Misplaced Pages

#267732

83-513: A photosphere is the region of a luminous object, usually a star, that is transparent to photons of certain wavelengths . Stars, except neutron stars , have no solid or liquid surface. Therefore, the photosphere is typically used to describe the Sun 's or another star 's visual surface. The term photosphere is derived from Ancient Greek roots, φῶς, φωτός/ phos , photos meaning "light" and σφαῖρα/ sphaira meaning "sphere", in reference to it being

166-411: A local wavelength . An example is shown in the figure. In general, the envelope of the wave packet moves at a speed different from the constituent waves. Using Fourier analysis , wave packets can be analyzed into infinite sums (or integrals) of sinusoidal waves of different wavenumbers or wavelengths. Louis de Broglie postulated that all particles with a specific value of momentum p have

249-429: 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 − 2 {\displaystyle -{\sqrt {2}}} Pa) and (1 atm + 2 {\displaystyle +{\sqrt {2}}} Pa), that is between 101323.6 and 101326.4 Pa. As the human ear can detect sounds with

332-407: A wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings . Wavelength is a characteristic of both traveling waves and standing waves , as well as other spatial wave patterns. The inverse of the wavelength

415-455: A circular aperture, the diffraction-limited image spot is known as an Airy disk ; the distance x in the single-slit diffraction formula is replaced by radial distance r and the sine is replaced by 2 J 1 , where J 1 is a first order Bessel function . The resolvable spatial size of objects viewed through a microscope is limited according to the Rayleigh criterion , the radius to

498-663: A given area as modified by the environment and understood by people, in context of the surrounding environment. There are, historically, six experimentally separable ways in which sound waves are analysed. They are: pitch , duration , loudness , timbre , sonic texture and spatial location . Some of these terms have a standardised definition (for instance in the ANSI Acoustical Terminology ANSI/ASA S1.1-2013 ). More recent approaches have also considered temporal envelope and temporal fine structure as perceptually relevant analyses. Pitch

581-529: A hueless, gray surface. It has a density of about 3 × 10 kg / m ; increasing with increasing depth. The Sun's photosphere is 100–400 kilometers thick. In the Sun's photosphere, the most ubiquitous phenomenon are granules — convection cells of plasma each approximately 1,000 km (620 mi) in diameter with hot rising plasma in the center and cooler plasma falling in the spaces between them, flowing at velocities of 7 km/s (4.3 mi/s). Each granule has

664-736: A lifespan of only about twenty minutes, resulting in a continually shifting "boiling" pattern. Grouping the typical granules are supergranules up to 30,000 km (19,000 mi) in diameter with lifespans of up to 24 hours and flow speeds of about 500 m/s (1,600 ft/s), carrying magnetic field bundles to the edges of the cells. Other magnetically related phenomena in the Sun's photosphere include sunspots and solar faculae dispersed between granules. These features are too fine to be directly observed on other stars; however, sunspots have been indirectly observed, in which case they are referred to as starspots . Wavelength In physics and mathematics , wavelength or spatial period of

747-468: A linear system the sinusoid is the unique shape that propagates with no shape change – just a phase change and potentially an amplitude change. The wavelength (or alternatively wavenumber or wave vector ) is a characterization of the wave in space, that is functionally related to its frequency, as constrained by the physics of the system. Sinusoids are the simplest traveling wave solutions, and more complex solutions can be built up by superposition . In

830-405: A medium such as air, water and solids as longitudinal waves and also as a transverse wave in solids . The sound waves are generated by a sound source, such as the vibrating diaphragm of a stereo speaker. The sound source creates vibrations in the surrounding medium. As the source continues to vibrate the medium, the vibrations propagate away from the source at the speed of sound , thus forming

913-488: A particular pitch is determined by pre-conscious examination of vibrations, including their frequencies and the balance between them. Specific attention is given to recognising potential harmonics. Every sound is placed on a pitch continuum from low to high. For example: white noise (random noise spread evenly across all frequencies) sounds higher in pitch than pink noise (random noise spread evenly across octaves) as white noise has more high frequency content. Duration

