exhalation. The behavior of the alveoli is largely dictated by LaPlace's law and surface tension. It takes some effort to breathe in because these tiny balloons must be inflated, but the elastic recoil of the tiny balloons assists us in the process of exhalation. If the elastic recoil of the alveoli is compromised, as in the case of emphysema, then it is difficult to exhale forcibly.

The difficulty of inspiration during the baby's first breath is great because all the balloons must be inflated from a

Inflation of alveoli

Index

LaPlace's law

concepts

ReferenceShier, et

al.Ch 19

collapsed state.

Respiratory System

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Inflating the Alveoli Inflating the alveoli in the process of respiration requires an excess pressure inside the alveoli relative to their surroundings. This is actually accomplished by making the pressure in the thoracic cavity negative with respect to atmospheric pressure.

The amount of net pressure required for inflation is dictated by the surface tension and radii of the tiny balloon-like alveoli. During inhalation the radii of the alveoli increase from about 0.05 mm to 0.1 mm . The normal mucous tissue fluid surrounding the alveoli has a nominal surface tension of about 50 dynes/cm so the required net outward pressure is:

Index

LaPlace's law

concepts

ReferenceShier, et

al.Ch 19

The remarkable property of the surfactant which coats the alveoli is that it reduces the surface tension by a factor of about 15 so that the 1 mmHg pressure differential is sufficient to inflate the alveoli. Other factors affecting the remarkable efficiency of oxygen transport across the lung membranes is characterized in Fick's Law.

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Surfactant Role in Respiration

Index

LaPlace's law

concepts

ReferenceShier, et

al.Ch 19

One of the remarkable phenomena in the process of respiration is the role of the fluid coating the walls of the alveoli of the lungs. This fluid, called a surfactant, lowers the surface tension of the balloon-like alveoli by about a factor of 15 compared to the normal mucous tissue fluid in which they are immersed. There appears to be a nearly constant amount of this surfactant per alveolus, so that when the alveoli are deflated it is more concentrated on the surface. Since the surface-tension-lowering effect of the surfactant depends on this concentration, it diminishes the required pressure for inflation of the alveoli at their most critical phase. For a given surface tension, the pressure to inflate a smaller bubble is greater. It is the surfactant which makes possible the inflation of the alveoli with only about 1 mmHg of pressure excess over their surroundings. The baby's first breath depends upon this surfactant and is made more difficult in premature infants by the incomplete formation of the surfactant.

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Alveoli and Exhalation Index

LaPlace's law

concepts

ReferenceShier, et

al.Ch 19

The alveoli of the lungs act much like balloons in that there is some effort involved to inflate them, but when the inflating pressure is released, the recoil of the elastic walls provides the pressure necessary to deflate them. The lungs are suspended in the thoracic cavity which is normally at a slight negative pressure. When the diaphragm is lowered, that pressure becomes more negative and the lungs expand into the cavity. Air from the atmosphere moves into the resulting partial vacuum and inflates the alveoli. One is aware of the effort, but it is not extreme as in the case of the baby's first breath . Once the alveoli are fully inflated, exhalation can be accomplished by merely relaxing the diaphragm, since the wall tension in all the tiny alveoli will act to force the air out of them. By forcing the diaphragm upward, we can exhale forcefully by adding the diaphragm effort to the recoil of the elastic alveoli. In diseases like emphysema, the elasticity of the alveoli is lost and exhalation becomes a laborious process.

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The Baby's First Breath Everyone knows that it is much more difficult to blow up a balloon for the first time. Why is that? For one thing, the applied pressure does not create much tension in the walls of a small balloon to start the stretching process necessary for inflation. According to LaPlace's law, the wall tension will be twice as large for a balloon of twice the radius. If it takes a certain applied pressure to overcome the elasticity of the large balloon and cause it to expand further, it will take twice as much pressure to start to expand the smaller balloon. All this makes it difficult for the baby to take its first breath -- all the balloons are small! The alveoli of the lungs are collapsed in the fetus and must be inflated in the process of inhalation. Thus the traditional spank on the bottom of the newborn to make him/her mad enough to make the effort for the first breath.

Index

LaPlace's law

concepts

Further difficulties are encountered by premature infants because the surfactant fluid which coats the alveoli to give them the appropriate wall tensions is formed in the later stages of pregnacy. Until that point, the alveoli are coated with fluid which has essentially the surface tension of water, much higher than that of the normal surfactant.

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Emphysema The disease of the lungs called emphysema or chronic obstructive pulmonary disease (COPD) results in the enlargement of the alveoli of the lungs as some are destroyed and others either enlarge or combine. The disease is one of the destructive effects of long-term smoking, but sometimes occurs in non-smokers. If the normal inhalation process inflates the alveoli to a larger radius, the implications of LaPlace's law are that the wall must have lost much of its elasticity. Normally it would take twice the pressure to inflate a constant tension membrane to twice its radius. Typically, the wall tension of the healthy alveoli is determined by the surface tension of the liquid which coats them, and with a uniform coating (called a surfactant), they will all inflate to a similar radius. The enlarged alveoli in the emphysema patient imply less elastic recoil during the process of exhalation. Exhalation requires effort from the diaphragm and in advanced stages of the disease, a patient will not be able to blow out a match.

