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I.S.T :

"Creativity requires the courage to let go of certainties.." - Erich Fromm

Educational Material

Biology

SPLEEN More...

The spleen is an organ found in virtually all vertebrate animals with important roles in regard to red blood cells and the immune system.^[1] In humans, it is located in the left upper quadrant of the abdomen. It removes old red blood cells and holds a reserve in case of hemorrhagic shock, especially in animals like horses (not in humans), while recycling iron.^[2] It synthesizes antibodies in its white pulp and removes, from blood and lymph node circulation, antibody-coated bacteria along with antibody-coated blood cells.^[2]^[3] Recently, it has been found to contain, in its reserve, half of the body's monocytes, within the red pulp, that, upon moving to injured tissue (such as the heart), turns into dendritic cells and macrophages while aiding "wound healing", or the healing of lacerations.^[4]^[5]^[6] It is one of the centers of activity of the reticuloendothelial system and can be considered analogous to a large lymph node as its absence leads to a predisposition toward certain infections.

Anatomy

The spleen, in healthy adult humans, is approximately 11 centimetres (4.3 in) in length. It usually weighs 150 grams (5.3 oz) and lies beneath the 9th to the 12th thoracic ribs.^[8]

Like the thymus, the spleen possesses only efferent lymphatic vessels.

The spleen is part of the lymphatic system.

The germinal centers are supplied by arterioles called penicilliary radicles.^[9]

The spleen is unique in respect to its development within the gut. While most of the gut viscera are endodermally derived (with the exception of the neural-crest derived suprarenal gland), the spleen is derived from mesenchymal tissue.^[10] Specifically, the spleen forms within, and from, the dorsal mesentery. However, it still shares the same blood supply — the celiac trunk — as the foregut organs.

Function

Area	Function	Composition
red pulp	Mechanical filtration of red blood cells. Reserve of monocytes^[4]	"sinuses" (or "sinusoids") which are filled with blood "splenic cords" of reticular fibers "marginal zone" bordering on white pulp
white pulp	Active immune response through humoral and cell-mediated pathways.	Composed of nodules, called Malpighian corpuscles. These are composed of: "lymphoid follicles" (or "follicles"), rich in B-lymphocytes "periarteriolar lymphoid sheaths" (PALS), rich in T-lymphocytes

Other functions of the spleen are less prominent, especially in the healthy adult:

Production of opsonins, properdin, and tuftsin.

Creation of red blood cells. While the bone marrow is the primary site of hematopoeisis in the adult, the spleen has important hematopoietic functions up until the fifth month of gestation. After birth, erythropoietic functions cease, except in some hematologic disorders. As a major lymphoid organ and a central player in the reticuloendothelial system, the spleen retains the ability to produce lymphocytes and, as such, remains an hematopoietic organ.

Storage of red blood cells and other formed elements. In horses roughly 30% of the red blood cells are stored there. The red blood cells can be released when needed.^[11] In humans, it does not act as a reservoir of blood cells.^[12] It can also store platelets in case of an emergency.

Storage of half the body's monocytes so that upon injury they can migrate to the injured tissue and transform into dendritic cells and macrophages and so assist wound healing.^[4]

Effect of removal

Surgical removal causes:^[5]

modest increases in circulating white blood cells and platelets,
diminished responsiveness to some vaccines,
increased susceptibility to infection by bacteria and protozoa

A 28-year follow up of 740 veterans of World War II, found that those who had been splenectomised showed a significant excess of mortality from pneumonia (6 from an expected 1.3) and a significant excess of mortality from ischaemic heart disease (4.1 from an expected 3) but not from other conditions.^[13]

Disorders

Disorders include splenomegaly, where the spleen is enlarged for various reasons, and asplenia, where the spleen is not present or functions abnormally.

Etymology and cultural views

The word spleen comes from the Greek σπλήν, and is the idiomatic equivalent of the heart in English, i.e. to be good-spleened (εὔσπλαγχνος) means to be good-hearted or compassionate.^[14]

In French, "splénétique" refers to a state of pensive sadness or melancholy. It has been popularized by the poet Charles Baudelaire (1821–1867) but was already used before in particular to the Romantic literature (18th century). The word for the organ is "la rate."

The connection between spleen (the organ) and melancholy (the temperament) comes from the humoral medicine of the ancient Greeks. One of the humours (body fluid) was the black bile, secreted by the spleen organ and associated with melancholy. In contrast, the Talmud (tractate Berachoth 61b) refers to the spleen as the organ of laughter while possibly suggesting a link with the humoral view of the organ. In the eighteenth- and nineteenth-century England, women in bad humour were said to be afflicted by the spleen, or the vapours of the spleen. In modern English, "to vent one's spleen" means to vent one's anger, e.g. by shouting, and can be applied to both males and females. Similarly, the English term "splenetic" is used to describe a person in a foul mood.

In Chinese, the spleen '脾 (pí)' counts as the seat of one's temperament and is thought to influence the individual's willpower. Analogous to "venting one's spleen," "發脾氣" is used as an expression for getting angry, although in the view of Traditional Chinese Medicine, the view of "脾" does not correspond to the anatomical "spleen." "脾" is a conceptual functional group that mainly has regards to digestion which, in some scholars' opinions, corresponds to the function of the liver.

Variation among vertebrates

In cartilagenous and ray-finned fish the spleen is normally a somewhat elongated organ, consisting primarily of red pulp, with only a small amount of white pulp. In lungfish, the spleen is not a distinct organ as it actually lies inside the serosal lining of the intestine. In many amphibians, especially frogs, it takes on the more rounded form and there is often a greater quantity of white pulp.^[15]

In reptiles, birds, and mammals, white pulp is always relatively plentiful, and in the latter two groups, the spleen is typically rounded, although it adjusts its shape somewhat to the arrangement of the surrounding organs. In the great majority of vertebrates, the spleen continues to produce red blood cells throughout life; it is only in mammals that this function is lost in the adult. Many mammals possess tiny spleen-like structures known as haemal nodes throughout the body, which presumably have the same function as the spleen proper.^[15]

The only vertebrates lacking a spleen are the lampreys and hagfishes. Even in these animals, there is a diffuse layer of haematopoeitic tissue within the gut wall, which has a similar structure to red pulp, and is presumably homologous with the spleen of higher vertebrates.