SECTION 10

#1732801113268

996-426: A regular lattice. This produces aliasing because the same vibration can be considered to have a variety of different wavelengths, as shown in the figure. Descriptions using more than one of these wavelengths are redundant; it is conventional to choose the longest wavelength that fits the phenomenon. The range of wavelengths sufficient to provide a description of all possible waves in a crystalline medium corresponds to

1079-432: A result, the change in direction upon entering a different medium changes with the wavelength of the wave. For electromagnetic waves the speed in a medium is governed by its refractive index according to where c is the speed of light in vacuum and n ( λ 0 ) is the refractive index of the medium at wavelength λ 0 , where the latter is measured in vacuum rather than in the medium. The corresponding wavelength in

1162-570: A spherical surface that is perceived to emit light. The surface of a star is defined to have a temperature given by the effective temperature in the Stefan–Boltzmann law . Various stars have photospheres of various temperatures. The Sun is composed primarily of the chemical elements hydrogen and helium ; they account for 74.9% and 23.8%, respectively, of the mass of the Sun in the photosphere. All heavier elements, colloquially called metals in stellar astronomy , account for less than 2% of

1245-404: A traveling wave. For example, the speed of light can be determined from observation of standing waves in a metal box containing an ideal vacuum. Traveling sinusoidal waves are often represented mathematically in terms of their velocity v (in the x direction), frequency f and wavelength λ as: where y is the value of the wave at any position x and time t , and A is the amplitude of

1328-531: A wavelength λ = h / p , where h is the Planck constant . This hypothesis was at the basis of quantum mechanics . Nowadays, this wavelength is called the de Broglie wavelength . For example, the electrons in a CRT display have a De Broglie wavelength of about 10  m . To prevent the wave function for such a particle being spread over all space, de Broglie proposed using wave packets to represent particles that are localized in space. The spatial spread of

1411-466: A 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 Since the human ear does not have a flat spectral response , sound pressures are often frequency weighted so that the measured level matches perceived levels more closely. The International Electrotechnical Commission (IEC) has defined several weighting schemes. A-weighting attempts to match

1494-488: Is also known as the Newton–Laplace equation. In this equation, K is the elastic bulk modulus, c is the velocity of sound, and ρ {\displaystyle \rho } is the density. Thus, the speed of sound is proportional to the square root of the ratio of the bulk modulus of the medium to its density. Those physical properties and the speed of sound change with ambient conditions. For example,

1577-424: Is also responsible for the familiar phenomenon in which light is separated into component colours by a prism . Separation occurs when the refractive index inside the prism varies with wavelength, so different wavelengths propagate at different speeds inside the prism, causing them to refract at different angles. The mathematical relationship that describes how the speed of light within a medium varies with wavelength

1660-399: Is an undesirable component that obscures a wanted signal. However, in sound perception it can often be used to identify the source of a sound and is an important component of timbre perception (see below). Soundscape is the component of the acoustic environment that can be perceived by humans. The acoustic environment is the combination of all sounds (whether audible to humans or not) within

1743-464: Is an undulatory motion that stays in one place. A sinusoidal standing wave includes stationary points of no motion, called nodes , and the wavelength is twice the distance between nodes. The upper figure shows three standing waves in a box. The walls of the box are considered to require the wave to have nodes at the walls of the box (an example of boundary conditions ), thus determining the allowed wavelengths. For example, for an electromagnetic wave, if

SECTION 20

#1732801113268

1826-403: Is called diffraction . Two types of diffraction are distinguished, depending upon the separation between the source and the screen: Fraunhofer diffraction or far-field diffraction at large separations and Fresnel diffraction or near-field diffraction at close separations. In the analysis of the single slit, the non-zero width of the slit is taken into account, and each point in the aperture

1909-459: Is called the spatial frequency . Wavelength is commonly designated by the Greek letter lambda ( λ ). The term "wavelength" is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids. Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to the frequency of

1992-478: 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 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. Noise is a term often used to refer to an unwanted sound. In science and engineering, noise

