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# La place law

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### La place law

1. 1. La Places Law Imagine blood flowing through a blood vessel which has a certain radius and a certainwall thickness. The blood vessel wall is stretched as a result of the difference between the bloodpressure inside the vessel and the surrounding pressure outside the vessel. La Places lawdescribes 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 tensionthere will be. On the other hand, the thicker the wall the less tension there is. Also, the larger theradius 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 theradius of the cylinder, and M is the thickness of the wall. An example of LaPlace Law is Dilatedcardiomyopathy. In this condition heart becomes greatly distended and the radius (R) of ventricleincreases. Therefore to create the same pressure (P) during ejection of the blood much larger
2. 2. wall tention (T) has be developed by the cardiac muscle. Thus dilated heart requires more energyto pump the same amount of blood as compared to the heart of normal size. The new surgicalprocedure, called ventricular remodeling, uses LaPlace principle to improve the function ofdilated, failing hearts. Imagine yourself blowing a balloon. The harder you blow the higher the air pressure insidethe balloon and the higher the pressure difference between the outside and inside of the balloonbecome. Since the pressure difference rises, the tension in the rubber walls of the balloon alsorises, and this is what causes the balloon to stretch. Now imagine you are blowing a balloonwhich is made of much thicker rubber. Now you will notice that the balloon is harder to inflatebecause more pressure difference is required to raise the tension in the walls of the balloon. Do you think this page missing something? Add it See other additions to this page. NextAbout This Site >Library >FAQ >7,000+ sitesby kids for kids
4. 4. Wall Tension Ind LaPl la concPascals 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 partsof the balloon. The variation is described by Laplaces Law.Once you have established the geometry of the balloon, then the tension, pressure and radius have adefinite relationship and could be used to measure tension or pressure. That is, if you have a gauge tomeasure pressure, then you can calculate the wall tension. In the interesting experiment of putting oneend of a balloon into liquid nitrogen, you can collapse one end of it by cooling while the other endstays essentially at its previous radius. This can be taken to imply that the pressure is not diminishingsignificantly since for a given tension, the pressure is related to the radius. Go BHyperPhysics***** Mechanics ***** Fluids R Nave
5. 5. LaPlaces LawThe larger the vessel radius, the larger the walltension required to withstand a given internal fluidpressure. Index LaPlaces law concepts Balloon exampleFor a given vessel radius and internal pressure, aspherical vessel will have half the wall tension of acylindrical vessel. Why does the wall tension increase with radius? Go BackHyperPhysics***** Mechanics ***** Fluids R Nave
6. 6. Why does wall tension increase with radius? Index LaPlaces law concepts Balloon exampleIf the upward part of the fluid pressure remains the same, then the downwardcomponent of the wall tension must remain the same. But if the curvature isless, then the total tension must be greater in order to get that same downwardcomponent of tension. Go BackHyperPhysics***** Mechanics ***** Fluids R Nave Index LaPlaces law Alveoli of the Lungs concepts Reference Shier, et al. Ch 19
7. 7. The oxygen exchange in the lungs takes placeacross the membranes of small balloon-likestructures called alveoli attached to thebranches of the bronchial passages. Thesealveoli inflate and deflate with inhalation andexhalation. The behavior of the alveoli islargely dictated by LaPlaces law and surfacetension. It takes some effort to breathe inbecause these tiny balloons must be inflated,but the elastic recoil of the tiny balloonsassists us in the process of exhalation. If theelastic recoil of the alveoli is compromised, asin the case of emphysema, then it is difficultto exhale forcibly.The difficulty of inspiration during the babys first breath is Inflation ofgreat because all the balloons must be inflated from a alveolicollapsed state. Respiratory System Go BackHyperPhysics***** Mechanics ***** Fluids R Nave
8. 8. Inflating the AlveoliInflating the alveoli in the process of respiration requires an excess pressureinside the alveoli relative to their surroundings. This is actually accomplishedby making the pressure in the thoracic cavity negative with respect toatmospheric pressure.The amount of net pressure required for inflation is dictated by the surfacetension and radii of the tiny balloon-like alveoli. During inhalation the radii ofthe alveoli increase from about 0.05 mm to 0.1 mm . The normal mucoustissue fluid surrounding the alveoli has a nominal surface tension of about 50dynes/cm so the required net outward pressure is: Index LaPlaces law concepts ReferenceThe remarkable property of Shier, etthe surfactant which coats al.the alveoli is that it reduces Ch 19the surface tension by afactor of about 15 so thatthe 1 mmHg pressuredifferential is sufficient toinflate the alveoli. Otherfactors affecting theremarkable efficiency ofoxygen transport across thelung membranes ischaracterized in FicksLaw. Go BackHyperPhysics***** Mechanics ***** Fluids R Nave
9. 9. Surfactant Role in RespirationOne of the remarkable phenomena in theprocess of respiration is the role of the fluidcoating the walls of the alveoli of the lungs.This fluid, called a surfactant, lowers thesurface tension of the balloon-like alveoli byabout a factor of 15 compared to the normal Indexmucous tissue fluid in which they areimmersed. There appears to be a nearly LaPlacesconstant amount of this surfactant per lawalveolus, so that when the alveoli are deflated conceptsit is more concentrated on the surface. Sincethe surface-tension-lowering effect of the Referencesurfactant depends on this concentration, it Shier, etdiminishes the required pressure for inflation al.of the alveoli at their most critical phase. For a Ch 19given surface tension, the pressure to inflate asmaller bubble is greater. It is the surfactantwhich makes possible the inflation of thealveoli with only about 1 mmHg of pressureexcess over their surroundings. The babysfirst breath depends upon this surfactant and ismade more difficult in premature infants bythe incomplete formation of the surfactant. Go BackHyperPhysics***** Mechanics ***** Fluids R Nave