Physics

DIPOLES More...

In physics, there are two kinds of dipoles:

An electric dipole is a separation of positive and negative charges. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some (usually small) distance. A permanent electric dipole is called an electret.
A magnetic dipole is a closed circulation of electric current. A simple example of this is a single loop of wire with some constant current flowing through it.^[1]^[2]

Dipoles can be characterized by their dipole moment, a vector quantity. For the simple electric dipole given above, the electric dipole moment would point from the negative charge towards the positive charge, and have a magnitude equal to the strength of each charge times the separation between the charges. For the current loop, the magnetic dipole moment would point through the loop (according to the right hand grip rule), with a magnitude equal to the current in the loop times the area of the loop.

In addition to current loops, the electron, among other fundamental particles, is said to have a magnetic dipole moment. This is because it generates a magnetic field that is identical to that generated by a very small current loop. However, to the best of our knowledge, the electron's magnetic moment is not due to a current loop, but is instead an intrinsic property of the electron. It is also possible that the electron has an electric dipole moment, although this has not yet been observed (see electron electric dipole moment for more information).

Contour plot of an electrical dipole, with equipotential surfaces indicated

A permanent magnet, such as a bar magnet, owes its magnetism to the intrinsic magnetic dipole moment of the electron. The two ends of a bar magnet are referred to as poles (not to be confused with monopoles), and are labeled "north" and "south." The dipole moment of the bar magnet points from its magnetic south to its magnetic north pole. What can be confusing is that the "north" and "south" convention for magnetic dipoles is the opposite of that used to describe Earth's geographic and magnetic poles, so that Earth's geomagnetic north pole is the south pole of its dipole moment. (This should not be difficult to remember; it simply means that the north pole of a bar magnet is the one that points north if used as a compass.)

The only known mechanisms for the creation of magnetic dipoles are by current loops or quantum-mechanical spin since the existence of magnetic monopoles has never been experimentally demonstrated.

Classification

Electric dipole field lines

Magnetic dipole field lines

A physical dipole consists of two equal and opposite point charges: in the literal sense, two poles. Its field at large distances (i.e., distances large in comparison to the separation of the poles) depends almost entirely on the dipole moment as defined above. A point (electric) dipole is the limit obtained by letting the separation tend to 0 while keeping the dipole moment fixed. The field of a point dipole has a particularly simple form, and the order-1 term in the multipole expansion is precisely the point dipole field.

Although there are no known magnetic monopoles in nature, there are magnetic dipoles in the form of the quantum-mechanical spin associated with particles such as electrons (although the accurate description of such effects falls outside of classical electromagnetism). A theoretical magnetic point dipole has a magnetic field of the exact same form as the electric field of an electric point dipole. A very small current-carrying loop is approximately a magnetic point dipole; the magnetic dipole moment of such a loop is the product of the current flowing in the loop and the (vector) area of the loop.

Any configuration of charges or currents has a 'dipole moment', which describes the dipole whose field is the best approximation, at large distances, to that of the given configuration. This is simply one term in the multipole expansion when the charge ("monopole moment") is 0 — as it always is for the magnetic case, since there are no magnetic monopoles. The dipole term is the dominant one at large distances: Its field falls off in proportion to 1/r³, as compared to 1/r⁴ for the next (quadrupole) term and higher powers of 1/r for higher terms, or 1/r² for the monopole term.

Molecular dipoles

Many molecules have such dipole moments due to non-uniform distributions of positive and negative charges on the various atoms. Such is the case with polar compounds like hydroxide (OH⁻), where electron density is shared unequally between atoms.

A molecule with a permanent dipole moment is called a polar molecule. A molecule is polarized when it carries an induced dipole. The physical chemist Peter J. W. Debye was the first scientist to study molecular dipoles extensively, and, as a consequence, dipole moments are measured in units named debye in his honor.

With respect to molecules, there are three types of dipoles:

Permanent dipoles: These occur when two atoms in a molecule have substantially different electronegativity: One atom attracts electrons more than another, becoming more negative, while the other atom becomes more positive. See dipole-dipole attractions.
Instantaneous dipoles: These occur due to chance when electrons happen to be more concentrated in one place than another in a molecule, creating a temporary dipole. See instantaneous dipole.
Induced dipoles: These can occur when one molecule with a permanent dipole repels another molecule's electrons, "inducing" a dipole moment in that molecule. See induced-dipole attraction.

More generally, an induced dipole of any polarizable charge distribution ρ (remember that a molecule has a charge distribution) is caused by an electric field external to ρ. This field may, for instance, originate from an ion or polar molecule in the vicinity of ρ or may be macroscopic (e.g., a molecule between the plates of a charged capacitor). The size of the induced dipole is equal to the product of the strength of the external field and the dipole polarizability of ρ.

Typical gas phase values of some chemical compounds in debye units:^[3]

carbon dioxide: 0
carbon monoxide: 0.112
ozone: 0.53
phosgene: 1.17
water vapor: 1.85
hydrogen cyanide: 2.98
cyanamide: 4.27
potassium bromide: 10.41

These values can be obtained from measurement of the dielectric constant. When the symmetry of a molecule cancels out a net dipole moment, the value is set at 0. The highest dipole moments are in the range of 10 to 11. From the dipole moment information can be deduced about the molecular geometry of the molecule. For example the data illustrate that carbon dioxide is a linear molecule but ozone is not.