2075-424: Is commonly used for diagnostics and treatment. Infrasound is sound waves with frequencies lower than 20 Hz. Although sounds of such low frequency are too low for humans to hear as a pitch, these sound are heard as discrete pulses (like the 'popping' sound of an idling motorcycle). Whales, elephants and other animals can detect infrasound and use it to communicate. It can be used to detect volcanic eruptions and

2158-445: Is defined as "(a) Oscillation in pressure, stress, particle displacement, particle velocity, etc., propagated in a medium with internal forces (e.g., elastic or viscous), or the superposition of such propagated oscillation. (b) Auditory sensation evoked by the oscillation described in (a)." Sound can be viewed as a wave motion in air or other elastic media. In this case, sound is a stimulus. Sound can also be viewed as an excitation of

2241-495: Is described by the Jacobi elliptic function of m th order, usually denoted as cn ( x ; m ) . Large-amplitude ocean waves with certain shapes can propagate unchanged, because of properties of the nonlinear surface-wave medium. If a traveling wave has a fixed shape that repeats in space or in time, it is a periodic wave . Such waves are sometimes regarded as having a wavelength even though they are not sinusoidal. As shown in

2324-418: Is heard; specif.: a. Psychophysics. Sensation due to stimulation of the auditory nerves and auditory centers of the brain, usually by vibrations transmitted in a material medium, commonly air, affecting the organ of hearing. b. Physics. Vibrational energy which occasions such a sensation. Sound is propagated by progressive longitudinal vibratory disturbances (sound waves)." This means that the correct response to

2407-413: Is known as a dispersion relation . Wavelength can be a useful concept even if the wave is not periodic in space. For example, in an ocean wave approaching shore, shown in the figure, the incoming wave undulates with a varying local wavelength that depends in part on the depth of the sea floor compared to the wave height. The analysis of the wave can be based upon comparison of the local wavelength with

2490-427: Is large compared to the slit separation d ) then the paths are nearly parallel, and the path difference is simply d sin θ . Accordingly, the condition for constructive interference is: where m is an integer, and for destructive interference is: Thus, if the wavelength of the light is known, the slit separation can be determined from the interference pattern or fringes , and vice versa . For multiple slits,

2573-465: Is perceived as how "long" or "short" a sound is and relates to onset and offset signals created by nerve responses to sounds. The duration of a sound usually lasts from the time the sound is first noticed until the sound is identified as having changed or ceased. Sometimes this is not directly related to the physical duration of a sound. For example; in a noisy environment, gapped sounds (sounds that stop and start) can sound as if they are continuous because

Photosphere - Misplaced Pages Continue

2656-457: Is perceived as how "low" or "high" a sound is and represents the cyclic, repetitive nature of the vibrations that make up sound. For simple sounds, pitch relates to the frequency of the slowest vibration in the sound (called the fundamental harmonic). In the case of complex sounds, pitch perception can vary. Sometimes individuals identify different pitches for the same sound, based on their personal experience of particular sound patterns. Selection of

2739-422: Is perceptible by humans has frequencies from about 20 Hz to 20,000 Hz. In air at standard temperature and pressure , the corresponding wavelengths of sound waves range from 17 m (56 ft) to 17 mm (0.67 in). Sometimes speed and direction are combined as a velocity vector ; wave number and direction are combined as a wave vector . Transverse waves , also known as shear waves, have

2822-488: Is related to position x via a squared sinc function : where L is the slit width, R is the distance of the pattern (on the screen) from the slit, and λ is the wavelength of light used. The function S has zeros where u is a non-zero integer, where are at x values at a separation proportion to wavelength. Diffraction is the fundamental limitation on the resolving power of optical instruments, such as telescopes (including radiotelescopes ) and microscopes . For

2905-458: Is taken as the source of one contribution to the beam of light ( Huygens' wavelets ). On the screen, the light arriving from each position within the slit has a different path length, albeit possibly a very small difference. Consequently, interference occurs. In the Fraunhofer diffraction pattern sufficiently far from a single slit, within a small-angle approximation , the intensity spread S