10. 10. Alveoli and ExhalationThe alveoli of the lungs act much likeballoons in that there is some effort involvedto inflate them, but when the inflatingpressure is released, the recoil of the elasticwalls provides the pressure necessary todeflate them. The lungs are suspended in the Indexthoracic cavity which is normally at a slightnegative pressure. When the diaphragm is LaPlaceslowered, that pressure becomes more negative lawand the lungs expand into the cavity. Air from conceptsthe atmosphere moves into the resultingpartial vacuum and inflates the alveoli. One is Referenceaware of the effort, but it is not extreme as in Shier, etthe case of the babys first breath . Once the al.alveoli are fully inflated, exhalation can be Ch 19accomplished by merely relaxing thediaphragm, since the wall tension in all thetiny alveoli will act to force the air out ofthem. By forcing the diaphragm upward, wecan exhale forcefully by adding the diaphragmeffort to the recoil of the elastic alveoli. Indiseases like emphysema, the elasticity of thealveoli is lost and exhalation becomes alaborious process. Go BackHyperPhysics***** Mechanics ***** Fluids R Nave
11. 11. The Babys First BreathEveryone knows that it is much more difficult to blow up a balloon for the firsttime. Why is that? For one thing, the applied pressure does not create muchtension in the walls of a small balloon to start the stretching process necessaryfor inflation. According to LaPlaces law, the wall tension will be twice aslarge for a balloon of twice the radius. If it takes a certain applied pressure to Indexovercome the elasticity of the large balloon and cause it to expand further, itwill take twice as much pressure to start to expand the smaller balloon. All this LaPlacesmakes it difficult for the baby to take its first breath -- all the balloons are lawsmall! The alveoli of the lungs are collapsed in the fetus and must be inflated conceptsin the process of inhalation. Thus the traditional spank on the bottom of thenewborn to make him/her mad enough to make the effort for the first breath.Further difficulties are encountered by premature infants because thesurfactant fluid which coats the alveoli to give them the appropriate walltensions is formed in the later stages of pregnacy. Until that point, the alveoliare coated with fluid which has essentially the surface tension of water, muchhigher than that of the normal surfactant. Go BackHyperPhysics***** Mechanics ***** Fluids R Nave EmphysemaThe disease of the lungs called emphysema or chronic obstructivepulmonary disease (COPD) results in the enlargement of the alveoli of the Indexlungs as some are destroyed and others either enlarge or combine. Thedisease is one of the destructive effects of long-term smoking, but LaPlacessometimes occurs in non-smokers. If the normal inhalation process inflates lawthe alveoli to a larger radius, the implications of LaPlaces law are that the conceptswall must have lost much of its elasticity. Normally it would take twice thepressure to inflate a constant tension membrane to twice its radius. ReferenceTypically, the wall tension of the healthy alveoli is determined by the Canadiansurface tension of the liquid which coats them, and with a uniform coating Lung(called a surfactant), they will all inflate to a similar radius. The enlarged Associationalveoli in the emphysema patient imply less elastic recoil during the processof exhalation. Exhalation requires effort from the diaphragm and inadvanced stages of the disease, a patient will not be able to blow out amatch.
12. 12. Besides the loss of elasticity of the alveolar walls, the larger size of thecompartments implies a smaller surface area for a given volume. Becausethe oxygen exchange from the air to the blood is proportional to the area ofthe exchange membrane, this diminishes the rate of oxygen transfer. R Go BackHyperPhysics***** Mechanics ***** Fluids Nave Tension in Arterial Walls IndexThe tension in the walls of arteries and veins in the human body is a classic LaPlacesexample of LaPlaces law. This geometrical law applied to a tube or pipe says lawthat for a given internal fluid pressure, the wall tension will be proportional to conceptsthe radius of the vessel.
13. 13. The implication of thislaw for the largearteries, which havecomparable bloodpressures, is that thelarger arteries musthave stronger wallssince an artery of twicethe radius must be ableto withstand twice thewall tension. Arteriesare reinforced byfibrous bands tostrengthen them againstthe risks of ananeurysm. The tinycapillaries rely on theirsmall size. Demonstration with balloon Go BackHyperPhysics***** Mechanics ***** Fluids R Nave Capillary WallsThe walls of the capillaries of the human circulatory system are so thin as toappear transparent under a microscope, yet they withstand a pressure up toabout half of the full blood pressure. LaPlaces law gives insight into how theyare able to withstand such pressures: their small size implies that the wall Indextension for a given internal pressure is much smaller than that of the largerarteries. LaPlaces lawGiven a peak blood pressure of about 120 mmHg at the left ventricle, the conceptspressure at the beginning of the capillary system may be on the order of 50mmHg. The large radii of the large arteries imply that for pressures in thatrange they must have strong walls to withstand the large resulting wall tension.The larger arteries provide much less resistance to flow than the smaller vesselsaccording to Poiseuilles law, and thus the drop in pressure across them is onlyabout half the total drop. The capillaries offer large resistances to flow, but
14. 14. dont require much strength in their walls. Go BackHyperPhysics***** Mechanics ***** Fluids R Nave Danger of AneurysmsThe larger arteries of the body are subject to higher wall tensions than thesmaller arteries and capillaries. This wall tension follows the dictates ofLaPlaces law, a geometrical relationship which shows that the wall tension isproportional to the radius for a given blood pressure. If an artery wall develops aweak spot and expands as a result, it might seem that the expansion would Indexprovide 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 LaPlacesvessel may continue to expand in what is called an aneurysm. Unchecked, this lawcondition will lead to rupture of the vessel, so aneurysms require prompt conceptsmedical attention.A localized weak spot in an artery might gain some temporary tension relief byexpanding toward a spherical shape, since a spherical membrane has half thewall tension for a given radius. Minimizing membrane tension is why soapbubbles tend to form a spherical shape. But for an expanding artery, forming anear-spherical shape cannot be depended upon to give sufficient tension relief.