Quantum mechanical dipole operator

Consider a collection of N particles with charges q_i and position vectors r_i. For instance, this collection may be a molecule consisting of electrons, all with charge −e, and nuclei with charge eZ_i, where Z_i is the atomic number of the i^th nucleus. The physical quantity (observable) dipole has the quantum mechanical operator:

$\mathfrak{p} = \sum_{i=1}^N \, q_i \, \mathbf{r}_i \, .$

Atomic dipoles

A non-degenerate (S-state) atom can have only a zero permanent dipole. This fact follows quantum mechanically from the inversion symmetry of atoms. All 3 components of the dipole operator are antisymmetric under inversion with respect to the nucleus,

$\mathfrak{I} \;\mathfrak{p}\; \mathfrak{I}^{-1} = - \mathfrak{p},$

where $\stackrel{\mathfrak{p}}{}$ is the dipole operator and $\stackrel{\mathfrak{I}}{}\,$ is the inversion operator. The permanent dipole moment of an atom in a non-degenerate state (see degenerate energy level) is given as the expectation (average) value of the dipole operator,

$\langle \mathfrak{p} \rangle = \langle\, S\, | \mathfrak{p} |\, S \,\rangle,$

where $|\, S\, \rangle$ is an S-state, non-degenerate, wavefunction, which is symmetric or antisymmetric under inversion: $\mathfrak{I}\,|\, S\, \rangle= \pm |\, S\, \rangle$ . Since the product of the wavefunction (in the ket) and its complex conjugate (in the bra) is always symmetric under inversion and its inverse,

$\langle \mathfrak{p} \rangle = \langle\, \mathfrak{I}^{-1}\, S\, | \mathfrak{p} |\, \mathfrak{I}^{-1}\, S \,\rangle = \langle\, S\, | \mathfrak{I}\, \mathfrak{p} \, \mathfrak{I}^{-1}| \, S \,\rangle = -\langle \mathfrak{p} \rangle$

it follows that the expectation value changes sign under inversion. We used here the fact that $\mathfrak{I}\,$ , being a symmetry operator, is unitary: $\mathfrak{I}^{-1} = \mathfrak{I}^{*}\,$ and by definition the Hermitian adjoint $\mathfrak{I}^*\,$ may be moved from bra to ket and then becomes $\mathfrak{I}^{**} = \mathfrak{I}\,$ . Since the only quantity that is equal to minus itself is the zero, the expectation value vanishes,

$\langle \mathfrak{p}\rangle = 0.$

In the case of open-shell atoms with degenerate energy levels, one could define a dipole moment by the aid of the first-order Stark effect. This gives a non-vanishing dipole (by definition proportional to a non-vanishing first-order Stark shift) only if some of the wavefunctions belonging to the degenerate energies have opposite parity; i.e., have different behavior under inversion. This is a rare occurrence, but happens for the excited H-atom, where 2s and 2p states are "accidentally" degenerate (see this article for the origin of this degeneracy) and have opposite parity (2s is even and 2p is odd).

Field from a magnetic dipole

See also: Magnet#Two models for magnets: magnetic poles and atomic currents

Magnitude

The far-field strength, B, of a dipole magnetic field is given by

$B(m, r, \lambda) = \frac {\mu_0} {4\pi} \frac {m} {r^3} \sqrt {1+3\sin^2\lambda} \, ,$

where

B is the strength of the field, measured in teslas

r is the distance from the center, measured in metres

λ is the magnetic latitude (equal to 90° − θ) where θ is the magnetic colatitude, measured in radians or degrees from the dipole axis^{[note 1]}

m is the dipole moment (VADM=virtual axial dipole moment), measured in ampere square-metres (A·m²), which equals joules per tesla

μ₀ is the permeability of free space, measured in henries per metre.

Conversion to cylindrical coordinates is achieved using r² = z² + ρ² and

$\lambda = \arcsin\left(\frac{z}{\sqrt{z^2+\rho^2}}\right)$

where ρ is the perpendicular distance from the z-axis. Then,

$B(\rho,z) = \frac{\mu_0 m}{4 \pi (z^2+\rho^2)^{3/2}} \sqrt{1+\frac{3 z^2}{z^2 + \rho^2}}$

Vector form

The field itself is a vector quantity:

$\mathbf{B}(\mathbf{m}, \mathbf{r}) = \frac {\mu_0} {4\pi r^3} \left(3(\mathbf{m}\cdot\hat{\mathbf{r}})\hat{\mathbf{r}}-\mathbf{m}\right) + \frac{2\mu_0}{3}\mathbf{m}\delta^3(\mathbf{r})$

where

B is the field

r is the vector from the position of the dipole to the position where the field is being measured

r is the absolute value of r: the distance from the dipole

$\hat{\mathbf{r}} = \mathbf{r}/r$ is the unit vector parallel to r;

m is the (vector) dipole moment

μ₀ is the permeability of free space

δ³ is the three-dimensional delta function.^{[note 2]}

This is exactly the field of a point dipole, exactly the dipole term in the multipole expansion of an arbitrary field, and approximately the field of any dipole-like configuration at large distances.

Magnetic vector potential

The vector potential A of a magnetic dipole is

$\mathbf{A}(\mathbf{r}) = \frac {\mu_0} {4\pi r^2} (\mathbf{m}\times\hat{\mathbf{r}})$

with the same definitions as above.

Field from an electric dipole

The electrostatic potential at position r due to an electric dipole at the origin is given by:

$\Phi(\mathbf{r}) = \frac{1}{4\pi\varepsilon_0}\,\frac{\mathbf{p}\cdot\hat{\mathbf{r}}}{r^2}$

where

$\hat{\mathbf{r}}$ is a unit vector in the direction of r', p is the (vector) dipole moment, and ε₀ is the permittivity of free space.

This term appears as the second term in the multipole expansion of an arbitrary electrostatic potential Φ(r). If the source of Φ(r) is a dipole, as it is assumed here, this term is the only non-vanishing term in the multipole expansion of Φ(r). The electric field from a dipole can be found from the gradient of this potential:

$\mathbf{E} = - \nabla \Phi =\frac {1} {4\pi\epsilon_0} \left(\frac{3(\mathbf{p}\cdot\hat{\mathbf{r}})\hat{\mathbf{r}}-\mathbf{p}}{r^3}\right) - \frac{1}{3\epsilon_0}\mathbf{p}\delta^3(\mathbf{r})$

where E is the electric field and δ³ is the 3-dimensional delta function.^{[note 2]} This is formally identical to the magnetic field of a point magnetic dipole; only a few names have changed.

Torque on a dipole

Since the direction of an electric field is defined as the direction of the force on a positive charge, electric field lines point away from a positive charge and toward a negative charge.

When placed in an electric or magnetic field, equal but opposite forces arise on each side of the dipole creating a torque τ:

$\boldsymbol{\tau} = \mathbf{p} \times \mathbf{E}$

for an electric dipole moment p (in coulomb-meters), or

$\boldsymbol{\tau} = \mathbf{m} \times \mathbf{B}$

for a magnetic dipole moment m (in ampere-square meters).