2988-417: Is used in the interferometer . A simple example is an experiment due to Young where light is passed through two slits . As shown in the figure, light is passed through two slits and shines on a screen. The path of the light to a position on the screen is different for the two slits, and depends upon the angle θ the path makes with the screen. If we suppose the screen is far enough from the slits (that is, s

3071-521: The brain . Only acoustic waves that have frequencies lying between about 20 Hz and 20 kHz, the audio frequency range, elicit an auditory percept in humans. In air at atmospheric pressure, these represent sound waves with wavelengths of 17 meters (56 ft) to 1.7 centimeters (0.67 in). Sound waves above 20  kHz are known as ultrasound and are not audible to humans. Sound waves below 20 Hz are known as infrasound . Different animal species have varying hearing ranges . Sound

3154-422: The cosine phase instead of the sine phase when describing a wave is based on the fact that the cosine is the real part of the complex exponential in the wave The speed of a wave depends upon the medium in which it propagates. In particular, the speed of light in a medium is less than in vacuum , which means that the same frequency will correspond to a shorter wavelength in the medium than in vacuum, as shown in

3237-401: 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. Sound waves may be viewed using parabolic mirrors and objects that produce sound. The energy carried by an oscillating sound wave converts back and forth between the potential energy of

3320-483: The hearing range for humans or sometimes it relates to a particular animal. Other species have different ranges 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

3403-443: The speed of sound is 343 m/s (at room temperature and atmospheric pressure ). The wavelengths of sound frequencies audible to the human ear (20  Hz –20 kHz) are thus between approximately 17  m and 17  mm , respectively. Somewhat higher frequencies are used by bats so they can resolve targets smaller than 17 mm. Wavelengths in audible sound are much longer than those in visible light. A standing wave

Photosphere - Misplaced Pages Continue

3486-404: The additional property, polarization , which is not a characteristic of longitudinal sound waves. The speed of sound depends on the medium the waves pass through, and is a fundamental property of the material. The first significant effort towards measurement of the speed of sound was made by Isaac Newton . He believed the speed of sound in a particular substance was equal to the square root of

3569-512: The basis of all sound waves. They can be used to describe, in absolute terms, every sound we hear. In order to understand the sound more fully, a complex wave such as the one shown in a blue background on the right of this text, is usually separated into its component parts, which are a combination of various sound wave frequencies (and noise). Sound waves are often simplified to a description in terms of sinusoidal plane waves , which are characterized by these generic properties: Sound that

3652-399: The box has ideal conductive walls, the condition for nodes at the walls results because the conductive walls cannot support a tangential electric field, forcing the wave to have zero amplitude at the wall. The stationary wave can be viewed as the sum of two traveling sinusoidal waves of oppositely directed velocities. Consequently, wavelength, period, and wave velocity are related just as for

3735-499: The central bright portion (radius to first null of the Airy disk ) of the image diffracted by a circular aperture, a measure most commonly used for telescopes and cameras, is: Sound wave In physics , sound is a vibration that propagates as an acoustic wave through a transmission medium such as a gas, liquid or solid. In human physiology and psychology , sound is the reception of such waves and their perception by

3818-569: The direction and wavenumber of a plane wave in 3-space , parameterized by position vector r . In that case, the wavenumber k , the magnitude of k , is still in the same relationship with wavelength as shown above, with v being interpreted as scalar speed in the direction of the wave vector. The first form, using reciprocal wavelength in the phase, does not generalize as easily to a wave in an arbitrary direction. Generalizations to sinusoids of other phases, and to complex exponentials, are also common; see plane wave . The typical convention of using

3901-411: The duration of theta wave cycles. This means that at short durations, a very short sound can sound softer than a longer sound even though they are presented at the same intensity level. Past around 200 ms this is no longer the case and the duration of the sound no longer affects the apparent loudness of the sound. Timbre is perceived as the quality of different sounds (e.g. the thud of a fallen rock,

3984-401: The equation c = γ ⋅ p / ρ {\displaystyle c={\sqrt {\gamma \cdot p/\rho }}} . Since K = γ ⋅ p {\displaystyle K=\gamma \cdot p} , the final equation came up to be c = K / ρ {\displaystyle c={\sqrt {K/\rho }}} , which