15. 15. Demonstration with balloon Go BackHyperPhysics***** Mechanics ***** Fluids R Navehttp://hyperphysics.phy-astr.gsu.edu/Hbase/lapcon.html Ear and Hearing This is an active graphic. Click anywhere on it for more detail. Index Hearing concepts Go BackHyperPhysics***** Sound R Nave
16. 16. The Outer EarSound energy spreads out from its sources. For a point source of sound, itspreads out according to the inverse square law. For a given sound intensity, alarger ear captures more of the wave and hence more sound energy.The outer ear structures act as part of the ears preamplifier to enhance thesensitivity of hearing. Index Hearing conceptsThe auditory canal acts as a closed tube resonator, enhancing sounds in therange 2-5 kiloHertz. Go BackHyperPhysics***** Sound R Nave
17. 17. The Tympanic MembraneThe tympanic membrane or "eardrum" receives vibrations traveling up theauditory canal and transfers them through the tiny ossicles to the oval window,the port into the inner ear.The eardrum is Active graphicsome fifteentimes larger thanthe oval windowof the inner ear, Indexgiving anamplification of Hearingabout fifteen conceptscompared to acase where the Zemlinsound pressureinteracted withthe oval windowalone.The tympanicmembrane isvery thin, about0.1 mm, but it isresilient and You may reach information about the nearby structures ofstrong.(Zemlin) the ear by clicking on the item of interest on the illustration. Go BackHyperPhysics***** Sound R Nave
18. 18. Sound IntensitySound intensity is defined as the sound power per unit area. The usualcontext is the measurement of sound intensity in the air at a listenerslocation. The basic units are watts/m2 or watts/cm2 . Many sound intensitymeasurements are made relative to a standard threshold of hearingintensity I0 : Index Sound level measurementThe most common approach to sound intensity measurement is to use thedecibel scale: Loudness conceptsDecibels measure the ratio of a given intensity I to the threshold of hearingintensity , so that this threshold takes the value 0 decibels (0 dB). To assesssound loudness, as distinct from an objective intensity measurement, thesensitivity of the ear must be factored in. R Go BackHyperPhysics***** Sound Nave
19. 19. Sound PressureSince audible sound consists of pressure waves, one of the ways toquantify the sound is to state the amount of pressure variation relative toatmospheric pressure caused by the sound. Because of the great sensitivityof human hearing, the threshold of hearing corresponds to a pressurevariation less than a billionth of atmospheric pressure.The standard threshold of hearing can be stated in terms of pressure andthe sound intensity in decibels can be expressed in terms of the soundpressure: Index Sound level measurementThe pressure P here is to be understood as the amplitude of the pressurewave. The power carried by a traveling wave is proportional to the squareof the amplitude. The factor of 20 comes from the fact that the logarithmof the square of a quantity is equal to 2 x the logarithm of the quantity.Since common microphones such as dynamic microphones produce avoltage which is proportional to the sound pressure, then changes in soundintensity incident on the microphone can be calculated fromwhere V1 and V2 are the measured voltage amplitudes . R Go BackHyperPhysics***** Sound Nave
20. 20. Threshold of HearingSound level measurements in decibels are generally referenced to astandard threshold of hearing at 1000 Hz for the human ear which can bestated in terms of sound intensity: Indexor in terms of sound pressure: Sound level measurementThis value has wide acceptance as a nominal standard threshold andcorresponds to 0 decibels. It represents a pressure change of less than onebillionth of standard atmospheric pressure. This is indicative of theincredible sensitivity of human hearing. The actual average threshold ofhearing 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 varieswith frequency, as illustrated by the measured hearing curves. R Go BackHyperPhysics***** Sound Nave
21. 21. Threshold of PainThe nominal dynamic range of human hearing is from the standardthreshold of hearing to the threshold of pain. A nominal figure for thethreshold of pain is 130 decibels, but that which may be considered painfulfor one may be welcomed as entertainment by others. Generally, youngerpersons are more tolerant of loud sounds than older persons because theirprotective mechanisms are more effective. This tolerance does not makethem immune to the damage that loud sounds can produce. Index Sound level measurementSome sources quote 120 dB as the pain threshold and define the audiblesound frequency range as ending at about 20,000 Hz where the thresholdof hearing and the threshold of pain meet. R Go BackHyperPhysics***** Sound Nave
22. 22. LoudnessLoudness is not simply sound intensity!Sound loudness is a subjective term describing the strength of the earsperception of a sound. It is intimately related to sound intensity but can by no Indexmeans be considered identical to intensity. The sound intensity must befactored by the ears sensitivity to the particular frequencies contained in the Loudnesssound. This is the kind of information contained in equal loudness curves for conceptsthe human ear. It must also be considered that the ears response to increasingsound intensity is a "power of ten" or logarithmic relationship. This is one of Hearingthe motivations for using the decibel scale to measure sound intensity. A conceptsgeneral "rule of thumb" for loudness is that the power must be increased byabout a factor of ten to sound twice as loud. To more realistically assess soundloudness, the ears sensitivity curves are factored in to produce a phon scale forloudness. The factor of ten rule of thumb can then be used to produce the sonescale of loudness. In practical sound level measurement, filter contours such asthe A, B, and C contours are used to make the measuring instrument morenearly approximate the ear. Go BackHyperPhysics***** Sound R Nave "Rule of Thumb" for Loudness IndexA widely used "rule of thumb" for the loudness of a particular sound is that thesound must be increased in intensity by a factor of ten for the sound to be Loudnessperceived as twice as loud. A common way of stating it is that it takes 10 violins conceptsto sound twice as loud as one violin. Another way to state the rule is to say thatthe loudness doubles for every 10 phon increase in the sound loudness level. HearingAlthough this rule is widely used, it must be emphasized that it is an conceptsapproximate general statement based upon a great deal of investigation ofaverage human hearing but it is not to be taken as a hard and fast rule.
