Waves. Surface acoustic waves

International scientific and practical conference

"First steps into science"

Research

"Waves on the surface of the water."

Dychenkova Anastasia,

Safronova Alena,

Supervisor:

Educational institution:

MBOU Secondary School No. 52, Bryansk.

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The main properties of waves are:

1) absorption;

2) scattering;

3) reflection;

4) refraction;

5) interference;

8) polarization.

It should be noted that the wave nature of any process is proved by the phenomena of interference and diffraction.

Let's look at some properties of waves in more detail:

Formation of standing waves.

When direct and reflected traveling waves superpose, a standing wave appears. It is called standing because, firstly, nodes and antinodes do not move in space, and secondly, it does not transfer energy in space.

A stable standing wave is formed if an integer number of half-waves fits along the length L.

Any elastic body (for example, a string) with free vibrations has a fundamental tone and overtones. The more overtones an elastic body has, the more beautiful it sounds.

Examples of applications of standing waves:

Wind musical instruments (organ, trumpet)

Stringed musical instruments (guitar, piano, violin)

Tuning forks

Wave interference.

Wave interference is a stable distribution over time of the amplitude of oscillations in space when coherent waves are superimposed.

They have the same frequencies;

Phase shift of waves arriving at this point, a constant value, that is, does not depend on time.

At a given point, a minimum is observed during interference if the difference in the wave paths is equal to an odd number of half-waves.

At a given point, a maximum is observed during interference if the wave path difference is equal to an even number of half-waves or an integer number of wavelengths.

During interference, a redistribution of wave energy occurs, that is, almost no energy arrives at the minimum point, and more of it arrives at the maximum point.

Wave diffraction.

Waves are able to bend around obstacles. Thus, sea waves freely bend around a stone protruding from the water if its dimensions are less than the wavelength or comparable to it. Behind the stone, the waves propagate as if it were not there at all. In exactly the same way, the wave from a stone thrown into a pond bends around a twig sticking out of the water. Only behind an obstacle of a large size, compared to the wavelength, is a “shadow” formed: waves do not penetrate beyond the obstacle.

Sound waves also have the ability to bend around obstacles. You can hear a car honking around the corner of the house when the car itself is not visible. In the forest, trees obscure your comrades. To avoid losing them, you start screaming. Sound waves, unlike light, freely bend around tree trunks and carry your voice to your comrades.

Diffraction is the phenomenon of violation of the law of rectilinear propagation of waves in a homogeneous medium or the bending of waves around obstacles.

There is a screen with a slit in the path of the wave:

Slit length is a lot longer waves. No diffraction is observed.

The length of the slit is commensurate with the wavelength. Diffraction is observed.

There is an obstacle in the path of the wave:

The size of the obstacle is much larger than the wavelength. No diffraction is observed.

The size of the obstacle is commensurate with the wavelength. Diffraction is observed (the wave bends around an obstacle).

Condition for observing diffraction: the wavelength is commensurate with the size of the obstacle, gap or barrier

Practical part.

To carry out the experiments, we used the “Wave Bath” device

Interference of two circular waves.

Pour water into the bath. We lower the nozzle into it to form two circular waves.

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Alternating light and dark stripes. At those points where the phases are the same, the amplitude of oscillations increases;

The sources are coherent.

Circular wave.

Interference of incident and reflected waves.

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Conclusion: to observe interference, the wave sources must be coherent.

Interference of plane waves.

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Standing waves.

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1. Attach a nozzle to create a plane wave in the vibrator and get a stable picture of plane waves on the screen.

2. We installed a reflector barrier parallel to the wave front.

3. Assemble an analogue of a corner reflector from two obstacles and immerse it in the cuvette. You will see the standing wave as a two-dimensional (mesh) structure.

4. The criterion for obtaining a standing wave is the transition of the surface shape at the points where the antinodes are located from convex (light points) to concave (dark points) without any displacement of these points.

Diffraction of a wave by an obstacle.

We obtained a stable picture of plane wave radiation. Place an obstacle – an eraser – at a distance of approximately 50 mm from the emitter.

Reducing the size of the eraser, we get the following: (a is the length of the eraser)

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a = 8 cm a = 7mm

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a = 4.5 mm a = 1.5 mm

Conclusion: diffraction is not observed if, a > λ, diffraction is observed,

if a< λ, следовательно, волна огибает препятствия.

Determination of wavelength.

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Wavelength λ is the distance between adjacent crests or troughs. The image on the screen is enlarged 2 times compared to the real object.

