3 examples of longitudinal waves

7 Real Life Examples Of Longitudinal Waves

Have you ever noticed a slinky or a spring waving back and forth, just like shown below? This type of motion in which particles move along the direction of the wave back and forth is a longitudinal motion.

Longitudinal waves are the waves in which the particles of the medium propagates along the direction of the motion. Simply, particles travel along the direction of the motion or a wave. They are composed of compression (when particles/wave move close to each other) and rarefaction (when particles/wave move away). They require a medium to travel.

Let’s explore the examples of Longitudinal wave in our daily life.

1. Speaking on the mic

A sound wave is a significant example of a longitudinal wave. When a speaker speaks some words in front of the microphone, he/she hit the air thousands of time per second at different frequencies. The sound particles travel along with the air particles and enter the mic to produce sound.

2. Clapping

When we clap while singing a birthday song or on any other occasion, do you know, what makes our hand produce that familiar sound of a clap. When we applaud, we compress and displace the air particles between our hands for a part of a second, which produces the sound of a clap we are familiar with.

All of us are familiar with the sound of a drum, and most of us have also tried hitting the drum in different beats. When we hit the drum with the mallet, drum head vibrates and produce soundwaves. The soundwaves are generated because the drum head moves outward and inward, making air particles to move (vibrate) in the same direction.

4. Tsunami Waves

Tsunamis cause damage to coastal regions and that’s why people residing in coastal areas are afraid of them. Most people think that sea waves are a transverse wave as they go up and down. However, sea waves, including Tsunami, are the example of both transverse as well as a longitudinal wave. When the waves reach the shore or smaller areas, they become smaller and thinner, and water particles move parallel to the wave, hence making it a longitudinal wave.

5. Earthquake (Seismic-P wave)

It is said that animals can sense the earthquake waves much before humans. They have the ability to sense the seismic P waves, which travel only in the interior of the earth. Even humans can feel a little bump and rattle of these waves, but they are mostly unnoticeable to us. The P waves are the fastest, and they require a medium to travel (solid and liquid). These waves cause the interior of the earth (tectonic plates) to move back and forth in a longitudinal manner, which leads to the surface waves (seismic S wave), which we can feel.

6. Vibration in Window Panels after a Thunder

Whenever it is raining heavily, and thunders are there, you might have noticed the vibration in window panels of your home; it happens because of sound waves. Lightning causes an increase in the air pressure and temperature, which creates a shock wave of sound that we hear like a loud boom and cause our window panels to vibrate.

7. Music Woofers

Have you ever noticed the movement of the woofer cone; moving in and out or ever felt air pressure on your hand when you try to cover the mouth of a woofer? It’s because woofers work on the phenomenon of a longitudinal wave. They move the air particles in or out, producing sound.

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Sours: https://studiousguy.com/real-life-examples-longitudinal-wave/

The pattern of disturbances is of two types or in other words the formation of waves is done in two different methods. We know that the energy of the particles in motion is transmitted in the form of waves. Depending on the type of motion two forms of waves are classified, the first one is a longitudinal wave and the second is a Transverse wave. The longitudinal motion or the longitudinal wave are found when the energy has to be transmitted within the medium. Whereas the transverse waves are formed at the surface.

The best example of longitudinal waves is the sound wave, in order to receive the sound wave we definitely require a medium which is generally an air medium. This is the main reason why the sound waves can not propagate in a vacuum. In this article, we will discuss what are longitudinal waves, examples of longitudinal waves, formation of longitudinal waves, etc…

Examples of Longitudinal Waves:

The longitudinal waves are mechanical waves and these are readily used in nature for transmitting energy from one point to another within the medium. There are several examples of longitudinal waves. Sound waves are the most common example of longitudinal waves, pressure waves, spring waves, etc… Let’s have a look at these examples in detail to understand the concept of longitudinal waves.

1. Sound Waves in the Air:

Yes, the sound waves are longitudinal in nature. When we speak, the sound wave propagates through the air medium and reaches the audience. The sound waves are the best example of a longitudinal wave and are produced by vibrating or disturbing the motion of the particles that travel through a conductive medium. An example of sound waves in a longitudinal direction of propagation is the tuning fork. In sound waves, the amplitude of the wave is always the difference between the maximum pressure caused by the wave and the pressure of the undisturbed air. The propagation speed of sound depends upon the type, composition of the medium, and temperature through which it will propagate.