The resulting torque will tend to align the dipole with the applied field, which in the case of an electric dipole, yields a potential energy of

$U = -\mathbf{p} \cdot \mathbf{E}$ .

The energy of a magnetic dipole is similarly

$U = -\mathbf{m} \cdot \mathbf{B}$ .

[edit] Dipole radiation

Real-time evolution of the electric field of an oscillating electric dipole. The dipole is located at (60,60) in the graph, oscillating at 1 Hz in the vertical direction

Perception of sound

Human ear

For humans, hearing is normally limited to frequencies between about 12 Hz and 20,000 Hz (20 kHz)^[2], although these limits are not definite. The upper limit generally decreases with age. Other species have a different range of hearing. For example, dogs can perceive vibrations higher than 20 kHz. As a signal perceived by one of the major senses, sound is used by many species for detecting danger, navigation, predation, and communication. Earth's atmosphere, water, and virtually any physical phenomenon, such as fire, rain, wind, surf, or earthquake, produces (and is characterized by) its unique sounds. Many species, such as frogs, birds, marine and terrestrial mammals, have also developed special organs to produce sound. In some species, these have evolved to produce song and speech. Furthermore, humans have developed culture and technology (such as music, telephone and radio) that allows them to generate, record, transmit, and broadcast sound.

Physics of sound

The mechanical vibrations that can be interpreted as sound are able to travel through all forms of matter: gases, liquids, solids, and plasmas. The matter that supports the sound is called the medium. Sound cannot travel through vacuum.

Longitudinal and transverse waves

Sinusoidal waves of various frequencies; the bottom waves have higher frequencies than those above. The horizontal axis represents time.

Sound is transmitted through gases, plasma, and liquids as longitudinal waves, also called compression waves. Through solids, however, it can be transmitted as both longitudinal and transverse waves. Longitudinal sound waves are waves of alternating pressure deviations from the equilibrium pressure, causing local regions of compression and rarefaction, while transverse waves (in solids) are waves of alternating shear stress at right angle to the direction of propagation.

Matter in the medium is periodically displaced by a sound wave, and thus oscillates. The energy carried by the sound wave converts back and forth between the potential energy of the extra compression (in case of longitudinal waves) or lateral displacement strain (in case of transverse waves) of the matter and the kinetic energy of the oscillations of the medium.

Sound wave properties and characteristics

Sound waves are characterized by the generic properties of waves, which are frequency, wavelength, period, amplitude, intensity, speed, and direction (sometimes speed and direction are combined as a velocity vector, or wavelength and direction are combined as a wave vector).

Transverse waves, also known as shear waves, have an additional property of polarization.

Sound characteristics can depend on the type of sound waves (longitudinal versus transverse) as well as on the physical properties of the transmission medium^{[citation needed]}.

Speed of sound

U.S. Navy F/A-18 breaking the sound barrier. The white halo is formed by condensed water droplets which are thought to result from a drop in air pressure around the aircraft (see Prandtl-Glauert Singularity).^[3]^[4]

The speed of sound depends on the medium through which the waves are passing, and is often quoted as a fundamental property of the material. In general, the speed of sound is proportional to the square root of the ratio of the elastic modulus (stiffness) of the medium to its density. Those physical properties and the speed of sound change with ambient conditions. For example, the speed of sound in gases depends on temperature. In 20 °C (68 °F) air at the sea level, the speed of sound is approximately 343 m/s (1,230 km/h; 767 mph) using the formula "v = (331 + 0.6T) m/s". In fresh water, also at 20 °C, the speed of sound is approximately 1,482 m/s (5,335 km/h; 3,315 mph). In steel, the speed of sound is about 5,960 m/s (21,460 km/h; 13,330 mph).^[5] The speed of sound is also slightly sensitive (a second-order anharmonic effect) to the sound amplitude, which means that there are nonlinear propagation effects, such as the production of harmonics and mixed tones not present in the original sound (see parametric array).

Acoustics and noise

The scientific study of the propagation, absorption, and reflection of sound waves is called acoustics. Noise is a term often used to refer to an unwanted sound. In science and engineering, noise is an undesirable component that obscures a wanted signal.

Sound pressure level

Main article: Sound pressure

Sound measurements
Sound pressure p
Particle velocity v
Particle velocity level (SVL)
(Sound velocity level)
Particle displacement ξ
Sound intensity I
Sound intensity level (SIL)
Sound power P_ac
Sound power level (SPL)
Sound energy density E
Sound energy flux q
Surface S
Acoustic impedance Z
Speed of sound c v • d • e

Sound pressure is defined as the difference between the average local pressure of the medium outside of the sound wave in which it is traveling through (at a given point and a given time) and the pressure found within the sound wave itself within that same medium. A square of this difference (i.e. a square of the deviation from the equilibrium pressure) is usually averaged over time and/or space, and a square root of such average is taken to obtain a root mean square (RMS) value. For example, 1 Pa RMS sound pressure (94 dBSPL) in atmospheric air implies that the actual pressure in the sound wave oscillates between (1 atm $-\sqrt{2}$ Pa) and (1 atm $+\sqrt{2}$ Pa), that is between 101323.6 and 101326.4 Pa. Such a tiny (relative to atmospheric) variation in air pressure at an audio frequency will be perceived as quite a deafening sound, and can cause hearing damage, according to the table below.

As the human ear can detect sounds with a very wide range of amplitudes, sound pressure is often measured as a level on a logarithmic decibel scale. The sound pressure level (SPL) or L_p is defined as

$L_\mathrm{p}=10\, \log_{10}\left(\frac{{p}^2}{{p_\mathrm{ref}}^2}\right) =20\, \log_{10}\left(\frac{p}{p_\mathrm{ref}}\right)\mbox{ dB}$

where p is the root-mean-square sound pressure and

p ref

is a reference sound pressure. Commonly used reference sound pressures, defined in the standard ANSI S1.1-1994, are 20 µPa in air and 1 µPa in water. Without a specified reference sound pressure, a value expressed in decibels cannot represent a sound pressure level.

Since the human ear does not have a flat spectral response, sound pressures are often frequency weighted so that the measured level will match perceived levels more closely. The International Electrotechnical Commission (IEC) has defined several weighting schemes. A-weighting attempts to match the response of the human ear to noise and A-weighted sound pressure levels are labeled dBA. C-weighting is used to measure peak levels.