23. 23. Why is it that doubling the sound intensity to the ear does not produce adramatic increase in loudness? We cannot give answers with completeconfidence, but it appears that there are saturation effects. Nerve cells havemaximum rates at which they can fire, and it appears that doubling the soundenergy to the sensitive inner ear does not double the strength of the nerve signalto the brain. This is just a model, but it seems to correlate with the generalobservations which suggest that something like ten times the intensity isrequired to double the signal from the innner ear.One difficulty with this "rule of thumb" for loudness is that it is applicable onlyto adding loudness for identical sounds. If a second sound is widely enoughseparated in frequency to be outside the critical band of the first, then this ruledoes not apply at all.While not a precise rule even for the increase of the same sound, the rule hasconsiderable utility along with the just noticeable difference in sound intensitywhen judging the significance of changes in sound level. Go BackHyperPhysics***** Sound R Nave
24. 24. Adding LoudnessWhen one sound is produced and another sound is added, the increase inloudness perceived depends upon its frequency relation to the first sound.Insight into this process can be obtained from the place theory of pitchperception. If the second sound is widely separated in pitch from the first, thenthey do not compete for the same nerve endings on the basilar membrane of theinner ear. Adding a second sound of equal loudness yields a total sound abouttwice as loud. But if the two sounds are close together in frequency, within acritical band, then the saturation effects in the organ of Corti are such that theperceived combined loudness is only slightly greater than either sound alone.This is the condition which leads to the commonly used rule of thumb for Indexloudness addition. Loudness concepts Hearing concepts Go BackHyperPhysics***** Sound R Nave
25. 25. Critical BandWhen two sounds of equal loudness when sounded separately are closetogether in pitch, their combined loudness when sounded together will be onlyslightly louder than one of them alone. They may be said to be in the samecritical band where they are competing for the same nerve endings on the Indexbasilar membrane of the inner ear. According the the place theory of pitchperception, sounds of a given frequency will excite the nerve cells of the Hearingorgan of Corti only at a specific place. The available receptors show saturation conceptseffects which lead to the general rule of thumb for loudness by limiting theincrease in neural response. References Rossing,If the two sounds are widely separated in pitch, the perceived loudness of the Science ofcombined tones will be considerably greater because they do not overlap on Soundthe basilar membrane and compete for the same hair cells. The phenomenonof the critical band has been widely investigated. BackusBackus reports that this critical band is about 90 Hz wide for sounds below Zwicker, et200 Hz and increases to about 900 Hz for frequencies around 5000 Hertz. It is al.suggested that this corresponds to a roughly constant length on the basilarmembrane of length about 1.2 mm and involving some 1300 hair cells. If thetones are far apart in frequency (not within a critical band), the combinedsound may be perceived as twice as loud as one alone. Illustration of critical band Go BackHyperPhysics***** Sound R Nave
26. 26. Critical Band MeasurementFor low frequencies the critical band is about 90 Hz wide. For higherfrequencies, it is between a whole tone and 1/3 octave wide. Index Center Critical Freq (Hz) bandwidth (Hz) Hearing 100 90 concepts 200 90 Reference 500 110 Rossing, Science of 1000 150 Sound 2000 280 5000 700 10000 1200 Rossing 2nd Ed p74 Go BackHyperPhysics***** Sound R Nave Pure Tone Audiometry IndexThe testing of hearing is most often carried out by establishing the threshold ofhearing, the softest sound which can be perceived in a controlled environment. HearingIt is typical to do this testing with pure tones by providing calibrated tones to a conceptsperson via earphones, allowing that person to increase the level until it can justbe heard. Various strategies are used, but pure tone audiometry with tones Dangersstarting at about 125 Hz and increasing by octaves, half-octaves, or third- of Loudoctaves to about 8000 Hz is typical. Hearing tests of right and left ears are Soundsgenerally done independently. The results of such tests are summarized inaudiograms.