2. The Primary Waves of an Earthquake:

It is said that animals can sense earthquake waves much before humans. They have the ability to sense the seismic P waves, which travel only in the interior of the earth. Even humans can experience a little bump and rattle of these waves, but they are mostly unnoticeable to us. The P waves are the fastest waves, and they require a medium to travel either solid or liquid. The P waves cause the interior of the earth i.e., tectonic plates to move back and forth (in other words to oscillate)  in a longitudinal manner, which leads to the surface waves i.e., seismic S waves, which we can feel.

3. The Vibration in a Spring:

Consider a small spring, suppose we knock the end of the spring, the waves that formed will flow through the spring. The waves formed will propagate within the spring and hence they are considered to be the longitudinal waves. At the same time, if one end of the spring is fixed, the waves will propagate in up and down direction resulting in transverse waves.

[Image will be uploaded soon]

4. The Tsunami Waves:

We know that tsunamis are dangerous natural disasters that may lead to severe loss to human beings. Tsunamis cause damage to coastal regions (sea shore) and that’s the reason why people residing in coastal regions are afraid of them. Most people think that sea waves are transverse waves as they keep travelling in to and fro motion i.e., they go up and down continuously. However, water or sea waves, including Tsunami, are an example of both transverse as well as a longitudinal wave. When the waves reach the shore or remote areas, they become comparatively smaller and thinner, and water molecules move parallel to the wave, hence making it a longitudinal wave.

Transverse and Longitudinal Waves:

Let us understand what are transverse and longitudinal waves with the following list of differences. Both the longitudinal and transverse play an important role in elaborating the concept of sound. Thus the major difference between the transverse wave and longitudinal wave are as follows:

 Sl. No Longitudinal Waves Transverse Waves 1. longitudinal wave definition:To define longitudinal waves, it is the type of disturbance, such that the particles will be executing the to and fro motion about their mean position will have longitudinal waves. Transverse wave definition:The particles executing the up and down motion about their mean position will have transverse waves. 2. The longitudinal waves consist of compression and rarefaction, hence they are also referred to as the compressional wave. The transverse waves consist of crest and trough. 3. Longitudinal waves can propagate through any media, such as the longitudinal can propagate through a gas medium, air medium, water, solids, etc... Transverse waves can only propagate only through solids and at the surfaces of the liquid medium. 4. The longitudinal waves are graphically represented by the density-distance graph. The transverse waves are graphically represented by the displacement-distance graph. 5. In longitudinal waves, the pressure and density will be during maximum for compression and minimum during rarefaction In transverse waves, there is no variation in the value of density and pressure. 6. Examples of longitudinal waves:Sound waves, Vibration in spring, Tsunami waves, etc... Examples of transverse waves:Electromagnetic waves, water waves caused by external disturbance, etc... 7. [Image will be uploaded soon] [Image will be uploaded soon]

These are some major and important differences between the longitudinal waves and the transverse wave.

Did You Know:

• Dogs are sensitive to sound at a higher frequency than humans, allowing them to hear noises that humans can not.

• Sound waves are used by many animals to detect danger, warning them of possible attacks before they happen.

• Sound can not travel through a vacuum (an area empty of matter), it requires a medium.

• The speed of sound is around 767 miles per hour.

• The loud noise you create by cracking a whip occurs because the tip is moving with a high frequency and speed it breaks the speed of sound.

Sours: https://www.vedantu.com/physics/longitudinal-wave

Longitudinal and transverse waves

In longitudinal waves, the vibrations are parallel to the direction of wave travel.

Examples of longitudinal waves include:

• sound waves
• ultrasound waves
• seismic P-waves

One way to remember the movement of particles in longitudinal waves is to use the ‘P’ sound: longitudinal waves such as seismic P-waves may be thought of as pressure or push waves as the particles move parallel to the wave.

Demonstrating longitudinal waves

Longitudinal waves show areas of compression and rarefaction:

• compressions are regions of high pressure due to particles being close together
• rarefactions are regions of low pressure due to particles being spread further apart

In the diagram, the compressions move from left to right and energy is transferred from left to right. However, none of the particles are transported along a longitudinal wave. Instead, they move backwards and forwards between compressions as the wave is transmitted through the medium.

Transverse waves

In tranverse waves, the vibrations are at right angles to the direction of wave travel.

Examples of transverse waves include:

• ripples on the surface of water
• vibrations in a guitar string
• a Mexican wave in a sports stadium
• electromagnetic waves – eg light waves, microwaves, radio waves
• seismic S-waves

One way to remember the movement of particles in transverse waves is to use the ‘S’ sound: transverse waves such as seismic S-waves may be thought of as shake or shear waves as the particles move from side-to-side – crossing the direction of wave travel.