λ =6 mm / 2 = 3mm.

The wavelength does not depend on the configuration of the emitter (flat or round wave). λ =6 mm / 2 = 3mm.

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The wavelength λ depends on the frequency of the vibrator; increasing the frequency of the vibrator, the wavelength will decrease.

λ =4 mm / 2 = 2mm.

Conclusions.

1. To observe interference, the wave sources must be coherent.

2. Diffraction is not observed if the width of the obstacle is greater than the wavelength; diffraction is observed if the width of the obstacle is less than the wavelength, therefore, the wave bends around the obstacles.

3. The wavelength does not depend on the configuration of the emitter (flat or round wave).

4. The wavelength depends on the frequency of the vibrator, increasing the frequency of the vibrator - the wavelength will decrease.

5. This work can be used when studying wave phenomena in grade 9 and grade 11.

Bibliography:

1. Landsberg physics textbook. M.: Nauka, 1995.

2., Kikoin 9th grade. M.: Education, 1997.

3. Encyclopedia for children. Avanta +. T.16, 2000.

4. Savelyev general physics. Book 1.M.: Science, 2000.

5. Internet resources:

http://en. wikipedia. org/wiki/Wave

http://www. /article/index. php? id_article=1898

http://www. /node/1785

DEFINITION

Running waves are called waves that transfer energy in space. Energy transfer in waves is quantitatively characterized by the energy flux density vector. This vector is called the flux vector. (For elastic waves – the Umov vector).

Theory about the traveling wave equation

When we talk about the movement of a body, we mean the movement of the body itself in space. In the case of wave motion we're talking about not about the movement of a medium or field, but about the movement of an excited state of a medium or field. In a wave, a certain state, initially localized in one place in space, is transferred (moved) to other, neighboring points in space.

The state of the environment or field at a given point in space is characterized by one or more parameters. Such parameters, for example, in a wave formed on a string, is the deviation of a given section of the string from the equilibrium position (x), in a sound wave in the air, this is a quantity characterizing the compression or expansion of , in are the modules of the vectors and . The most important concept for any wave is phase. Phase refers to the state of the wave at a given point and at this moment time described by the corresponding parameters. For example, the phase of an electromagnetic wave is given by the modules of the vectors and . The phase changes from point to point. Thus, the wave phase in a mathematical sense is a function of coordinates and time. The concept of wave surface is related to the concept of phase. This is a surface, all points of which at a given time are in the same phase, i.e. this is the constant phase surface.

The concepts of wave surface and phase allow us to carry out some classification of waves according to the nature of their behavior in space and time. If wave surfaces move in space (for example, ordinary waves on the surface of water), then the wave is called a traveling wave.

Traveling waves can be divided into: and cylindrical.

Traveling plane wave equation

In exponential form, the spherical wave equation is:

Where – complex amplitude. Everywhere, except for the singular point r=0, the function x satisfies the wave equation.

Cylindrical traveling wave equation:

where r is the distance from the axis.

Where – complex amplitude.

Examples of problem solving

EXAMPLE 1

Exercise	A plane undamped sound wave is excited by a source of oscillations of the source frequency a. Write the equation of oscillations of the source x(0,t), if at the initial moment the displacement of the source points is maximum.
Solution	Let us write the equation of the traveling wave, knowing that it is plane: We use w= in the equation, write (1.1) at the initial moment of time (t=0): From the conditions of the problem it is known that at the initial moment the displacement of the source points is maximum. Hence, . We get: , from here at the point where the source is located (i.e. at r=0).

Wave(Wave, surge, sea) - formed due to the adhesion of particles of liquid and air; sliding along the smooth surface of the water, at first the air creates ripples, and only then, acting on its inclined surfaces, gradually develops agitation of the water mass. Experience has shown that water particles do not have forward motion; moves only vertically. Sea waves are the movement of water on the sea surface that occurs at certain intervals.

The highest point of the wave is called comb or the top of the wave, and the lowest point is sole. Height of a wave is the distance from the crest to its base, and length this is the distance between two ridges or soles. The time between two crests or troughs is called period waves.

Main causes

On average, the height of a wave during a storm in the ocean reaches 7-8 meters, usually it can stretch in length - up to 150 meters and up to 250 meters during a storm.

In most cases, sea waves are formed by the wind. The strength and size of such waves depend on the strength of the wind, as well as its duration and “acceleration” - the length of the path along which the wind acts on the water surface. Sometimes the waves that hit the coast can originate thousands of kilometers from the coast. But there are many other factors in the occurrence of sea waves: these are the tidal forces of the Moon and the Sun, fluctuations in atmospheric pressure, eruptions of underwater volcanoes, underwater earthquakes, and the movement of sea vessels.