27. 27. Audiograms comparehearing to the normalthreshold of hearing, whichvaries with frequency asillustrated by the hearingcurves. The audiogram isnormalized to the hearingcurve so that a straighthorizontal line at 0 represents Click on illustration for further details.normal hearing. Hearing loss Go BackHyperPhysics***** Sound R Nave Audiogram Showing Presbycusis IndexThe progressive loss of high frequency sensitivity with aging is typical, andis called presbycusis. The loss of the high frequencies can make it difficult to Hearingunderstand speech, since the intelligible differences in speech sounds are conceptsoften in the range above 2000 Hz. ReferencesWhen hearing Nave &aids are used, it Speak up! Quit mumbling! Naveis important to Ch. 18amplify the Older persons may have difficulty understanding speechhigh clearly because of progressive loss of high frequency Backusfrequencies, hearing. Ch. 5since it isuncommon for
28. 28. there to besignificant lossat lowfrequencies.Audiograms areimportant forthe prescribingof hearing aids. R Go BackHyperPhysics***** Sound Nave
29. 29. Audiograms Showing Hearing LossAudiograms can help with the diagnosis of various types of hearingdisorders. Specific geometries of curves are found to be typical ofpresbycusis, and a characteristic notch in the hearing curve may be the Indexsignature of damage by a sudden loud sound like a gunshot or a firecrackerexplosion close to the ear. Hearing concepts References Nave & NaveThe curves are Ch. 18normalized sothat a straight Backushorizontal line Ch. 5represents equalloudness. R Go BackHyperPhysics***** Sound Nave
30. 30. Hearing LossHearing loss is typically described as being conductive, sensorineural, ormixed.Conductive hearing loss refers to an impairment of ones ability to conductairborne sound through the middle ear to the inner ear. Scar tissue orotosclerosis, the abnormal growth of bone within the middle ear, can lead torestricted movement of the ossicles. Recently it has been shown that there canalso be conductive problems with the basilar membrane of the inner ear thatreduce the efficiency of energy transfer to the hair cells (Holt).Sensorineural hearing loss refers to impairment of the sensory unitconsisting of the auditory nerve and the hair cells that excite it. IndexSometimes the distinction between these two types of hearing loss can be Hearingmade with a simple tuning fork test. If the tuning fork cannot be heard when conceptssounded in air, then the base of the tuning fork is placed against the hard bonebehind the ear. If the person can now hear it by conduction through the bone, Dangers ofthen conductive hearing loss is indicated. It in cannot be heard by either air or Loudbone conduction, then sensorineural loss is indicated. Sounds Reference The "power of ten" or logarithmic Holt Hearing Loss nature of hearing response is0 to -15 dB Normal range evident in the fact that a loss in ASHA-16 to -40 dB Minimal loss sensitivity by a factor of 10,000, or -40 decibels, is still at the edge of-26 to -15 dB Mild loss "minimal loss". By the admittedly-41 to -55 dB Moderate loss simplistic "rule of thumb" for loudness, this -40dB sound would-56 to -70 dB Moderate/severe loss still be 1/16 as loud as the 0 dB-71 to -90 dB Severe loss reference. 0 dB in this table represents the normal hearing> -91 dB Profound loss threshold, or 0 dB Hearing Level.American Speech and Hearing The categories of hearing loss areAssociation based on measurements at 500, 1000 and 2000 Hz. Assessment of hearing loss Hearing Aids Go BackHyperPhysics***** Sound R Nave
31. 31. 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 atiny speaker that projects the amplified sound into the ear canal. A typicalmodern hearing aid would employ an electret condenser microphone - smalland rugged with a high signal-to-noise ratio. The frequency range ofapplication is typically 100-10,000 Hz. While some assistance may berendered by bone conduction, this discussion will be limited to hearing aidsthat operate by sounds produced in the air. Wearing Styles IndexITE In-the-ear A basic hearing aid may be called a linear circuit aid, implying that it simply amplifies any ambient sound Hearing Behind-the- that reaches it. It is important for such a hearing aid conceptsBTE ear to contour the amplification to the nature of theITC In-the-canal hearing loss of the individual, which typically means Dangers of amplifying high frequencies more than low Loud Completely frequencies. Presbycusis, the progressive loss of high SoundsCIC in-the-canal frequency hearing with age, often calls for Worn on amplification of high frequencies with little or no References body bass boost. A basic hearing aid may have three HoltBody frequency bands to permit the amplification to be (profound loss) adjusted based on the audiogram. GoldenbergThe next step up in sophistication of the hearing aid would be to employsome kind of audio "compression". Compression implies the adjustment ofthe "gain" or degree of amplification based on the input level, it being apractical fact that louder sounds wouldnt need as much amplification. Thiscompression would reduce the amplification for loud sounds either at themicrophone end or at the speaker end. Some types of compression are called"adaptive compression" in that some logic is used to compress some kindsof 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
32. 32. units monitor incoming sounds and automatically change the gain, outputand frequency response. The K-AMP approach detects and amplifies onlyquiet sounds while leaving louder ones unaltered.Currently under very active development are the digital programmablehearing aids that use a digital signal processor (dsp). They can beprogrammed to more nearly fit the detailed needs of an individual user andopen the door to more sophisticated approaches to assisting the user. Sincethe understanding of human speech is often the highest priority, and sincespeech has identifiable characteristics like vocal formants, some steps canbe made to program the hearing aid to amplify speech sounds more thansome distinctly different other types of sounds. A friend with a digitalhearing aid told me something like "I leaned over an expressway bridge andlistened to the traffic noise. After a short time there was a kind of burblingsound like the hearing aid was trying to make voices out of this sound." Anintriguing idea, that we might get enough sophistication into hearing aids torecognize and selectively amplify the sounds of meaningful humancommunication.Another approach to hearing assistance is the cochlear implant. Currentlyvery expensive and in the experimental stage, it is one of the futurepossibilities.(Tal Berkowitz is acknowledged for investigative work on this topic.) Assessment of hearing loss R Go BackHyperPhysics***** Sound Nave