Index

LaPlace's law

concepts

ReferenceCanadian

Lung Association

Besides the loss of elasticity of the alveolar walls, the larger size of the compartments implies a smaller surface area for a given volume. Because the oxygen exchange from the air to the blood is proportional to the area of the exchange membrane, this diminishes the rate of oxygen transfer.

 

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Tension in Arterial Walls The tension in the walls of arteries and veins in the human body is a classic example of LaPlace's law. This geometrical law applied to a tube or pipe says that for a given internal fluid pressure, the wall tension will be proportional to the radius of the vessel.

The implication of this law for the large arteries, which have comparable blood pressures, is that the larger arteries must have stronger walls since an artery of twice the radius must be able to withstand twice the wall tension. Arteries are reinforced by fibrous bands to strengthen them against the risks of an aneurysm. The tiny capillaries rely on their small size.

Demonstration with balloon

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LaPlace's law

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Capillary Walls The walls of the capillaries of the human circulatory system are so thin as to appear transparent under a microscope, yet they withstand a pressure up to about half of the full blood pressure. LaPlace's law gives insight into how they are able to withstand such pressures: their small size implies that the wall tension for a given internal pressure is much smaller than that of the larger arteries.

Given a peak blood pressure of about 120 mmHg at the left ventricle, the pressure at the beginning of the capillary system may be on the order of 50 mmHg. The large radii of the large arteries imply that for pressures in that range they must have strong walls to withstand the large resulting wall tension. The larger arteries provide much less resistance to flow than the smaller vessels according to Poiseuille's law, and thus the drop in pressure across them is only about half the total drop. The capillaries offer large resistances to flow, but don't require much strength in their walls.

Index

LaPlace's law

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Danger of Aneurysms The larger arteries of the body are subject to higher wall tensions than the

Index

LaPlace's law

smaller arteries and capillaries. This wall tension follows the dictates of LaPlace's law, a geometrical relationship which shows that the wall tension is proportional to the radius for a given blood pressure. If an artery wall develops a weak spot and expands as a result, it might seem that the expansion would provide some relief, but in fact the opposite is true. In a classic "vicious cycle", the expansion subjects the weakened wall to even more tension. The weakened vessel may continue to expand in what is called an aneurysm. Unchecked, this condition will lead to rupture of the vessel, so aneurysms require prompt medical attention.

A localized weak spot in an artery might gain some temporary tension relief by expanding toward a spherical shape, since a spherical membrane has half the wall tension for a given radius. Minimizing membrane tension is why soap bubbles tend to form a spherical shape. But for an expanding artery, forming a near-spherical shape cannot be depended upon to give sufficient tension relief.

Demonstration with balloon

concepts

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http://hyperphysics.phy-astr.gsu.edu/Hbase/lapcon.html

Ear and HearingThis is an active graphic. Click anywhere on it for more detail.

Index

Hearing concepts

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The Outer EarSound energy spreads out from its sources. For a point source of sound, it spreads out according to the inverse square law. For a given sound intensity, a larger ear captures more of the wave and hence more sound energy.

The outer ear structures act as part of the ear's preamplifier to enhance the sensitivity of hearing.

Index

Hearing concepts

The auditory canal acts as a closed tube resonator, enhancing sounds in the range 2-5 kiloHertz.

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The Tympanic MembraneThe tympanic membrane or "eardrum" receives vibrations traveling up the auditory canal and transfers them through the tiny ossicles to the oval window, the port into the inner ear.

The eardrum is some fifteen times larger than the oval window of the inner ear, giving an amplification of about fifteen compared to a case where the sound pressure interacted with the oval window

Active graphic

Index

Hearing concepts

Zemlin

alone.

The tympanic membrane is very thin, about 0.1 mm, but it is resilient and strong.(Zemlin)

You may reach information about the nearby structures of the ear by clicking on the item of interest on the illustration.

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Sound IntensitySound intensity is defined as the sound power per unit area. The usual context is the measurement of sound intensity in the air at a listener's location. The basic units are watts/m2 or watts/cm2 . Many sound intensity measurements are made relative to a standard threshold of hearing intensity I0 :

The most common approach to sound intensity measurement is to use the decibel scale:

Index

Sound level measurement

Loudness concepts

Decibels measure the ratio of a given intensity I to the threshold of hearing intensity , so that this threshold takes the value 0 decibels (0 dB). To assess sound loudness, as distinct from an objective intensity measurement, the sensitivity of the ear must be factored in.

 

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Sound PressureSince audible sound consists of pressure waves, one of the ways to quantify the sound is to state the amount of pressure variation relative to atmospheric pressure caused by the sound. Because of the great sensitivity of human hearing, the threshold of hearing corresponds to a pressure variation less than a billionth of atmospheric pressure.