Waves observed in other water bodies can be of two types:

1) Wind created by the wind, taking on a steady character after the wind ceases to act and called established waves, or swell; Wind waves are created due to the action of wind (movement of air masses) on the surface of the water, that is, injection. The reason for the oscillatory movements of the waves becomes easy to understand if you notice the effect of the same wind on the surface of a wheat field. The inconstancy of wind flows, which create waves, is clearly visible.

2) Waves of movement, or standing waves, are formed as a result of strong tremors at the bottom during earthquakes or excited, for example, by a sharp change in atmospheric pressure. These waves are also called single waves.

Unlike tides and currents, waves do not move masses of water. The waves move, but the water remains in place. A boat that rocks on the waves does not float away with the wave. She will be able to move slightly along an inclined slope only thanks to the force of earth's gravity. Water particles in a wave move along rings. The further these rings are from the surface, the smaller they become and, finally, disappear completely. Being in a submarine at a depth of 70-80 meters, you will not feel the effect of sea waves even during the most severe storm on the surface.

Types of sea waves

Waves can travel great distances without changing shape and losing virtually no energy, long after the wind that caused them has died down. Breaking on the shore, sea waves release enormous energy accumulated during the journey. The force of continuously breaking waves changes the shape of the shore in different ways. The spreading and rolling waves wash the shore and are therefore called constructive. Waves crashing onto the shore gradually destroy it and wash away the beaches that protect it. That's why they are called destructive.

Low, wide, rounded waves away from the shore are called swells. Waves cause water particles to describe circles and rings. The size of the rings decreases with depth. As the wave approaches the sloping shore, the water particles in it describe increasingly flattened ovals. Approaching the shore, the sea waves can no longer close their ovals, and the wave breaks. In shallow water, the water particles can no longer close their ovals, and the wave breaks. Headlands are formed from harder rock and erode more slowly than adjacent sections of the coast. Steep, high sea waves undermine the rocky cliffs at the base, creating niches. Cliffs sometimes collapse. The terrace, smoothed by the waves, is all that remains of the rocks destroyed by the sea. Sometimes water rises along vertical cracks in the rock to the top and breaks out to the surface, forming a funnel. The destructive force of the waves widens the cracks in the rock, forming caves. When the waves wear away at the rock on both sides until they meet at a break, arches are formed. When the top of the arch falls into the sea, stone pillars remain. Their foundations are undermined and the pillars collapse, forming boulders. The pebbles and sand on the beach are the result of erosion.

Destructive waves gradually erode the coast and carry away sand and pebbles from sea beaches. Bringing the full weight of their water and washed-away material onto slopes and cliffs, the waves destroy their surface. They squeeze water and air into every crack, every crevice, often with explosive energy, gradually separating and weakening the rocks. The broken rock fragments are used for further destruction. Even the hardest rocks are gradually destroyed, and the land on the shore changes under the influence of waves. Waves can destroy the seashore with amazing speed. In Lincolnshire, England, erosion (destruction) is advancing at a rate of 2 m per year. Since 1870, when the largest lighthouse in the United States was built at Cape Hatteras, the sea has washed away beaches 426 m inland.

Tsunami

Tsunami These are waves of enormous destructive power. They are caused by underwater earthquakes or volcanic eruptions and can cross oceans faster than a jet plane: 1000 km/h. In deep waters, they can be less than one meter, but, approaching the shore, they slow down and grow to 30-50 meters before collapsing, flooding the shore and sweeping away everything in their path. 90% of all recorded tsunamis occurred in Pacific Ocean.

The most common reasons.

About 80% of tsunami generation cases are underwater earthquakes. During an earthquake under water, a mutual vertical displacement of the bottom occurs: part of the bottom sinks, and part rises. Oscillatory movements occur vertically on the surface of the water, tending to return to the original level - the average sea level - and generate a series of waves. Not every underwater earthquake is accompanied by a tsunami. Tsunamigenic (that is, generating a tsunami wave) is usually an earthquake with a shallow source. The problem of recognizing the tsunamigenicity of an earthquake has not yet been solved, and warning services are guided by the magnitude of the earthquake. The most powerful tsunamis are generated in subduction zones. Also, it is necessary for the underwater shock to resonate with the wave oscillations.