4067-439: 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 displacement velocity of particles of the medium. Although there are many complexities relating to the transmission of sounds, at the point of reception (i.e. the ears), sound is readily dividable into two simple elements: pressure and time. These fundamental elements form

4150-406: The fastest in solid atomic hydrogen at about 36,000 m/s (129,600 km/h; 80,530 mph). Sound pressure is the difference, in a given medium, between average local pressure and the pressure in the sound wave. 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 this average provides

4233-407: The figure at right. This change in speed upon entering a medium causes refraction , or a change in direction of waves that encounter the interface between media at an angle. For electromagnetic waves , this change in the angle of propagation is governed by Snell's law . The wave velocity in one medium not only may differ from that in another, but the velocity typically varies with wavelength. As

SECTION 50

#1732801113268

4316-400: The figure, wavelength is measured between consecutive corresponding points on the waveform. Localized wave packets , "bursts" of wave action where each wave packet travels as a unit, find application in many fields of physics. A wave packet has an envelope that describes the overall amplitude of the wave; within the envelope, the distance between adjacent peaks or troughs is sometimes called

4399-471: The first null of the Airy disk, to a size proportional to the wavelength of the light used, and depending on the numerical aperture : where the numerical aperture is defined as N A = n sin ⁡ θ {\displaystyle \mathrm {NA} =n\sin \theta \;} for θ being the half-angle of the cone of rays accepted by the microscope objective . The angular size of

4482-481: The hearing mechanism that results in the perception of sound. In this case, sound is a sensation . Acoustics is the interdisciplinary science that deals with the study of mechanical waves in gasses, liquids, and solids including vibration , sound, ultrasound, and infrasound. A scientist who works in the field of acoustics is an acoustician , while someone working in the field of acoustical engineering may be called an acoustical engineer . An audio engineer , on

4565-417: The independent propagation of sinusoidal components. The wavelength λ of a sinusoidal waveform traveling at constant speed v {\displaystyle v} is given by where v {\displaystyle v} is called the phase speed (magnitude of the phase velocity ) of the wave and f {\displaystyle f} is the wave's frequency . In a dispersive medium ,

4648-426: The information for timbre identification. Even though a small section of the wave form from each instrument looks very similar, differences in changes over time between the clarinet and the piano are evident in both loudness and harmonic content. Less noticeable are the different noises heard, such as air hisses for the clarinet and hammer strikes for the piano. Sonic texture relates to the number of sound sources and

4731-440: The interaction between them. The word texture , in this context, relates to the cognitive separation of auditory objects. In music, texture is often referred to as the difference between unison , polyphony and homophony , but it can also relate (for example) to a busy cafe; a sound which might be referred to as cacophony . Spatial location represents the cognitive placement of a sound in an environmental context; including

4814-405: The light is not altered, just where it shows up. The notion of path difference and constructive or destructive interference used above for the double-slit experiment applies as well to the display of a single slit of light intercepted on a screen. The main result of this interference is to spread out the light from the narrow slit into a broader image on the screen. This distribution of wave energy

4897-411: The local water depth. Waves that are sinusoidal in time but propagate through a medium whose properties vary with position (an inhomogeneous medium) may propagate at a velocity that varies with position, and as a result may not be sinusoidal in space. The figure at right shows an example. As the wave slows down, the wavelength gets shorter and the amplitude increases; after a place of maximum response,

4980-415: The mass, with oxygen (roughly 1% of the Sun's mass), carbon (0.3%), neon (0.2%), and iron (0.2%) being the most abundant. The Sun 's photosphere has a temperature between 4,400 and 6,600  K (4,130 and 6,330 °C) (with an effective temperature of 5,772  K (5,499 °C)) meaning human eyes perceive it as an overwhelmingly bright surface, and with sufficiently strong neutral density filter, as

5063-407: The medium is When wavelengths of electromagnetic radiation are quoted, the wavelength in vacuum usually is intended unless the wavelength is specifically identified as the wavelength in some other medium. In acoustics, where a medium is essential for the waves to exist, the wavelength value is given for a specified medium. The variation in speed of light with wavelength is known as dispersion , and