Examples of sound pressure and sound pressure levels

Source of sound	RMS sound pressure	sound pressure level
Source of sound	Pa	dB re 20 µPa
Theoretical limit for undistorted sound at 1 atmosphere environmental pressure	101,325	191
1883 Krakatoa eruption		approx 180 at 100 miles
Stun grenades		170-180
rocket launch equipment acoustic tests		approx. 165
threshold of pain	100	134
hearing damage during short-term effect	20	approx. 120
jet engine, 100 m distant	6–200	110–140
jackhammer, 1 m distant / discotheque	2	approx. 100
hearing damage from long-term exposure	0.6	approx. 85
traffic noise on major road, 10 m distant	0.2–0.6	80–90
moving automobile, 10 m distant	0.02–0.2	60–80
TV set – typical home level, 1 m distant	0.02	approx. 60
normal talking, 1 m distant	0.002–0.02	40–60
very calm room	0.0002–0.0006	20–30
quiet rustling leaves, calm human breathing	0.00006	10
auditory threshold at 2 kHz – undamaged human ears	0.00002	0

Equipment for dealing with sound

Equipment for generating or using sound includes musical instruments, hearing aids, sonar systems and sound reproduction and broadcasting equipment. Many of these use electro-acoustic transducers such as microphones and loudspeakers

FRICTION More...

Friction is the force resisting the relative lateral (tangential) motion of solid surfaces, fluid layers, or material elements in contact. It is usually subdivided into several varieties:

Dry friction resists relative lateral motion of two solid surfaces in contact. Dry friction is also subdivided into static friction between non-moving surfaces, and kinetic friction (sometimes called sliding friction or dynamic friction) between moving surfaces.

Lubricated friction^[1] or fluid friction^[2]^[3] resists relative lateral motion of two solid surfaces separated by a layer of gas or liquid.

Fluid friction is also used to describe the friction between layers within a fluid that are moving relative to each other.^[4]^[5]

Skin friction is a component of drag, the force resisting the motion of a solid body through a fluid.

Internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation.^[5]

Friction is not a fundamental force, as it is derived from electromagnetic force between charged particles, including electrons, protons, atoms, and molecules, and so cannot be calculated from first principles, but instead must be found empirically. When contacting surfaces move relative to each other, the friction between the two surfaces converts kinetic energy into thermal energy, or heat. Contrary to earlier explanations, kinetic friction is now understood not to be caused by surface roughness but by chemical bonding between the surfaces.^[6] Surface roughness and contact area, however, do affect kinetic friction for micro- and nano-scale objects where surface area forces dominate inertial forces

History

Several famous scientists and engineers contributed to our understanding of friction. They include Leonardo da Vinci, Guillaume Amontons, John Theophilus Desaguliers, Leonard Euler, and Charles-Augustin de Coulomb. Their findings are codified into these laws:^[8]

The force of friction is directly proportional to the applied load. (Amontons' 1st Law)
The force of friction is independent of the apparent area of contact. (Amontons' 2nd Law) (Amontons' 2nd Law does not work for elastic, deformable materials. For example, wider tires on cars provide more traction than narrow tires for a given vehicle mass because of surface deformation of the tire)^{[citation needed]}
Kinetic friction is independent of the sliding velocity. (Coulomb's Law of Friction)

Coulomb friction

Coulomb friction, named after Charles-Augustin de Coulomb, is a model used to calculate the force of dry friction. It is governed by the equation:

$F_\mathrm{f} \leq \mu F_\mathrm{n}$

where

$F_\mathrm{f}\,$ is the force exerted by friction (in the case of equality, the maximum possible magnitude of this force).
$\mu\,$ is the coefficient of friction, which is an empirical property of the contacting materials,
$F_\mathrm{n}\,$ is the normal force exerted between the surfaces.

For surfaces at rest relative to each other $\mu = \mu_\mathrm{s}\,$ , where $\mu_\mathrm{s}\,$ is the coefficient of static friction. This is usually larger than its kinetic counterpart. The Coulomb friction $F_\mathrm{f}\,$ may take any value from zero up to $\mu F_\mathrm{n}\,$ , and the direction of the frictional force against a surface is opposite to the motion that surface would experience in the absence of friction. Thus, in the static case, the frictional force is exactly what it must be in order to prevent motion between the surfaces; it balances the net force tending to cause such motion. In this case, rather than providing an estimate of the actual frictional force, the Coulomb approximation provides a threshold value for this force, above which motion would commence.

For surfaces in relative motion $\mu = \mu_\mathrm{k}\,$ , where $\mu_\mathrm{k}\,$ is the coefficient of kinetic friction. The Coulomb friction is equal to $F_\mathrm{f}\,$ , and the frictional force on each surface is exerted in the direction opposite to its motion relative to the other surface.

This approximation mathematically follows from the assumptions that surfaces are in atomically close contact only over a small fraction of their overall area, that this contact area is proportional to the normal force (until saturation, which takes place when all area is in atomic contact), and that frictional force is proportional to the applied normal force, independently of the contact area (you can see the experiments on friction from Leonardo Da Vinci). Such reasoning aside, however, the approximation is fundamentally an empirical construction. It is a rule of thumb describing the approximate outcome of an extremely complicated physical interaction. The strength of the approximation is its simplicity and versatility – though in general the relationship between normal force and frictional force is not exactly linear (and so the frictional force is not entirely independent of the contact area of the surfaces), the Coulomb approximation is an adequate representation of friction for the analysis of many physical systems.

Coefficient of friction

The coefficient of friction (COF), also known as a frictional coefficient or friction coefficient and symbolized by the Greek letter μ, is a dimensionless scalar value which describes the ratio of the force of friction between two bodies and the force pressing them together. The coefficient of friction depends on the materials used; for example, ice on steel has a low coefficient of friction, while rubber on pavement has a high coefficient of friction. Coefficients of friction range from near zero to greater than one – under good conditions, a tire on concrete may have a coefficient of friction of 1.7.^{[citation needed]}

When the surfaces are conjoined, Coulomb friction becomes a very poor approximation (for example, adhesive tape resists sliding even when there is no normal force, or a negative normal force). In this case, the frictional force may depend strongly on the area of contact. Some drag racing tires are adhesive in this way. However, despite the complexity of the fundamental physics behind friction, the relationships are accurate enough to be useful in many applications.