Landslides. Tsunamis of this type occur more frequently than estimated in the 20th century (about 7% of all tsunamis). Often an earthquake causes a landslide and it also generates a wave. On July 9, 1958, an earthquake in Alaska caused a landslide in Lituya Bay. A mass of ice and earth rocks collapsed from a height of 1100 m. A wave was formed that reached a height of more than 524 m on the opposite shore of the bay. Cases of this kind are quite rare and are not considered as a standard. But underwater landslides occur much more often in river deltas, which are no less dangerous. An earthquake can cause a landslide and, for example, in Indonesia, where shelf sedimentation is very large, landslide tsunamis are especially dangerous, as they occur regularly, causing local waves more than 20 meters high.

Volcanic eruptions account for approximately 5% of all tsunami events. Large underwater eruptions have the same effect as earthquakes. In large volcanic explosions, not only are waves generated from the explosion, but water also fills the cavities of the erupted material or even the caldera, resulting in a long wave. A classic example is the tsunami generated after the Krakatoa eruption in 1883. Huge tsunamis from the Krakatoa volcano were observed in harbors around the world and destroyed a total of more than 5,000 ships and killed about 36,000 people.

Signs of a tsunami.

• Sudden fast the withdrawal of water from the shore over a considerable distance and the drying of the bottom. The further the sea recedes, the higher the tsunami waves can be. People who are on the shore and do not know about dangers, may stay out of curiosity or to collect fish and shells. In this case, it is necessary to leave the shore as soon as possible and move as far away from it as possible - this rule should be followed when, for example, in Japan, on the Indian Ocean coast of Indonesia, or Kamchatka. In the case of a teletsunami, the wave usually approaches without the water receding.
• Earthquake. The epicenter of an earthquake is usually in the ocean. On the coast, the earthquake is usually much weaker, and often there is no earthquake at all. In tsunami-prone regions, there is a rule that if an earthquake is felt, it is better to move further from the coast and at the same time climb a hill, thus preparing in advance for the arrival of the wave.
• Unusual drift ice and other floating objects, formation of cracks in fast ice.
• Huge reverse faults at the edges of stationary ice and reefs, the formation of crowds and currents.

rogue waves

rogue waves(Roaming waves, monster waves, freak waves - anomalous waves) - giant waves that arise in the ocean, more than 30 meters high, have behavior unusual for sea waves.

Just 10-15 years ago, scientists considered sailors’ stories about gigantic killer waves that appear out of nowhere and sink ships as just maritime folklore. For a long time wandering waves were considered fiction, since they did not fit into any mathematical model that existed at that time for calculating the occurrence and their behavior, because waves with a height of more than 21 meters cannot exist in the oceans of planet Earth.

One of the first descriptions of a monster wave dates back to 1826. Its height was more than 25 meters and it was noticed in the Atlantic Ocean near the Bay of Biscay. Nobody believed this message. And in 1840, the navigator Dumont d'Urville risked appearing at a meeting of the French Geographical Society and declaring that he had seen a 35-meter wave with his own eyes. Those present laughed at him. But there were stories about huge ghost waves that suddenly appeared in the middle of the ocean even with little storm, and their steepness resembled sheer walls of water, it became more and more.

Historical evidence of rogue waves

So, in 1933, the US Navy ship Ramapo was caught in a storm in the Pacific Ocean. For seven days the ship was tossed about by the waves. And on the morning of February 7, a shaft of incredible height suddenly crept up from behind. First, the ship was thrown into a deep abyss, and then lifted almost vertically onto a mountain of foaming water. The crew, who were lucky enough to survive, recorded a wave height of 34 meters. It moved at a speed of 23 m/sec, or 85 km/h. So far, this is considered the highest rogue wave ever measured.

During World War II, in 1942, the Queen Mary liner carried 16 thousand American military personnel from New York to the UK (by the way, a record for the number of people transported on one ship). Suddenly a 28-meter wave appeared. “The upper deck was at its usual height, and suddenly - suddenly! - it suddenly went down,” recalled Dr. Norval Carter, who was on board the ill-fated ship. The ship tilted at an angle of 53 degrees - if the angle had been even three degrees more, death would have been inevitable. The story of "Queen Mary" formed the basis of the Hollywood film "Poseidon".

However, on January 1, 1995, on the Dropner oil platform in the North Sea off the coast of Norway, a wave with a height of 25.6 meters, called the Dropner wave, was first recorded by instruments. The Maximum Wave project allowed us to take a fresh look at the causes of the death of dry cargo ships that transported containers and other important cargo. Further studies recorded three weeks throughout to the globe more than 10 single giant waves, the height of which exceeded 20 meters. New project received the name Wave Atlas, which provides for the compilation of a worldwide map of observed monster waves and its subsequent processing and addition.