The standard threshold of hearing can be stated in terms of pressure and the sound intensity in decibels can be expressed in terms of the sound pressure:

The pressure P here is to be understood as the amplitude of the pressure wave. The power carried by a traveling wave is proportional to the square of the amplitude. The factor of 20 comes from the fact that the logarithm

Index

Sound level measurement

of the square of a quantity is equal to 2 x the logarithm of the quantity. Since common microphones such as dynamic microphones produce a voltage which is proportional to the sound pressure, then changes in sound intensity incident on the microphone can be calculated from

where V1 and V2 are the measured voltage amplitudes .

 

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Threshold of HearingSound level measurements in decibels are generally referenced to a standard threshold of hearing at 1000 Hz for the human ear which can be stated in terms of sound intensity:

or in terms of sound pressure:

This value has wide acceptance as a nominal standard threshold and corresponds to 0 decibels. It represents a pressure change of less than one billionth of standard atmospheric pressure. This is indicative of the

Index

Sound level measurement

incredible sensitivity of human hearing. The actual average threshold of hearing at 1000 Hz is more like 2.5 x 10-12 watts/m2 or about 4 decibels, but zero decibels is a convenient reference. The threshold of hearing varies with frequency, as illustrated by the measured hearing curves.

 

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Threshold of PainThe nominal dynamic range of human hearing is from the standard threshold of hearing to the threshold of pain. A nominal figure for the threshold of pain is 130 decibels, but that which may be considered painful for one may be welcomed as entertainment by others. Generally, younger persons are more tolerant of loud sounds than older persons because their protective mechanisms are more effective. This tolerance does not make them immune to the damage that loud sounds can produce.

Some sources quote 120 dB as the pain threshold and define the audible sound frequency range as ending at about 20,000 Hz where the threshold of hearing and the threshold of pain meet.

Index

Sound level measurement

 

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Loudness

Loudness is not simply sound intensity!Sound loudness is a subjective term describing the strength of the ear's perception of a sound. It is intimately related to sound intensity but can by no means be considered identical to intensity. The sound intensity must be factored by the ear's sensitivity to the particular frequencies contained in the sound. This is the kind of information contained in equal loudness curves for the human ear. It must also be considered that the ear's response to increasing sound intensity is a "power of ten" or logarithmic relationship. This is one of the motivations for using the decibel scale to measure sound intensity. A general "rule of thumb" for loudness is that the power must be increased by about a factor of ten to sound twice as loud. To more realistically assess sound loudness, the ear's sensitivity curves are factored in to produce a phon scale for loudness. The factor of ten rule of thumb can then be used to produce the sone scale of loudness. In practical sound level measurement, filter contours such as the A, B, and C contours are used to make the measuring instrument more nearly approximate the ear.

Index

Loudness concepts

Hearing concepts

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"Rule of Thumb" for LoudnessA widely used "rule of thumb" for the loudness of a particular sound is that the sound must be increased in intensity by a factor of ten for the sound to be perceived as twice as loud. A common way of stating it is that it takes 10 violins to sound twice as loud as one violin. Another way to state the rule is to say that the loudness doubles for every 10 phon increase in the sound loudness level. Although this rule is widely used, it must be emphasized that it is an approximate general statement based upon a great deal of investigation of average human hearing but it is not to be taken as a hard and fast rule.

Index

Loudness concepts

Hearing concepts

Why is it that doubling the sound intensity to the ear does not produce a dramatic increase in loudness? We cannot give answers with complete confidence, but it appears that there are saturation effects. Nerve cells have maximum rates at which they can fire, and it appears that doubling the sound energy to the sensitive inner ear does not double the strength of the nerve signal to the brain. This is just a model, but it seems to correlate with the general observations which suggest that something like ten times the intensity is required to double the signal from the innner ear.

One difficulty with this "rule of thumb" for loudness is that it is applicable only to adding loudness for identical sounds. If a second sound is widely enough separated in frequency to be outside the critical band of the first, then this rule does not apply at all.

While not a precise rule even for the increase of the same sound, the rule has considerable utility along with the just noticeable difference in sound intensity when judging the significance of changes in sound level.

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Adding LoudnessWhen one sound is produced and another sound is added, the increase in loudness perceived depends upon its frequency relation to the first sound. Insight into this process can be obtained from the place theory of pitch perception. If the second sound is widely separated in pitch from the first, then they do not compete for the same nerve endings on the basilar membrane of the inner ear. Adding a second sound of equal loudness yields a total sound about twice as loud. But if the two sounds are close together in frequency, within a critical band, then the saturation effects in the organ of Corti are such that the perceived combined loudness is only slightly greater than either sound alone. This is the condition which leads to the commonly used rule of thumb for loudness addition.

Index

Loudness concepts

Hearing concepts

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Critical BandWhen two sounds of equal loudness when sounded separately are close together in pitch, their combined loudness when sounded together will be only slightly louder than one of them alone. They may be said to be in the same critical band where they are competing for the same nerve endings on the basilar membrane of the inner ear. According the the place theory of pitch perception, sounds of a given frequency will excite the nerve cells of the organ of Corti only at a specific place. The available receptors show saturation effects which lead to the general rule of thumb for loudness by limiting the increase in neural response.