The force of friction is always exerted in a direction that opposes movement (for kinetic friction) or potential movement (for static friction) between the two surfaces. For example, a curling stone sliding along the ice experiences a kinetic force slowing it down. For an example of potential movement, the drive wheels of an accelerating car experience a frictional force pointing forward; if they did not, the wheels would spin, and the rubber would slide backwards along the pavement. Note that it is not the direction of movement of the vehicle they oppose, it is the direction of (potential) sliding between tire and road.

The coefficient of friction is an empirical measurement – it has to be measured experimentally, and cannot be found through calculations. Rougher surfaces tend to have higher effective values. Most dry materials in combination have friction coefficient values between 0.3 and 0.6. Values outside this range are rarer, but teflon, for example, can have a coefficient as low as 0.04. A value of zero would mean no friction at all, an elusive property – even magnetic levitation vehicles have drag. Rubber in contact with other surfaces can yield friction coefficients from 1 to 2. Occasionally it is maintained that µ is always < 1, but this is not true. While in most relevant applications µ < 1, a value above 1 merely implies that the force required to slide an object along the surface is greater than the normal force of the surface on the object. For example, silicone rubber or acrylic rubber-coated surfaces have a coefficient of friction that can be substantially larger than 1.

Both static and kinetic coefficients of friction depend on the pair of surfaces in contact; their values are usually approximately determined experimentally. For a given pair of surfaces, the coefficient of static friction is usually larger than that of kinetic friction; in some sets the two coefficients are equal, such as teflon-on-teflon.

In the case of kinetic friction, the direction of the friction force may or may not match the direction of motion: a block sliding atop a table with rectilinear motion is subject to friction directed along the line of motion; an automobile making a turn is subject to friction acting perpendicular to the line of motion (in which case it is said to be 'normal' to it). The direction of the static friction force can be visualized as directly opposed to the force that would otherwise cause motion, were it not for the static friction preventing motion. In this case, the friction force exactly cancels the applied force, so the net force given by the vector sum, equals zero. It is important to note that in all cases, Newton's first law of motion holds.

While it is often stated that the COF is a "material property," it is better categorized as a "system property." Unlike true material properties (such as conductivity, dielectric constant, yield strength), the COF for any two materials depends on system variables like temperature, velocity, atmosphere and also what are now popularly described as aging and deaging times; as well as on geometric properties of the interface between the materials. For example, a copper pin sliding against a thick copper plate can have a COF that varies from 0.6 at low speeds (metal sliding against metal) to below 0.2 at high speeds when the copper surface begins to melt due to frictional heating. The latter speed, of course, does not determine the COF uniquely; if the pin diameter is increased so that the frictional heating is removed rapidly, the temperature drops, the pin remains solid and the COF rises to that of a 'low speed' test.^{[citation needed]}

The normal force

Block on a ramp (top) and corresponding free body diagram of just the block (bottom).

Main article: Normal force

The normal force is defined as the net force compressing two parallel surfaces together; and its direction is perpendicular to the surfaces. In the simple case of a mass resting on a horizontal surface, the only component of the normal force is the force due to gravity, where $N=mg\,$ . In this case, the magnitude of the friction force is the product of the mass of the object, the acceleration due to gravity, and the coefficient of friction. However, the coefficient of friction is not a function of mass or volume; it depends only on the material. For instance, a large aluminum block has the same coefficient of friction as a small aluminum block. However, the magnitude of the friction force itself depends on the normal force, and hence the mass of the block.

If an object is on a level surface and the force tending to cause it to slide is horizontal, the normal force $N\,$ between the object and the surface is just its weight, which is equal to its mass multiplied by the acceleration due to earth's gravity, g. If the object is on a tilted surface such as an inclined plane, the normal force is less, because less of the force of gravity is perpendicular to the face of the plane. Therefore, the normal force, and ultimately the frictional force, is determined using vector analysis, usually via a free body diagram. Depending on the situation, the calculation of the normal force may include forces other than gravity.

Approximate coefficients of friction

Materials		Static friction, $\mu_s\,$
Materials		Dry & clean	Lubricated
Aluminum	Steel	0.61
Copper	Steel	0.53
Brass	Steel	0.51
Cast iron	Copper	1.05
Cast iron	Zinc	0.85
Concrete (wet)	Rubber	0.30
Concrete (dry)	Rubber	1.0
Concrete	Wood	0.62^[9]
Copper	Glass	0.68
Glass	Glass	0.94
Metal	Wood	0.2-0.6^[9]	0.2 (wet)^[9]
Polythene	Steel	0.2^[10]	0.2^[10]
Steel	Steel	0.80^[10]	0.16^[10]
Steel	Teflon	0.04^[10]	0.04^[10]
Teflon	Teflon	0.04^[10]	0.04^[10]
Wood	Wood	0.25-0.5^[9]	0.2 (wet)^[9]

The slipperiest solid known, discovered in 1999, dubbed BAM (for the elements boron, aluminum, and magnesium), has an approximate coefficient of friction of 0.02, about half that of Teflon.^[11]

Static friction

Static friction is friction between two solid objects that are not moving relative to each other. For example, static friction can prevent an object from sliding down a sloped surface. The coefficient of static friction, typically denoted as μ_s, is usually higher than the coefficient of kinetic friction.

The static friction force must be overcome by an applied force before an object can move. The maximum possible friction force between two surfaces before sliding begins is the product of the coefficient of static friction and the normal force: $f = \mu_s F_{n}\,$ . When there is no sliding occurring, the friction force can have any value from zero up to $F_{max}\,$ . Any force smaller than $F_{max}\,$ attempting to slide one surface over the other is opposed by a frictional force of equal magnitude and opposite direction. Any force larger than $F_{max}\,$ overcomes the force of static friction and causes sliding to occur. The instant sliding occurs, static friction is no longer applicable and kinetic friction becomes applicable.

An example of static friction is the force that prevents a car wheel from slipping as it rolls on the ground. Even though the wheel is in motion, the patch of the tire in contact with the ground is stationary relative to the ground, so it is static rather than kinetic friction.