Causes

There are several hypotheses about the causes of extreme waves. Many of them are deprived common sense. Most simple explanations are based on the analysis of a simple superposition of waves of different lengths. Estimates, however, show that the probability of extreme waves in such a scheme is too small. Another noteworthy hypothesis involves the possibility of focusing wave energy in some surface current structures. These structures, however, are too specific for an energy focusing mechanism to explain the systematic occurrence of extreme waves. The most reliable explanation for the occurrence of extreme waves should be based on the internal mechanisms of nonlinear surface waves without involving external factors.

Interestingly, such waves can be both crests and troughs, which is confirmed by eyewitnesses. Further research involves the effects of nonlinearity in wind waves, which can lead to the formation of small groups of waves (packets) or individual waves (solitons) that can travel long distances without significantly changing their structure. Similar packages have also been observed many times in practice. Characteristic Features Such groups of waves, confirming this theory, are that they move independently of other waves and have a small width (less than 1 km), and the heights drop off sharply at the edges.

However, it has not yet been possible to completely clarify the nature of the anomalous waves.

Surface acoustic waves(SAW) - elastic waves propagating along the surface of a solid body or along the boundary with other media. Surfactants are divided into two types: with vertical polarization and with horizontal polarization ( Love waves).

The most common special cases of surface waves include the following:

• Rayleigh waves(or Rayleigh), in the classical sense, propagating along the boundary of an elastic half-space with a vacuum or a fairly rarefied gaseous medium.
• on the border solid with liquid.
• , running along the boundary of a liquid and a solid body
• Stoneleigh Wave, propagating along the flat boundary of two solid media, the elastic moduli and density of which do not differ much.
• Love waves- surface waves with horizontal polarization (SH type), which can propagate in the elastic layer structure on an elastic half-space.

Encyclopedic YouTube

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✪ Seismic waves

✪ Longitudinal and transverse waves. Sound waves. Lesson 120

✪ Lecture seven: Waves

Subtitles

In this video I want to discuss seismic waves a little bit. Let's write down the topic. These are compressed molecules, they will crash into the molecules nearby and then the stone here will become denser. solids. And, depending on the environment, they move at different speeds. , they move at a speed of 5,000 m/s. Subtitles by the Amara.org community

In the air they move at a speed of 330 m/s, which is not so slow for everyday life.

In liquid they move at a speed of 1,500 m/s.

And in granite, from which most of the

Earth's surface

Earth's surface Rayleigh waves

Damped Rayleigh waves Damped Rayleigh-type waves at the solid-liquid interface. Continuous wave with vertical polarization , running along the boundary of a liquid and a solid at the speed of sound in a given medium.

If vibrations of its particles are excited in any place in an elastic (solid, liquid or gaseous) medium, then, due to the interaction between particles, this vibration will propagate in the medium from particle to particle with a certain speed

v . The process of propagation of vibrations in space is called wave.

A mechanical wave is the process of propagation of vibrations in an elastic medium, which is accompanied by the transfer of energy of a vibrating body from one point of the elastic medium to another.

Particles of the medium in which the elastic wave propagates are not drawn into the wave

forward motion

, they only oscillate around their equilibrium positions. Depending on the direction of particle oscillations relative to the direction of wave propagation, longitudinal and transverse waves are distinguished.

Elastic transverse waves can only arise in a medium that has shear resistance. Therefore, only longitudinal waves can occur in liquid and gaseous media. In a solid medium, both longitudinal and transverse waves can occur.

The geometric location of the points to which the oscillations reach at the moment of time t, called wave front(or wave front).

The geometric location of points oscillating in the same phase is called wave surface. The wave surface can be drawn through any point in space covered by the wave process. Consequently, there is an infinite number of wave surfaces, while there is only one wave front at each moment of time. Wave surfaces can be of any shape. In the simplest cases, they have the shape of a plane or sphere. Accordingly, the wave in these cases is called plane or spherical.

A line perpendicular to the wave surface is called a ray. The beam indicates the direction of wave propagation.

Distance, over which the wave propagates in a time equal to the period of oscillation of the particles of the medium, is called wavelength:

 v(m),

Where Damped Rayleigh-type waves at the solid-liquid interface.wave speed, T – period of oscillation.

The wavelength can also be defined as the distance between the nearest points of the medium oscillating with a phase difference equal to 2 .