If the two sounds are widely separated in pitch, the perceived loudness of the combined tones will be considerably greater because they do not overlap on the basilar membrane and compete for the same hair cells. The phenomenon of the critical band has been widely investigated.

Backus reports that this critical band is about 90 Hz wide for sounds below 200 Hz and increases to about 900 Hz for frequencies around 5000 Hertz. It is suggested that this corresponds to a roughly constant length on the basilar membrane of length about 1.2 mm and involving some 1300 hair cells. If the tones are far apart in frequency (not within a critical band), the combined sound may be perceived as twice as loud as one alone.

Illustration of critical band

Index

Hearing concepts

ReferencesRossing,

Science of Sound

Backus

Zwicker, et al.

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Critical Band MeasurementFor low frequencies the critical band is about 90 Hz wide. For higher frequencies, it is between a whole tone and 1/3 octave wide.

Index

Hearing concepts

ReferenceRossing,

Science of Sound

CenterFreq (Hz)

Criticalbandwidth (Hz)

100 90

200 90

500 110

1000 150

2000 280

5000 700

10000 1200

Rossing 2nd Ed p74

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Pure Tone AudiometryThe testing of hearing is most often carried out by establishing the threshold of hearing, the softest sound which can be perceived in a controlled environment. It is typical to do this testing with pure tones by providing calibrated tones to a person via earphones, allowing that person to increase the level until it can just be heard. Various strategies are used, but pure tone audiometry with tones starting at about 125 Hz and increasing by octaves, half-octaves, or third-octaves to about 8000 Hz is typical. Hearing tests of right and left ears are generally done independently. The results of such tests are summarized in audiograms.

Audiograms compare hearing to the normal threshold of hearing, which varies with frequency as illustrated by the hearing curves. The audiogram is normalized to the hearing curve so that a straight horizontal line at 0 represents normal hearing.

Click on illustration for further details.

Index

Hearing concepts

Dangers of Loud Sounds

Hearing loss

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Audiogram Showing PresbycusisThe progressive loss of high frequency sensitivity with aging is typical, and is called presbycusis. The loss of the high frequencies can make it difficult to understand speech, since the intelligible differences in speech sounds are often in the range above 2000 Hz.

When hearing aids are used, it is important to amplify the high frequencies, since it is uncommon for there to be significant loss at low frequencies. Audiograms are important for the prescribing of hearing aids.

Speak up! Quit mumbling!

Older persons may have difficulty understanding speech clearly because of progressive loss of high frequency hearing.

Index

Hearing concepts

ReferencesNave &

NaveCh. 18

BackusCh. 5

 

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Audiograms Showing Hearing LossAudiograms can help with the diagnosis of various types of hearing disorders. Specific geometries of curves are found to be typical of presbycusis, and a characteristic notch in the hearing curve may be the signature of damage by a sudden loud sound like a gunshot or a firecracker explosion close to the ear.

The curves are normalized so that a straight horizontal line represents equal loudness.

Index

Hearing concepts

ReferencesNave &

NaveCh. 18

BackusCh. 5

 

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Hearing LossHearing loss is typically described as being conductive, sensorineural, or mixed.

Conductive hearing loss refers to an impairment of one's ability to conduct airborne sound through the middle ear to the inner ear. Scar tissue or otosclerosis, the abnormal growth of bone within the middle ear, can lead to restricted movement of the ossicles. Recently it has been shown that there can also be conductive problems with the basilar membrane of the inner ear that reduce the efficiency of energy transfer to the hair cells (Holt).

Sensorineural hearing loss refers to impairment of the sensory unit consisting of the auditory nerve and the hair cells that excite it.

Sometimes the distinction between these two types of hearing loss can be made with a simple tuning fork test. If the tuning fork cannot be heard when sounded in air, then the base of the tuning fork is placed against the hard bone behind the ear. If the person can now hear it by conduction through the bone, then conductive hearing loss is indicated. It in cannot be heard by either air or bone conduction, then sensorineural loss is indicated.

Hearing Loss

0 to -15 dB Normal range

-16 to -40 dB Minimal loss

-26 to -15 dB Mild loss

-41 to -55 dB Moderate loss

-56 to -70 dB Moderate/severe loss

-71 to -90 dB Severe loss

> -91 dB Profound loss

American Speech and Hearing

The "power of ten" or logarithmic nature of hearing response is evident in the fact that a loss in sensitivity by a factor of 10,000, or -40 decibels, is still at the edge of "minimal loss". By the admittedly simplistic "rule of thumb" for loudness, this -40dB sound would still be 1/16 as loud as the 0 dB reference. 0 dB in this table represents the normal hearing threshold, or 0 dB Hearing Level.

Index

Hearing concepts

Dangers of Loud Sounds

ReferenceHolt

ASHA

Association The categories of hearing loss are based on measurements at 500, 1000 and 2000 Hz.

Assessment of hearing loss Hearing Aids

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Hearing AidsSometimes a satisfactory level of hearing can be restored by a hearing aid - a combination of a microphone to sense ambient sound, an amplifier, and a tiny speaker that projects the amplified sound into the ear canal. A typical modern hearing aid would employ an electret condenser microphone - small and rugged with a high signal-to-noise ratio. The frequency range of application is typically 100-10,000 Hz. While some assistance may be rendered by bone conduction, this discussion will be limited to hearing aids that operate by sounds produced in the air.