SECTION 60

#1732801113268

5146-461: The offset messages are missed owing to disruptions from noises in the same general bandwidth. This can be of great benefit in understanding distorted messages such as radio signals that suffer from interference, as (owing to this effect) the message is heard as if it was continuous. Loudness is perceived as how "loud" or "soft" a sound is and relates to the totalled number of auditory nerve stimulations over short cyclic time periods, most likely over

5229-482: The other hand, is concerned with the recording, manipulation, mixing, and reproduction of sound. Applications of acoustics are found in almost all aspects of modern society, subdisciplines include aeroacoustics , audio signal processing , architectural acoustics , bioacoustics , electro-acoustics, environmental noise , musical acoustics , noise control , psychoacoustics , speech , ultrasound , underwater acoustics , and vibration . Sound can propagate through

5312-413: The pattern is where q is the number of slits, and g is the grating constant. The first factor, I 1 , is the single-slit result, which modulates the more rapidly varying second factor that depends upon the number of slits and their spacing. In the figure I 1 has been set to unity, a very rough approximation. The effect of interference is to redistribute the light, so the energy contained in

5395-602: The phase speed itself depends upon the frequency of the wave, making the relationship between wavelength and frequency nonlinear. In the case of electromagnetic radiation —such as light—in free space , the phase speed is the speed of light , about 3 × 10  m/s . Thus the wavelength of a 100 MHz electromagnetic (radio) wave is about: 3 × 10  m/s divided by 10  Hz = 3 m. The wavelength of visible light ranges from deep red , roughly 700  nm , to violet , roughly 400 nm (for other examples, see electromagnetic spectrum ). For sound waves in air,

5478-580: The placement of a sound on both the horizontal and vertical plane, the distance from the sound source and the characteristics of the sonic environment. In a thick texture, it is possible to identify multiple sound sources using a combination of spatial location and timbre identification. Ultrasound is sound waves with frequencies higher than 20,000 Hz. Ultrasound is not different from audible sound in its physical properties, but cannot be heard by humans. Ultrasound devices operate with frequencies from 20 kHz up to several gigahertz. Medical ultrasound

5561-562: The pressure acting on it divided by its density: This was later proven wrong and the French mathematician Laplace corrected the formula by deducing that the phenomenon of sound travelling is not isothermal, as believed by Newton, but adiabatic . He added another factor to the equation— gamma —and multiplied γ {\displaystyle {\sqrt {\gamma }}} by p / ρ {\displaystyle {\sqrt {p/\rho }}} , thus coming up with

5644-423: The production of harmonics and mixed tones not present in the original sound (see parametric array ). If relativistic effects are important, the speed of sound is calculated from the relativistic Euler equations . In fresh water 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). Sound moves

5727-555: The question: " if a tree falls in a forest and no one is around to hear it, does it make a sound? " is "yes", and "no", dependent on whether being answered using the physical, or the psychophysical definition, respectively. The physical reception of sound in any hearing organism is limited to a range of frequencies. Humans normally hear sound frequencies between approximately 20  Hz and 20,000 Hz (20  kHz ), The upper limit decreases with age. Sometimes sound refers to only those vibrations with frequencies that are within

5810-443: 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. A distinct use of the term sound from its use in physics is that in physiology and psychology, where the term refers to the subject of perception by the brain. The field of psychoacoustics is dedicated to such studies. Webster's dictionary defined sound as: "1. The sensation of hearing, that which

5893-537: The short wavelength is associated with a high loss and the wave dies out. The analysis of differential equations of such systems is often done approximately, using the WKB method (also known as the Liouville–Green method ). The method integrates phase through space using a local wavenumber , which can be interpreted as indicating a "local wavelength" of the solution as a function of time and space. This method treats

5976-528: The sound is called the medium . Sound cannot travel through a vacuum . Studies has shown that sound waves are able to carry a tiny amount of mass and is surrounded by a weak gravitational field. Sound is transmitted through gases, plasma, and liquids as longitudinal waves , also called compression waves. It requires a medium to propagate. Through solids, however, it can be transmitted as both longitudinal waves and transverse waves . Longitudinal sound waves are waves of alternating pressure deviations from