33. 33. Sensitivity of Human EarThe human ear can respond to minute pressure variations in the air if they are inthe audible frequency range, roughly 20 Hz - 20 kHz. Index Hearing conceptsIt is capable of detecting pressure variations of less than one billionth ofatmospheric pressure. The threshold of hearing corresponds to air vibrations onthe order of a tenth of an atomic diameter. This incredible sensitivity isenhanced by an effective amplification of the sound signal by the outer andmiddle ear structures. Contributing to the wide dynamic range of human hearingare protective mechanisms that reduce the ears response to very loud sounds.Sound intensities over this wide range are usually expressed in decibels. Go BackHyperPhysics***** Sound R Nave
34. 34. Dynamic Range of HearingIn addition to its remarkable sensitivity, the human ear is capable ofresponding to the widest range of stimuli of any of the senses. The practicaldynamic range could be said to be from the threshold of hearing to thethreshold of pain: Threshold of Threshold of Pain Index Hearing Hearing I0 1013I0 = 10,000,000,000,000 I0 concepts 0 decibels 130 decibelsThis remarkable dynamic range is enhanced by an effective amplificationstructure which extends its low end and by a protective mechanism whichextends the high end. Dynamic levels of music Go BackHyperPhysics***** Sound R Nave
35. 35. Pitch ResolutionThe extremely small size of the cochlea and theextremely high resolution of human pitchperception cast doubt on the sufficiency of theplace theory to completely account for the humanears pitch resolution. Some typical data: Index turns, Hearing conceptsCochlea: about 3.2 cm length. Resolves about 1500 separate pitches Place with 16,000-20,000 hair cells. theory conceptsThis would require a separate detectable pitch for every 0.002 cm, which isphysically 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 ofthe membrane vibrations. Some pitch sharpening mechanism must beoperating. Go BackHyperPhysics***** Sound R Nave
36. 36. The structures of the outer and middle ear contribute to both the remarkablesensitivity and the wide dynamic range of human hearing. They can beconsidered to be both a pre-amplifier and a limiter for the human hearingprocess.The outer ear(pinna) collectsmore soundenergy than theear canal Indexwould receivewithout it and Hearingthus conceptscontributessome area Referenceamplification. Stevens & Warshofsky Tympanic Closed tube Ossicles (hammer, membraneThe numbers resonance of (eardrum) has some anvil and stirrup)here are just the auditory contribute a lever- 15x area of ovalrepresentative . canal window type amplification.. not precise enhances contributing an area when listening todata. 2000-5000 Hz soft sounds. amplification. Tympanic Outer ear Ossicles membrane 2x 3x 15xThe outer and middle ears contribute something like a factor of 100 or about20 decibels of amplification under optimum conditions. R Go BackHyperPhysics***** Sound Nave
37. 37. Audible SoundUsually "sound" is used to mean sound which can be perceived by the humanear, i.e., "sound" refers to audible sound unless otherwise classified. Areasonably standard definition of audible sound is that it is a pressure wavewith frequency between 20 Hz and 20,000 Hz and with an intensity above thestandard threshold of hearing. Since the ear is surrounded by air, or perhapsunder water, the sound waves are constrained to be longitudinal waves.Normal ranges of sound pressure and sound intensity may also be specified. Index Frequency: 20 Hz - 20,000 Hz (corresponds with pitch) Hearing concepts Intensity: 10-12 - 10 watts/m2 (0 to 130 decibels) Pressure: 2 x 10-5 - 60 Newtons/m2 2 x 10-10 - .0006 atmospheresFor an air temperature of 20°C where the sound speed is 344 m/s, the audiblesound waves have wavelengths from 0.0172 m (0.68 inches) to 17.2 meters(56.4 feet). Ultrasonic sound Go BackHyperPhysics***** Sound R Nave
38. 38. Index Hearing concepts Reference Stevens & Warshofsky DeBonis &In response to sustained loud sounds, muscle tension tightens the tympanic Donohuemembrane and, acting through the tendon connecting the hammer and anvil,repositions the ossicles to pull the stirrup back, lessening the transfer of force tothe oval window of the inner ear. This contributes to the ears wide dynamicrange.The stapedius muscle and the tensor tympani muscle act in response to loudsounds.(DeBonis & Donohue) More detail HyperPhysics***** Sound Go Back
39. 39. Loud Sound ResponseIn response to loudsounds, the tensortympani muscletightens the eardrumand through thetendon between thehammer and anvil and Indexshifts the stirrupbackward from the Hearingoval window of the conceptsinner ear. This shiftingof the ossicles reduces Referencethe transmitted force Stevens &to the inner ear, Warshofskyprotecting it.However, it is arelatively slow actionand cannot protect theear from sudden loudsounds like a gunshot.The process is lesseffective in older ears. Dynamic levels of music HyperPhysics***** Sound Go Back
40. 40. Young and Old EarsA young persons earcan provide a limitedamount of protectionfrom sustained loudsounds by shifting thestirrup backward sothat it doesnt exert as Indexmuch force on the ovalwindow. In the very Hearingyoung, the stirrup is conceptsthought to be capableof actually breaking Referencecontact with the oval Stevens &window, breaking the Warshofskydirect link to the innerear. In an older ear,the structures becomestiffer and cannotadjust backward asmuch. Older personsare generally lesstolerant of loudsounds. HyperPhysics***** Sound Go Back
41. 41. Index Hearing concepts Reference Stevens & Warshofsky DeBonis &In response to sustained loud sounds, muscle tension tightens the tympanic Donohuemembrane and, acting through the tendon connecting the hammer and anvil,repositions the ossicles to pull the stirrup back, lessening the transfer of force tothe oval window of the inner ear. This contributes to the ears wide dynamicrange.The stapedius muscle and the tensor tympani muscle act in response to loudsounds.(DeBonis & Donohue) More detail HyperPhysics***** Sound Go Back
42. 42. Loud Sound ResponseIn response to loudsounds, the tensortympani muscletightens the eardrumand through thetendon between thehammer and anvil and Indexshifts the stirrupbackward from the Hearingoval window of the conceptsinner ear. This shiftingof the ossicles reduces Referencethe transmitted force Stevens &to the inner ear, Warshofskyprotecting it.However, it is arelatively slow actionand cannot protect theear from sudden loudsounds like a gunshot.The process is lesseffective in older ears. Dynamic levels of music HyperPhysics***** Sound Go Back
43. 43. Young and Old EarsA young persons earcan provide a limitedamount of protectionfrom sustained loudsounds by shifting thestirrup backward sothat it doesnt exert as Indexmuch force on the ovalwindow. In the very Hearingyoung, the stirrup is conceptsthought to be capableof actually breaking Referencecontact with the oval Stevens &window, breaking the Warshofskydirect link to the innerear. In an older ear,the structures becomestiffer and cannotadjust backward asmuch. Older personsare generally lesstolerant of loudsounds. HyperPhysics***** Sound Go Back