Wearing Styles

ITE In-the-ear

BTEBehind-the-ear

ITC In-the-canal

CICCompletelyin-the-canal

Body

Worn on body (profound loss)

A basic hearing aid may be called a linear circuit aid, implying that it simply amplifies any ambient sound that reaches it. It is important for such a hearing aid to contour the amplification to the nature of the hearing loss of the individual, which typically means amplifying high frequencies more than low frequencies. Presbycusis, the progressive loss of high frequency hearing with age, often calls for amplification of high frequencies with little or no bass boost. A basic hearing aid may have three frequency bands to permit the amplification to be adjusted based on the audiogram.

Index

Hearing concepts

Dangers of Loud

Sounds

ReferencesHolt

Goldenberg

The next step up in sophistication of the hearing aid would be to employ some kind of audio "compression". Compression implies the adjustment of the "gain" or degree of amplification based on the input level, it being a practical fact that louder sounds wouldn't need as much amplification. This compression would reduce the amplification for loud sounds either at the microphone end or at the speaker end. Some types of compression are called "adaptive compression" in that some logic is used to compress some kinds of sounds more than others.

For those hearing aids that use adaptive compression, but not digital logic, some are classified under the headings ASP and K-AMP circuits. The ASP units monitor incoming sounds and automatically change the gain, output and frequency response. The K-AMP approach detects and amplifies only quiet sounds while leaving louder ones unaltered.

Currently under very active development are the digital programmable hearing aids that use a digital signal processor (dsp). They can be programmed to more nearly fit the detailed needs of an individual user and open the door to more sophisticated approaches to assisting the user. Since the understanding of human speech is often the highest priority, and since speech has identifiable characteristics like vocal formants, some steps can be made to program the hearing aid to amplify speech sounds more than some distinctly different other types of sounds. A friend with a digital hearing aid told me something like "I leaned over an expressway bridge and listened to the traffic noise. After a short time there was a kind of burbling sound like the hearing aid was trying to make voices out of this sound." An intriguing idea, that we might get enough sophistication into hearing aids to recognize and selectively amplify the sounds of meaningful human communication.

Another approach to hearing assistance is the cochlear implant. Currently very expensive and in the experimental stage, it is one of the future possibilities.

(Tal Berkowitz is acknowledged for investigative work on this topic.)

Assessment of hearing loss

 

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Sensitivity of Human EarThe human ear can respond to minute pressure variations in the air if they are in the audible frequency range, roughly 20 Hz - 20 kHz.

It is capable of detecting pressure variations of less than one billionth of atmospheric pressure. The threshold of hearing corresponds to air vibrations on the order of a tenth of an atomic diameter. This incredible sensitivity is enhanced by an effective amplification of the sound signal by the outer and middle ear structures. Contributing to the wide dynamic range of human hearing

Index

Hearing concepts

are protective mechanisms that reduce the ear's response to very loud sounds. Sound intensities over this wide range are usually expressed in decibels.

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Dynamic Range of HearingIn addition to its remarkable sensitivity, the human ear is capable of responding to the widest range of stimuli of any of the senses. The practical dynamic range could be said to be from the threshold of hearing to the threshold of pain:

Threshold of Hearing

Threshold of Pain

I0 1013I0 = 10,000,000,000,000 I0

0 decibels 130 decibels

This remarkable dynamic range is enhanced by an effective amplification structure which extends its low end and by a protective mechanism which extends the high end.

Dynamic levels of music

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Hearing concepts

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Pitch ResolutionThe extremely small size of the cochlea and the extremely high resolution of human pitch perception cast doubt on the sufficiency of the place theory to completely account for the human ear's pitch resolution. Some typical data:

Cochlea:

turns,

about 3.2 cm length.Resolves about 1500 separate pitcheswith 16,000-20,000 hair cells.

This would require a separate detectable pitch for every 0.002 cm, which is physically unreasonable for a simple peaking action on the membrane.

The normal human ear can detect the difference between 440 Hz and 441 Hz. It is hard to believe it could attain such resolution from selective peaking of the membrane vibrations. Some pitch sharpening mechanism must be operating.

Index

Hearing concepts

Place theory

concepts

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The structures of the outer and middle ear contribute to both the remarkable sensitivity and the wide dynamic range of human hearing. They can be considered to be both a pre-amplifier and a limiter for the human hearing process.

Index

Hearing concepts

ReferenceStevens &

Warshofsky

The outer ear (pinna) collects more sound energy than the ear canal would receive without it and thus contributes some area amplification.

The numbers here are just representative ... not precise data.

Closed tube resonance of the auditory canal enhances 2000-5000 Hz

Tympanic membrane (eardrum) has some 15x area of oval window contributing an area amplification.

Ossicles (hammer, anvil and stirrup) contribute a lever-type amplification when listening to soft sounds.