The maximum value of static friction, when motion is impending, is sometimes referred to as limiting friction,^[12] although this term is not used universally.^[4]

Kinetic friction

Kinetic (or dynamic) friction occurs when two objects are moving relative to each other and rub together (like a sled on the ground). The coefficient of kinetic friction is typically denoted as μ_k, and is usually less than the coefficient of static friction for the same materials.^[13]^[14] In fact, Richard Feynman reports that "with dry metals it is very hard to show any difference."^[15] Finally, new models are beginning to show how kinetic friction can be greater than static friction.^[16]

Examples of kinetic friction:

Kinetic friction is when two objects are rubbing against each other. Putting a book flat on a desk and moving it around is an example of kinetic friction.

Fluid friction is the interaction between a solid object and a fluid (liquid or gas), as the object moves through the fluid. The skin friction of air on an airplane or of water on a swimmer are two examples of fluid friction. This kind of friction is not only due to rubbing, which generates a force tangent to the surface of the object (such as sliding friction). It is also due to forces that are orthogonal to the surface of the object. These orthogonal forces significantly (and mainly, if relative velocity is high enough) contribute to fluid friction. Fluid friction is the classic name of this force. This name is no longer used in modern fluid dynamics. Since rubbing is not its only cause, in modern fluid dynamics the same force is typically referred to as drag or fluid resistance, while the force component due to rubbing is called skin friction. Notice that a fluid can in some cases exert, together with drag, a force orthogonal to the direction of the relative motion of the object (lift). The net force exerted by a fluid (drag + lift) is called fluidodynamic force (aerodynamic if the fluid is a gas, or hydrodynamic if the fluid is a liquid).

Angle of friction

For the friction angle between granular material, see Angle of repose.

For certain applications it is more useful to define static friction in terms of the maximum angle before which one of the items will begin sliding. This is called the angle of friction or friction angle. It is defined as:

$\tan{\theta} = \mu\,$

where $\theta\,$ is the angle from horizontal and $\mu\,$ is the static coefficient of friction between the objects.^[17] This formula can also be used to calculate $\mu\,$ from empirical measurements of the friction angle.

Friction at the atomic level

Determining the forces required to move atoms past each other is a challenge in designing nanomachines. In 2008 scientists for the first time were able to move a single atom across a surface, and measure the forces required. Using ultrahigh vacuum and nearly-zero temperature (5 K), they used a modified atomic force microscope to drag a cobalt atom, and a carbon monoxide molecule, across surfaces of copper and platinum.^[18]

Other types of friction

Rolling resistance

Main article: Rolling resistance

Rolling resistance is the force that resists the rolling of a wheel or other circular object along a surface caused by deformations in the object and/or surface. Generally the force of rolling resistance is less than that associated with kinetic friction.^[19] Typical values for the coefficient of rolling resistance are 0.001.^[20] One of the most common examples of rolling resistance is the movement of motor vehicle tires on a road, a process which generates heat and sound as by-products.^[21]

Triboelectric effect

Rubbing dissimilar materials against one another can cause a build-up of electrostatic charge, which can be hazardous if flammable gases or vapours are present. When the static build-up discharges, explosions can be caused by ignition of the flammable mixture.

Reducing friction

Devices

Devices such as wheels, ball bearings, roller bearings, and air cushion or other types of fluid bearings can change sliding friction into a much smaller type of rolling friction.

Many thermoplastic materials such as nylon, HDPE and PTFE are commonly used in low friction bearings. They are especially useful because the coefficient of friction falls with increasing imposed load.^{[citation needed]} For improved wear resistance, very high molecular weight grades are usually specified for heavy duty or critical bearings.

Lubricants

A common way to reduce friction is by using a lubricant, such as oil, water, or grease, which is placed between the two surfaces, often dramatically lessening the coefficient of friction. The science of friction and lubrication is called tribology. Lubricant technology is when lubricants are mixed with the application of science, especially to industrial or commercial objectives.

Superlubricity, a recently-discovered effect, has been observed in graphite: it is the substantial decrease of friction between two sliding objects, approaching zero levels. A very small amount of frictional energy would still be dissipated.

Lubricants to overcome friction need not always be thin, turbulent fluids or powdery solids such as graphite and talc; acoustic lubrication actually uses sound as a lubricant.

Another way to reduce friction between two parts is to superimpose micro-scale vibration to one of the parts. This can be sinusoidal vibration as used in ultrasound-assisted cutting or vibration noise, known as dither.

Energy of friction

According to the law of conservation of energy, no energy is destroyed due to friction, though it may be lost to the system of concern. Energy is transformed from other forms into heat. A sliding hockey puck comes to rest because friction converts its kinetic energy into heat. Since heat quickly dissipates, many early philosophers, including Aristotle, wrongly concluded that moving objects lose energy without a driving force.

When an object is pushed along a surface, the energy converted to heat is given by:

$E_{th} = \mu_\mathrm{k} \int F_\mathrm{n}(x) dx\,$

where

$F_{n}\,$ is the normal force,

$\mu_\mathrm{k}\,$ is the coefficient of kinetic friction,

$x\,$ is the coordinate along which the object transverses.

Work of friction

In the reference frame of the interface between two surfaces, static friction does no work, because there is never displacement between the surfaces. In the same reference frame, kinetic friction is always in the direction opposite the motion, and does negative work.^[22] However, friction can do positive work in certain frames of reference. One can see this by placing a heavy box on a rug, then pulling on the rug quickly. In this case, the box slides backwards relative to the rug, but moves forward relative to the frame of reference in which the floor is stationary. Thus, the kinetic friction between the box and rug accelerates the box in the same direction that the box moves, doing positive work.^[23]

The work done by friction can translate into deformation, wear, and heat that can affect the contact surface properties (even the coefficient of friction between the surfaces). This can be beneficial as in polishing. The work of friction is used to mix and join materials such as in the process of friction welding. Excessive erosion or wear of mating surfaces occur when work due frictional forces rise to unacceptable levels. Harder corrosion particles caught between mating surfaces (fretting) exacerbates wear of frictional forces. Bearing seizure or failure may result from excessive wear due to work of friction. As surfaces are worn by work due to friction, fit and surface finish of an object may degrade until it no longer functions properly.[

FREQUENCY More...

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency.

Definitions and units

For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a number of cycles, or periods, per unit time. In physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter f or by a Greek letter ν (nu).