44. 44. Spectral ColorsIn a rainbow or the separation of colors by a prism we see the continuousrange of spectral colors (the visible spectrum). A spectral color is composed ofa single wavelength and can be correlated with wavelength as shown in the Indexchart below ( a general guide and not a precise statement about color). It is safeenough to say that monochromatic light like the helium-neon laser is red (632 Visionnm) or that the 3-2 transition from the hydrogen spectrum is red ( 656 nm) conceptsbecause they fall in the appropriate wavelength range. But most coloredobjects give off a range of wavelengths and the characterization of color is Colormuch more than the statement of wavelength. Perceived colors can be mapped visionon a chromaticity diagram. Visible spectrum Go BackHyperPhysics***** Light and Vision R Nave
45. 45. ColorIt is common practice to define pure colors in terms of the wavelengths of lightas shown. This works well for spectral colors but it is found that manydifferent combinations of light wavelengths can produce the same perceptionof color.This progression from left to right is from long wavelength to shortwavelength, and from low frequency to high frequency light. The wavelengthsare commonly expressed in nanometers (1 nm = 10-9 m). The visible spectrumis roughly from 700 nm (red end) to 400 nm (violet end). The letter I in the Indexsequence above is for indigo - no longer commonly used as a color name. It isincluded above strictly for the reason of making the sequence easier to say as a Visionmnemonic, like a persons name: Roy G. Biv - a tradition in the discussion of conceptscolor. ColorThe inherently distinguishable characteristics of color are hue, saturation, and visionbrightness. Color measurement systems characterize colors in variousparameters which relate to hue, saturation, and brightness. They include the Visiblesubjective Munsell and Ostwald systems and the quantitative CIE color spectrumsystem.White light, or nearly white light from the Sun, contains a continuousdistribution of wavelengths. The light from the Sun is essentially that of ablackbody radiator at 5780 K. The wavelengths (spectral colors) of white lightcan be separated by a dispersive medium like a prism. Even more effectiveseparation can be achieved with a diffraction grating. Go Back
46. 46. HyperPhysics***** Light and Vision R Nave Refraction of LightRefraction is the bending of a wave when it enters a medium where its speedis different. The refraction of light when it passes from a fast medium to aslow medium bends the light ray toward the normal to the boundary betweenthe two media. The amount of bending depends on the indices of refraction ofthe two media and is described quantitatively by Snells Law.Refraction isresponsible for Indeximage Lensformation by conceptslenses and theeye.As the speed of light is reduced in the slower medium, the wavelength isshortened proportionately. The frequency is unchanged; it is a characteristic ofthe source of the light and unaffected by medium changes. Refraction and the eye Refraction of sound Refraction of light by water Go BackHyperPhysics***** Light and Vision R Nave
47. 47. Index of RefractionThe index of refraction is defined as the speed of light in vacuum divided bythe speed of light in the medium. IndexThe indices of refraction of some common substances are given below with a Lensmore complete description of the indices for optical glasses given elsewhere. conceptsThe values given are approximate and do not account for the small variation ofindex with light wavelength which is called dispersion. Refraction and the eye Refraction of sound Table of refractive indices Go BackHyperPhysics***** Light and Vision R Nave
48. 48. Snells LawSnells Law relates the indices of refraction n of the two media to thedirections of propagation in terms of the angles to the normal. Snells law canbe derived from Fermats Principle or from the Fresnel Equations. Enter data below, then click the symbol of the quantity you wish to calculate. Index Indices of refraction: Angles with surface normal: Lens concepts = = ° = = °Enter data and then click on the symbol for the quantity you wish to calculatein the active equation above. The numbers will not be forced to be consistentuntil you click on the quantity to calculate. Indices of refraction must begreater than or equal to 1, so values less than 1 do not represent a physicallypossible system.If the incident medium has the larger index of refraction, then the angle withthe normal is increased by refraction. The larger index medium is commonlycalled the "internal" medium, since air with n=1 is usually the surrounding or"external" medium. You can calculate the condition for total internal reflectionby setting the refracted angle = 90° and calculating the incident angle. Sinceyou cant refract the light by more than 90°, all of it will reflect for angles ofincidence greater than the angle which gives refraction at 90°. Go BackHyperPhysics***** Light and Vision R Nave
49. 49. Heat TransferThe transfer of heat is normally from a high temperature object to a lowertemperature object. Heat transfer changes the internal energy of both systemsinvolved according to the First Law of Thermodynamics. Index Heat transfer from a cold to a hotter region Radiation cooling time Go BackHyperPhysics***** Thermodynamics R Nave
50. 50. Heat ConductionConduction is heat transfer by means of molecular agitation within a materialwithout any motion of the material as a whole. If one end of a metal rod is at ahigher temperature, then energy will be transferred down the rod toward thecolder end because the higher speed particles will collide with the slower oneswith a net transfer of energy to the slower ones. For heat transfer between twoplane surfaces, such as heat loss through the wall of a house, the rate ofconduction heat transfer is: Index Heat Calculation transfer concepts = heat transferred in time = Heat = thermal conductivity of the barrier transfer examples = area = temperature = thickness of barrier Thermal conductivity table Discussion of thermal conductivity Home heat loss by conduction. Go BackHyperPhysics***** Thermodynamics R Nave
51. 51. Heat ConvectionConvection is heat transfer by mass motion of a fluid such as air or waterwhen 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 airexpands, becomes less dense, and rises (see Ideal Gas Law). Hot water islikewise less dense than cold water and rises, causing convection currentswhich transport energy. Index Heat transfer concepts Convection can also lead to circulation in a liquid, as in Heat the heating of a pot of water transfer over a flame. Heated water examples 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.