Outer ear2x

Tympanic membrane

15x

Ossicles3x

The outer and middle ears contribute something like a factor of 100 or about 20 decibels of amplification under optimum conditions.

 

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Audible SoundUsually "sound" is used to mean sound which can be perceived by the human ear, i.e., "sound" refers to audible sound unless otherwise classified. A reasonably standard definition of audible sound is that it is a pressure wave with frequency between 20 Hz and 20,000 Hz and with an intensity above the standard threshold of hearing. Since the ear is surrounded by air, or perhaps under water, the sound waves are constrained to be longitudinal waves. Normal ranges of sound pressure and sound intensity may also be specified.

Frequency: 20 Hz - 20,000 Hz (corresponds with pitch)

Intensity: 10-12 - 10 watts/m2 (0 to 130 decibels)

Pressure: 2 x 10-5 - 60 Newtons/m2 2 x 10-10 - .0006 atmospheres

For an air temperature of 20°C where the sound speed is 344 m/s, the audible sound waves have wavelengths from 0.0172 m (0.68 inches) to 17.2 meters (56.4 feet).

Ultrasonic sound

Index

Hearing concepts

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In response to sustained loud sounds, muscle tension tightens the tympanic membrane and, acting through the tendon connecting the hammer and anvil, repositions the ossicles to pull the stirrup back, lessening the transfer of force to the oval window of the inner ear. This contributes to the ear's wide dynamic range.

The stapedius muscle and the tensor tympani muscle act in response to loud sounds.(DeBonis & Donohue)

More detail

Index

Hearing concepts

ReferenceStevens &

Warshofsky

DeBonis & Donohue

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Loud Sound Response Index

Hearing concepts

Reference

In response to loud sounds, the tensor tympani muscle tightens the eardrum and through the tendon between the hammer and anvil and shifts the stirrup backward from the oval window of the inner ear. This shifting of the ossicles reduces the transmitted force to the inner ear, protecting it. However, it is a relatively slow action and cannot protect the ear from sudden loud sounds like a gunshot. The process is less effective in older ears.

Dynamic levels of music

Stevens & Warshofsky

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Young and Old Ears Index

Hearing concepts

ReferenceStevens &

Warshofsky

A young person's ear can provide a limited amount of protection from sustained loud sounds by shifting the stirrup backward so that it doesn't exert as much force on the oval window. In the very young, the stirrup is thought to be capable of actually breaking contact with the oval window, breaking the direct link to the inner ear. In an older ear, the structures become stiffer and cannot adjust backward as much. Older persons are generally less tolerant of loud sounds.

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In response to sustained loud sounds, muscle tension tightens the tympanic membrane and, acting through the tendon connecting the hammer and anvil, repositions the ossicles to pull the stirrup back, lessening the transfer of force to the oval window of the inner ear. This contributes to the ear's wide dynamic range.

The stapedius muscle and the tensor tympani muscle act in response to loud sounds.(DeBonis & Donohue)

More detail

Index

Hearing concepts

ReferenceStevens &

Warshofsky

DeBonis & Donohue

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Loud Sound Response

In response to loud sounds, the tensor tympani muscle tightens the eardrum and through the tendon between the hammer and anvil and shifts the stirrup backward from the oval window of the inner ear. This shifting of the ossicles reduces the transmitted force to the inner ear, protecting it. However, it is a relatively slow action and cannot protect the ear from sudden loud sounds like a gunshot. The process is less effective in older ears.

Dynamic levels of music

Index

Hearing concepts

ReferenceStevens &

Warshofsky

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Young and Old Ears Index

Hearing concepts

ReferenceStevens &

A young person's ear can provide a limited amount of protection from sustained loud sounds by shifting the stirrup backward so that it doesn't exert as much force on the oval window. In the very young, the stirrup is thought to be capable of actually breaking contact with the oval window, breaking the direct link to the inner ear. In an older ear, the structures become stiffer and cannot adjust backward as much. Older persons are generally less tolerant of loud sounds.

Warshofsky

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Spectral Colors

In a rainbow or the separation of colors by a prism we see the continuous range of spectral colors (the visible spectrum). A spectral color is composed of a single wavelength and can be correlated with wavelength as shown in the chart below ( a general guide and not a precise statement about color). It is safe enough to say that monochromatic light like the helium-neon laser is red (632 nm) or that the 3-2 transition from the hydrogen spectrum is red ( 656 nm) because they fall in the appropriate wavelength range. But most colored objects give off a range of wavelengths and the characterization of color is much more than the statement of wavelength. Perceived colors can be mapped on a chromaticity diagram.

Index

Vision concepts

Color vision

Visible spectrum

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Color

It is common practice to define pure colors in terms of the wavelengths of light as shown. This works well for spectral colors but it is found that many different combinations of light wavelengths can produce the same perception of color.

Index

Vision concepts

Color vision

Visible spectrum

This progression from left to right is from long wavelength to short wavelength, and from low frequency to high frequency light. The wavelengths are commonly expressed in nanometers (1 nm = 10-9 m). The visible spectrum is roughly from 700 nm (red end) to 400 nm (violet end). The letter I in the sequence above is for indigo - no longer commonly used as a color name. It is included above strictly for the reason of making the sequence easier to say as a mnemonic, like a person's name: Roy G. Biv - a tradition in the discussion of color.