Wave speed v .

Harmonic wave

A harmonic wave is a linear monochromatic wave propagating in an infinite dynamic system. In distributed systems, the general form of the wave is given by the equation:

Where A– some constant amplitude of the wave process, determined by the parameters of the system, the frequency of oscillations and the amplitude of the disturbing force; w = 2p/ T= 2pn – circular frequency of the wave process, T– period of the harmonic wave, n – frequency; k= 2p/l = w/ With– wave number, l – wave length, – wave propagation speed; – initial phase wave process, determined in a harmonic wave by the pattern of the influence of external disturbance. The phase speed of this wave is given by

traveling wave

traveling wave– a wave that, when propagating through a medium, transfers energy (as opposed to a standing wave). Examples: elastic wave in a rod, column of gas, liquid, electromagnetic wave along a long line, in a waveguide.

A traveling harmonic wave is a special case of stationary traveling waves; it is a propagating sinusoidal oscillation; it is the simplest wave motion.

Sound

Vibrations in the environment perceived by the organ of hearing are called sound.

Sound, in a broad sense - elastic waves, propagating in any elastic medium and creating mechanical vibrations in it; in a narrow sense, the subjective perception of these vibrations by the special sense organs of animals or humans.

The branch of physics that deals with the study of sound phenomena is called acoustics.

A sound wave is an elastic longitudinal wave, which represents zones of compression and rarefaction of an elastic medium (air), transmitted over a distance over time.

Sound waves are divided:

· audible sound – from 20 Hz (17 m) - to 20,000 Hz (17 mm);

· infrasound – below 20 Hz;

· ultrasound – above 20,000 Hz.

The speed of sound depends on the elastic properties of the medium and on temperature, for example:

in the air Damped Rayleigh-type waves at the solid-liquid interface.= 331 m/s (at t = 0 o C) and Damped Rayleigh-type waves at the solid-liquid interface.= 3317 m/s (at t = 1 0 C);

in water Damped Rayleigh-type waves at the solid-liquid interface.= 1400 m/s;

in steel Damped Rayleigh-type waves at the solid-liquid interface.=5000 m/s.

The sound produced by a harmoniously vibrating body is called a musical tone.

Each musical tone (do, re, mi, fa, sol, la, si) corresponds to a certain length and frequency of the sound wave.

Noise is a chaotic mixture of tones.

Wave interference

If several waves propagate in a medium, then the vibrations of the particles of the medium turn out to be geometric sum oscillations that the particles would make during the propagation of each of the waves separately. Waves overlap Each other,without disturbing(without distorting each other). That's what it is principle of wave superposition.

If two waves arriving at any point in space have a constant phase difference, such waves are called coherent. When coherent waves are added, a interference phenomenon.

Wave interference(from Latin inter - mutually, between each other and ferio - I hit, I hit) - mutual amplification or weakening of the amplitude of two or more coherent waves simultaneously propagating in space. Accompanied by alternating maxima and minima (antinodes) of intensity in space.

The result of interference (interference pattern) depends on the phase difference of the superimposed waves. During interference, wave energy is redistributed in space. This does not contradict the law of conservation of energy because, on average, for a large region of space, the energy of the resulting wave is equal to the sum of the energies of the interfering waves.

The necessary conditions to observe interference:

1) the waves must have the same (or close) frequencies so that the picture resulting from the superposition of waves does not change over time (or does not change very quickly so that it can be recorded in time);

2) the waves must be unidirectional (or have a similar direction); two perpendicular waves will never interfere (try adding two perpendicular sine waves!). In other words, the waves being added must have identical wave vectors (or closely directed ones).

The first condition is sometimes called temporal coherence,
second – spatial coherence.

Interference is typical for waves of any nature.

A very important case of interference is observed when two counterpropagating plane waves with the same amplitude are superimposed. The resulting oscillatory process is called standing wave . Almost standing waves arise when reflected from obstacles.

Interference of waves on the surface of water:

Standing waves

A very important case of interference is observed when two counterpropagating plane waves with the same amplitude are superimposed. Practically standing waves occur when waves are reflected from obstacles. A wave falling on an obstacle and a reflected wave running towards it, superimposing on each other, give a standing wave.

A standing wave is a special case of a traveling wave with .

That is, two identical periodic traveling waves (within the framework of the superposition principle), propagating in opposite directions, form a standing wave.

When a standing wave exists in a medium, there are points at which the amplitude of oscillations is zero. These points are called nodes standing wave. The points at which the oscillations have maximum amplitude are called antinodes.