52. 52. Convection is thought to play amajor role in transporting energyfrom the center of the Sun to thesurface, and in movements of thehot magma beneath the surface ofthe earth. The visible surface ofthe Sun (the photosphere) has agranular appearance with atypical dimension of a granulebeing 1000 kilometers. Theimage at right is from the NASASolar Physics website and iscredited to G. Scharmer and theSwedish Vacuum SolarTelescope. The granules aredescribed as convection cellswhich transport heat from theinterior of the Sun to the surface.In ordinary heat transfer on the Earth, it is difficult to quantify the effects ofconvection since it inherently depends upon small nonuniformities in anotherwise fairly homogeneous medium. In modeling things like the cooling ofthe human body, we usually just lump it in with conduction. Go BackHyperPhysics***** Thermodynamics R Nave
53. 53. Greenhouse EffectThe greenhouse effect refers to circumstances where the short wavelengths ofvisible light from the sun pass through a transparent medium and are absorbed,but the longer wavelengths of the infrared re-radiation from the heated objectsare unable to pass through that medium. The trapping of the long wavelengthradiation leads to more heating and a higher resultant temperature. Besides theheating of an automobile by sunlight through the windshield and the namesakeexample of heating the greenhouse by sunlight passing through sealed,transparent windows, the greenhouse effect has been widely used to describethe trapping of excess heat by the rising concentration of carbon dioxide in theatmosphere. The carbon dioxide strongly absorbs infrared and does not allowas much of it to escape into space. IndexSunlight warms yourcarIncreasing atmosphericcarbon dioxideGlobal warmingRole in the absence ofwater on Venus?A major part of the efficiency of the heating of an actual greenhouse is thetrapping of the air so that the energy is not lost by convection. Keeping the hotair from escaping out the top is part of the practical "greenhouse effect", but itis common usage to refer to the infrared trapping as the "greenhouse effect" inatmospheric applications where the air trapping is not applicable. Go BackHyperPhysics***** Thermodynamics R Nave
54. 54. Greenhouse Effect ExampleBright sunlight will effectively warm your car on a cold, clear day by thegreenhouse effect. The longer infrared wavelengths radiated by sun-warmedobjects do not pass readily through the glass. The entrapment of this energywarms the interior of the vehicle. The trapping of the hot air so that it cannotrise and lose the energy by convection also plays a major role. Short wavelengths Index of visible light are readily transmitted Blackbody through the radiation transparent concepts windshield. (Otherwise you wouldnt be able to see through it!)Shorter wavelengths of ultraviolet light are largely blocked by glass sincethey have greater quantum energies which have absorption mechanisms inthe glass. Even though you may be uncomfortably warm with bright sunlightstreaming through, you will not be sunburned. R Go BackHyperPhysics***** Thermodynamics Nave
55. 55. Increase in Greenhouse GasesThe increase in the concentration of carbon dioxide, one of the three majoratmospheric contributers to the greenhouse effect has been carefullydocumented at the Mauna Loa Observatory in Hawaii. The 1990 rate of increasewas about 0.4% per year. The interesting cyclic variations represent thereduction in carbon dioxide by photosynthesis during the growing season in thenorthern hemisphere.Current analysis suggests that the combustion of fossil fuels is a majorcontributer to the increase in the carbon dioxide concentration, suchcontributions being 2 to 5 times the effect of deforestation (Kraushaar &Ristinen). Increase in Atmospheric Carbon Dioxide Index References Kraushaar & Ristinen TrefilThe Mauna Loa monitoring station reports the carbon dioxide level in theatmosphere today as about 380 parts per million compared to 315 ppm in 1958when modern measurements were initiated. Measurements of air bubblestrapped in the Greenland ice sheet indicate concentrations of 270 ppm inpreindustrial times.
56. 56. 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 . Go BackHyperPhysics***** Thermodynamics R Nave
57. 57. Contributers to Greenhouse EffectThose gas molecules in the Earths atmosphere with three or more atoms arecalled "greenhouse gases" because they can capture outgoing infrared energyfrom the Earth, thereby warming the planet. The greenhouse gases includewater vapor with three atoms (H2O), ozone (O3), carbon dioxide (CO2), andmethane (CH4). Also, trace quantities of chloro-fluoro-carbons (CFCs) canhave a disproportionately large effect. Index Reference Kraushaar & RistinenTo attempt to quantify the effects of greenhouse gases on the globaltemperature, climatologists use the "radiative forcing" of the currentatmospheric content of these gases. Increase in greenhouse gases Greenhouse effect R Go BackHyperPhysics***** Thermodynamics Nave
58. 58. Global WarmingAn issue of major concern is the possible effect of the burning of fossil fuelsand other contributers to the increase of carbon dioxide in the atmosphere. Theaction of carbon dioxide and other greenhouse gases in trapping infraredradiation is called the greenhouse effect. It may measurably increase the overallaverage temperature of the Earth, which could have disastrous consequences.Sometimes the effects of the greenhouse effect are stated in terms of the albedoof the Earth, the overall average reflection coefficient. Index References Kraushaar & Ristinen Brohan, et al. SchneiderThis graphic of the global air temperature was posted by Phil Jones on behalf ofthe Climatic Research Unit, UK. The key reference used was Brohan, et al.Another depiction of the mean temperatures in the northern hemisphere wasdrawn from NOAA.
59. 59. Essentially any kind of tabulation you access will tell the same story. Thetemperature has gradually risen over the last 150 years.Because the potential consequences of global warming in terms of loss of snowcover, sea level rise, change in weather patterns, etc are so great, it is a majorsocietal concern. On the other hand, proposed measures to reduce humancontributions to greenhouse gases can also have great consequences. The largepotential impact combined with the ambiguities of the science has given rise tomany passionate extremes.Stephen Schneider of Stanford seems to me to be one of the more balanced
60. 60. voices. His website is a good source for relevant data. He discusses theproblems in the context of the Earths energy balance and the changes in theconcentrations 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 Go BackHyperPhysics***** Thermodynamics R Nave