6059-420: The sound wave. At a fixed distance from the source, the pressure , velocity , and displacement of the medium vary in time. At an instant in time, the pressure, velocity, and displacement vary in space. The particles of the medium do not travel with the sound wave. This is intuitively obvious for a solid, and the same is true for liquids and gases (that is, the vibrations of particles in the gas or liquid transport

6142-420: The special case of dispersion-free and uniform media, waves other than sinusoids propagate with unchanging shape and constant velocity. In certain circumstances, waves of unchanging shape also can occur in nonlinear media; for example, the figure shows ocean waves in shallow water that have sharper crests and flatter troughs than those of a sinusoid, typical of a cnoidal wave , a traveling wave so named because it

6225-417: The speed of sound in gases depends on temperature. In 20 °C (68 °F) air at sea level, the speed of sound is approximately 343 m/s (1,230 km/h; 767 mph) using the formula v  [m/s] = 331 + 0.6  T  [°C] . The speed of sound is also slightly sensitive, being subject to a second-order anharmonic effect, to the sound amplitude, which means there are non-linear propagation effects, such as

6308-509: The strength of the electric and the magnetic field vary. Water waves are variations in the height of a body of water. In a crystal lattice vibration , atomic positions vary. The range of wavelengths or frequencies for wave phenomena is called a spectrum . The name originated with the visible light spectrum but now can be applied to the entire electromagnetic spectrum as well as to a sound spectrum or vibration spectrum . In linear media, any wave pattern can be described in terms of

6391-529: The system locally as if it were uniform with the local properties; in particular, the local wave velocity associated with a frequency is the only thing needed to estimate the corresponding local wavenumber or wavelength. In addition, the method computes a slowly changing amplitude to satisfy other constraints of the equations or of the physical system, such as for conservation of energy in the wave. Waves in crystalline solids are not continuous, because they are composed of vibrations of discrete particles arranged in

6474-566: The vibrations, while the average position of the particles over time does not change). During propagation, waves can be reflected , refracted , or attenuated by the medium. The behavior of sound propagation is generally affected by three things: When sound is moving through a medium that does not have constant physical properties, it may be refracted (either dispersed or focused). The mechanical vibrations that can be interpreted as sound can travel through all forms of matter : gases, liquids, solids, and plasmas . The matter that supports

6557-427: The wave packet, and the spread of the wavenumbers of sinusoids that make up the packet, correspond to the uncertainties in the particle's position and momentum, the product of which is bounded by Heisenberg uncertainty principle . When sinusoidal waveforms add, they may reinforce each other (constructive interference) or cancel each other (destructive interference) depending upon their relative phase. This phenomenon

6640-456: The wave vectors confined to the Brillouin zone . This indeterminacy in wavelength in solids is important in the analysis of wave phenomena such as energy bands and lattice vibrations . It is mathematically equivalent to the aliasing of a signal that is sampled at discrete intervals. The concept of wavelength is most often applied to sinusoidal, or nearly sinusoidal, waves, because in

6723-426: The wave. They are also commonly expressed in terms of wavenumber k (2π times the reciprocal of wavelength) and angular frequency ω (2π times the frequency) as: in which wavelength and wavenumber are related to velocity and frequency as: or In the second form given above, the phase ( kx − ωt ) is often generalized to ( k ⋅ r − ωt ) , by replacing the wavenumber k with a wave vector that specifies

6806-427: The wave: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths. Wavelength depends on the medium (for example, vacuum, air, or water) that a wave travels through. Examples of waves are sound waves , light , water waves and periodic electrical signals in a conductor . A sound wave is a variation in air pressure , while in light and other electromagnetic radiation

6889-430: The whir of a drill, the tone of a musical instrument or the quality of a voice) and represents the pre-conscious allocation of a sonic identity to a sound (e.g. "it's an oboe!"). This identity is based on information gained from frequency transients, noisiness, unsteadiness, perceived pitch and the spread and intensity of overtones in the sound over an extended time frame. The way a sound changes over time provides most of

#267732