In SI units, the unit of frequency is hertz (Hz), named after the German physicist Heinrich Hertz. For example, 1 Hz means that an event repeats once per second.

A traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated RPM. 60 RPM equals one hertz.^[1]

The period is usually denoted as T, and is the reciprocal of the frequency f:

$T = \frac{1}{f}.$

The SI unit for period is the second.

Measurement

By counting

To calculate the frequency of an event, the number of occurrences of the event within a fixed time interval are counted, and then divided by the length of the time interval.

If the frequency is not too high, it is more accurate to measure the time taken for a fixed number of occurrences, rather than the number of occurrences within a fixed time.^[2] The latter method introduces a random error into the count of between zero and one count, so on average half a count. This is called gating error and causes an average error in the calculated frequency of Δf = 1/2T_m, or a fractional error of Δf/f = 1/2fT_m where T_m is the timing interval and f is the measured frequency. This error decreases with frequency, so it is a problem at low frequencies where the number of counts N is small.

Frequency counters

Higher frequencies are usually measured with a frequency counter. This is an electronic instrument which measures the frequency of an applied repetitive electronic signal and displays the result in hertz on a digital display. Cyclic processes that are not electrical, such as the rotation rate of a shaft, mechanical vibrations, or sound waves are converted to a repetitive electronic signal by transducers and the signal is applied to a frequency counter. Frequency counters can currently cover the range up to about 100 GHz. This represents the limit of direct counting methods; frequencies above this must be measured by indirect methods.

Heterodyne methods

Above the range of frequency counters, frequencies of electromagnetic signals are often measured indirectly by means of heterodyning (frequency conversion). A reference signal of a known frequency near the unknown frequency. is mixed with the unknown frequency in a nonlinear mixing device. This creates a heterodyne or "beat" signal at the difference between the two frequencies, which is low enough to be measured by a frequency counter. Of course this process just measures the unknown frequency by its offset from the reference frequency, which must be determined by some other method. To reach higher frequencies, several stages of heterodyning can be used. Current research is extending this method to infrared and light frequencies (optical heterodyne detection).

Frequency of waves

Frequency has an inverse relationship to the concept of wavelength, simply, frequency is inversely proportional to wavelength λ (lambda). The frequency f is equal to the phase velocity v of the wave divided by the wavelength λ of the wave:

$f = \frac{v}{\lambda}.$

In the special case of electromagnetic waves moving through a vacuum, then v = c , where c is the speed of light in a vacuum, and this expression becomes:

$f = \frac{c}{\lambda}.$

When waves from a monochromatic source travel from one medium to another, their frequency remains exactly the same — only their wavelength and speed change.

Examples

Physics of light

Radiant energy is energy which is propagated in the form of electromagnetic waves. Most people think of natural sunlight or electrical light, when considering this form of energy. The type of light which we perceive through our optical sensors (eyes) is classified as white light, and is composed of a range of colors (red, orange, yellow, green, blue, indigo, violet) over a range of wavelengths, or frequencies.

Visible (white) light is only a small fraction of the entire spectrum of electromagnetic radiation. At the short end of that wavelength scale is ultraviolet (UV) light from the sun, which cannot be seen. At the longer end of that spectrum is infrared (IR) light, which is used for night vision and other heat-seeking devices. At even shorter wavelengths than UV are X-rays and Gamma-rays. At longer wavelengths than IR are microwaves, radio waves, electromagnetic waves in megahertz and kHz range, as well as natural waves with frequencies in the millihertz and microhertz range. A 2 millihertz wave has a wavelength approximately equal to the distance from the earth to the sun. A microhertz wave would extend 0.0317 light years. A nanohertz wave would extend 31.6881 light years.

Complete spectrum of electromagnetic radiation with the visible portion highlighted

Electromagnetic radiation is classified according to the frequency (or wavelength) of the light wave. This includes (in order of increasing frequency): natural electromagnetic waves, radio waves, microwaves, terahertz radiation, infrared (IR) radiation, visible light, ultraviolet (UV) radiation, X-rays and gamma rays. Of these, natural electromagnetic waves have the longest wavelengths and gamma rays have the shortest. A small window of frequencies, called the visible spectrum or light, is sensed by the eye of various organisms, with variations of the limits of this narrow spectrum.

Physics of sound

Sound is vibration transmitted through a solid, liquid, or gas; particularly, sound means those vibrations composed of frequencies capable of being detected by ears. For humans, hearing is limited to frequencies between about 20 Hz and 20,000 Hz (20 kHz), with the upper limit generally decreasing with age. Other species have a different range of hearing. For example, some dog breeds can perceive vibrations up to 60,000 Hz.^[3] As a signal perceived by one of the major senses, sound is used by many species for detecting danger, navigation, predation, and communication.

Other examples

In Europe, Africa, Australia, Southern South America, most of Asia, and Russia, the frequency of the alternating current in household electrical outlets is 50 Hz (close to the tone G), whereas in North America and Northern South America, the frequency of the alternating current is 60 Hz (between the tones B♭ and B — that is, a minor third above the European frequency). The frequency of the 'hum' in an audio recording can show where the recording was made — in countries utilizing the European, or the American grid frequency.

Period versus frequency

As a matter of convenience, longer and slower waves, such as ocean surface waves, tend to be described by wave period rather than frequency. Short and fast waves, like audio and radio, are usually described by their frequency instead of period. These commonly used conversions are listed below:

Frequency	1 mHz (10^-3)	1 Hz (10⁰)	1 kHz (10³)	1 MHz (10⁶)	1 GHz (10⁹)	1 THz (10¹²)
Period (time)	1 ks (10³)	1 s (10⁰)	1 ms (10^-3)	1 µs (10^-6)	1 ns (10^-9)	1 ps (10^-12)

Other types of frequency

Angular frequency ω is defined as the rate of change in the orientation angle (during rotation), or in the phase of a sinusoidal waveform (e.g. in oscillations and waves):

$\omega=2\pi f\,$ .

Angular frequency is measured in radians per second (rad/s).

Spatial frequency is analogous to temporal frequency, but the time axis is replaced by one or more spatial displacement axes.
Wavenumber is the spatial analogue of angular frequency. In case of more than one spacial dimension, wavenumber is a vector quantity.