The inherently distinguishable characteristics of color are hue, saturation, and brightness. Color measurement systems characterize colors in various parameters which relate to hue, saturation, and brightness. They include the subjective Munsell and Ostwald systems and the quantitative CIE color system.

White light, or nearly white light from the Sun, contains a continuous distribution of wavelengths. The light from the Sun is essentially that of a blackbody radiator at 5780 K. The wavelengths (spectral colors) of white light can be separated by a dispersive medium like a prism. Even more effective separation can be achieved with a diffraction grating.

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Refraction of Light Index

Refraction is the bending of a wave when it enters a medium where it's speed is different. The refraction of light when it passes from a fast medium to a slow medium bends the light ray toward the normal to the boundary between the two media. The amount of bending depends on the indices of refraction of the two media and is described quantitatively by Snell's Law.

Refraction is responsible for image formation by lenses and the eye. As the speed of light is reduced in the slower medium, the wavelength is shortened proportionately. The frequency is unchanged; it is a characteristic of the source of the light and unaffected by medium changes.

Refraction and the eye Refraction of sound

Refraction of light by water

Lens concepts

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Index of RefractionThe index of refraction is defined as the speed of light in vacuum divided by the speed of light in the medium.

Index

Lens concepts

The indices of refraction of some common substances are given below with a more complete description of the indices for optical glasses given elsewhere. The values given are approximate and do not account for the small variation of index with light wavelength which is called dispersion.

Refraction and the eye Refraction of sound

Table of refractive indices

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Snell's LawSnell's Law relates the indices of refraction n of the two media to the directions of propagation in terms of the angles to the normal. Snell's law can be derived from Fermat's Principle or from the Fresnel Equations.

Index

Lens concepts

Enter data below, then click the symbol of the quantity you wish to calculate.

Indices of refraction:

=

=

Angles with surface normal:

= °

= °

Enter data and then click on the symbol for the quantity you wish to calculate in the active equation above. The numbers will not be forced to be consistent until you click on the quantity to calculate. Indices of refraction must be greater than or equal to 1, so values less than 1 do not represent a physically possible system.

If the incident medium has the larger index of refraction, then the angle with the normal is increased by refraction. The larger index medium is commonly called the "internal" medium, since air with n=1 is usually the surrounding or "external" medium. You can calculate the condition for total internal reflection by setting the refracted angle = 90° and calculating the incident angle. Since you can't refract the light by more than 90°, all of it will reflect for angles of incidence greater than the angle which gives refraction at 90°.

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Heat Transfer The transfer of heat is normally from a high temperature object to a lower temperature object. Heat transfer changes the internal energy of both systems involved according to the First Law of Thermodynamics.

Heat transfer from a cold to a hotter region

Radiation cooling time

Index

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Heat Conduction Conduction is heat transfer by means of molecular agitation within a material without any motion of the material as a whole. If one end of a metal rod is at a higher temperature, then energy will be transferred down the rod toward the colder end because the higher speed particles will collide with the slower ones with a net transfer of energy to the slower ones. For heat transfer between two plane surfaces, such as heat loss through the wall of a house, the rate of conduction heat transfer is:

Index

Heat transfer concepts

Heat transfer

examples

Calculation

= heat transferred in time =

= thermal conductivity of the barrier

= area

= temperature

= thickness of barrier

Thermal conductivity table

Discussion of thermal conductivity

Home heat loss by conduction.

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Heat Convection Convection is heat transfer by mass motion of a fluid such as air or water when the heated fluid is caused to move away from the source of heat, carrying energy with it. Convection above a hot surface occurs because hot air expands, becomes less dense, and rises (see Ideal Gas Law). Hot water is likewise less dense than cold water and rises, causing convection currents which transport energy.

Index

Heat transfer concepts

Heat transfer

examples

Convection can also lead to circulation in a liquid, as in the heating of a pot of water over a flame. Heated water expands and becomes more buoyant. Cooler, more dense water near the surface descends and patterns of circulation can be formed, though they will not be as regular as suggested in the drawing.

Convection cells are visible in the heated cooking oil in the pot at left. Heating the oil produces changes in the index of refraction of the oil, making the cell boundaries visible. Circulation patterns form, and presumably the wall-like structures visible are the boundaries between the circulation patterns.

Convection is thought to play a major role in transporting energy from the center of the Sun to the surface, and in movements of the hot magma beneath the surface of the earth. The visible surface of the Sun (the photosphere) has a granular appearance with a typical dimension of a granule being 1000 kilometers. The image at right is from the NASA Solar Physics website and is credited to G. Scharmer and the Swedish Vacuum Solar Telescope. The granules are described as convection cells which transport heat from the interior of the Sun to the surface.

In ordinary heat transfer on the Earth, it is difficult to quantify the effects of convection since it inherently depends upon small nonuniformities in an otherwise fairly homogeneous medium. In modeling things like the cooling of the human body, we usually just lump it in with conduction.

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Greenhouse Effect The greenhouse effect refers to circumstances where the short wavelengths of visible light from the sun pass through a transparent medium and are absorbed, but the longer wavelengths of the infrared re-radiation from the heated objects are unable to pass through that medium. The trapping of the long wavelength radiation leads to more heating and a higher resultant temperature. Besides the

Index

heating of an automobile by sunlight through the windshield and the namesake example of heating the greenhouse by sunlight passing through sealed, transparent windows, the greenhouse effect has been widely used to describe the trapping of excess heat by the rising concentration of carbon dioxide in the atmosphere. The carbon dioxide strongly absorbs infrared and does not allow as much of it to escape into space.

Sunlight warms your car

Increasing atmospheric carbon dioxide

Global warming

Role in the absence of water on Venus?

A major part of the efficiency of the heating of an actual greenhouse is the trapping of the air so that the energy is not lost by convection. Keeping the hot air from escaping out the top is part of the practical "greenhouse effect", but it is common usage to refer to the infrared trapping as the "greenhouse effect" in atmospheric applications where the air trapping is not applicable.

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Greenhouse Effect Example Bright sunlight will effectively warm your car on a cold, clear day by the greenhouse effect. The longer infrared wavelengths radiated by sun-warmed objects do not pass readily through the glass. The entrapment of this energy warms the interior of the vehicle. The trapping of the hot air so that it cannot rise and lose the energy by convection also plays a major role.

Index

Blackbody radiation concepts

Short wavelengths of visible light are readily transmitted through the transparent windshield. (Otherwise you wouldn't be able to see through it!)

Shorter wavelengths of ultraviolet light are largely blocked by glass since they have greater quantum energies which have absorption mechanisms in the glass. Even though you may be uncomfortably warm with bright sunlight streaming through, you will not be sunburned.

 

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Increase in Greenhouse Gases The increase in the concentration of carbon dioxide, one of the three major atmospheric contributers to the greenhouse effect has been carefully documented at the Mauna Loa Observatory in Hawaii. The 1990 rate of increase was about 0.4% per year. The interesting cyclic variations represent the reduction in carbon dioxide by photosynthesis during the growing season in the northern hemisphere.

Current analysis suggests that the combustion of fossil fuels is a major contributer to the increase in the carbon dioxide concentration, such contributions being 2 to 5 times the effect of deforestation (Kraushaar & Ristinen).

Index

ReferencesKraushaar & Ristinen

Trefil

Increase in Atmospheric Carbon Dioxide

The Mauna Loa monitoring station reports the carbon dioxide level in the atmosphere today as about 380 parts per million compared to 315 ppm in 1958 when modern measurements were initiated. Measurements of air bubbles trapped in the Greenland ice sheet indicate concentrations of 270 ppm in preindustrial times.

These are sketches of the graphs produced in the IPCC 2007 report of the increase in key greenhouse gases. They make clear that most of the increase of the last thousand years has occurred in the past 200 years. The radiative forcing of these gases is related to their concentration .

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Contributers to Greenhouse Effect Those gas molecules in the Earth's atmosphere with three or more atoms are called "greenhouse gases" because they can capture outgoing infrared energy from the Earth, thereby warming the planet. The greenhouse gases include water vapor with three atoms (H2O), ozone (O3), carbon dioxide (CO2), and methane (CH4). Also, trace quantities of chloro-fluoro-carbons (CFC's) can have a disproportionately large effect.

Index

ReferenceKraushaar & Ristinen

To attempt to quantify the effects of greenhouse gases on the global temperature, climatologists use the "radiative forcing" of the current atmospheric content of these gases.

Increase in greenhouse gases Greenhouse effect

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Global Warming An issue of major concern is the possible effect of the burning of fossil fuels and other contributers to the increase of carbon dioxide in the atmosphere. The action of carbon dioxide and other greenhouse gases in trapping infrared radiation is called the greenhouse effect. It may measurably increase the overall average temperature of the Earth, which could have disastrous consequences. Sometimes the effects of the greenhouse effect are stated in terms of the albedo of the Earth, the overall average reflection coefficient.

Index

ReferencesKraushaar & Ristinen

Brohan, et al.

Schneider

This graphic of the global air temperature was posted by Phil Jones on behalf of the Climatic Research Unit, UK. The key reference used was Brohan, et al.

Another depiction of the mean temperatures in the northern hemisphere was drawn from NOAA.

Essentially any kind of tabulation you access will tell the same story. The

temperature has gradually risen over the last 150 years.

Because the potential consequences of global warming in terms of loss of snow cover, sea level rise, change in weather patterns, etc are so great, it is a major societal concern. On the other hand, proposed measures to reduce human contributions to greenhouse gases can also have great consequences. The large potential impact combined with the ambiguities of the science has given rise to many passionate extremes.

Stephen Schneider of Stanford seems to me to be one of the more balanced voices. His website is a good source for relevant data. He discusses the problems in the context of the Earth's energy balance and the changes in the concentrations of greenhouse gases.

Increase in greenhouse gases Greenhouse effect

Modeling the human impact on global worming

Skeptical views of global warming

Longer term temperature variations

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