Demonstrating transverse waves

Transverse waves are often demonstrated by moving a rope rapidly up and down.

In the diagram the rope moves up and down, producing peaks and troughs. Energy is transferred from left to right. However, none of the particles are transported along a transverse wave. The particles move up and down as the wave is transmitted through the medium.

Sours: https://www.bbc.co.uk/bitesize/guides/zs86v9q/revision/2
Transverse and Longitudinal Waves

Longitudinal wave

Waves in which the direction of media displacement is parallel to the direction of travel

Plane pressure pulse wave

Longitudinal waves are waves in which the vibration of the medium is parallel to the direction the wave travels and displacement of the medium is in the same (or opposite) direction of the wave propagation. Mechanical longitudinal waves are also called compressional or compression waves, because they produce compression and rarefaction when traveling through a medium, and pressure waves, because they produce increases and decreases in pressure. A wave along the length of a stretched Slinky toy, where the distance between coils increases and decreases, is a good visualization. Real-world examples include sound waves (vibrations in pressure, a particle of displacement, and particle velocity propagated in an elastic medium) and seismic P-waves (created by earthquakes and explosions).

The other main type of wave is the transverse wave, in which the displacements of the medium are at right angles to the direction of propagation. Transverse waves, for instance, describe some bulk sound waves in solid materials (but not in fluids); these are also called "shear waves" to differentiate them from the (longitudinal) pressure waves that these materials also support.

Nomenclature

"Longitudinal waves" and "transverse waves" have been abbreviated by some authors as "L-waves" and "T-waves", respectively, for their own convenience.[1] While these two abbreviations have specific meanings in seismology (L-wave for Love wave[2] or long wave[3]) and electrocardiography (see T wave), some authors chose to use "l-waves" (lowercase 'L') and "t-waves" instead, although they are not commonly found in physics writings except for some popular science books.[4]

Sound waves

Further information: Acoustic theory

In the case of longitudinal harmonic sound waves, the frequency and wavelength can be described by the formula

where:

• y is the displacement of the point on the traveling sound wave;
Representation of the propagation of an omnidirectional pulse wave on a 2d grid (empirical shape)
• x is the distance from the point to the wave's source;
• t is the time elapsed;
• y0 is the amplitude of the oscillations,
• c is the speed of the wave; and
• ω is the angular frequency of the wave.

The quantity x/c is the time that the wave takes to travel the distance x.

The ordinary frequency (f) of the wave is given by

The wavelength can be calculated as the relation between a wave's speed and ordinary frequency.

For sound waves, the amplitude of the wave is the difference between the pressure of the undisturbed air and the maximum pressure caused by the wave.

Sound's propagation speed depends on the type, temperature, and composition of the medium through which it propagates.

Pressure waves

The equations for sound in a fluid given above also apply to acoustic waves in an elastic solid. Although solids also support transverse waves (known as S-waves in seismology), longitudinal sound waves in the solid exist with a velocity and wave impedance dependent on the material's density and its rigidity, the latter of which is described (as with sound in a gas) by the material's bulk modulus.[5]

Electromagnetics

Maxwell's equations lead to the prediction of electromagnetic waves in a vacuum, which is strictly transverse waves, that is, the electric and magnetic fields of which the wave consists are perpendicular to the direction of the wave's propagation.[6] However plasma waves are longitudinal since these are not electromagnetic waves but density waves of charged particles, but which can couple to the electromagnetic field.[6][7][8]

After Heaviside's attempts to generalize Maxwell's equations, Heaviside concluded that electromagnetic waves were not to be found as longitudinal waves in "free space" or homogeneous media.[9] Maxwell's equations, as we now understand them, retain that conclusion: in free-space or other uniform isotropic dielectrics, electro-magnetic waves are strictly transverse. However electromagnetic waves can display a longitudinal component in the electric and/or magnetic fields when traversing birefringent materials, or inhomogeneous materials especially at interfaces (surface waves for instance) such as Zenneck waves.[10]

In the development of modern physics, Alexandru Proca (1897-1955) was known for developing relativistic quantum field equations bearing his name (Proca's equations) which apply to the massive vector spin-1 mesons. In recent decades some other theorists, such as Jean-Pierre Vigier and Bo Lehnert of the Swedish Royal Society, have used the Proca equation in an attempt to demonstrate photon mass [11] as a longitudinal electromagnetic component of Maxwell's equations, suggesting that longitudinal electromagnetic waves could exist in a Dirac polarized vacuum. However photon rest mass is strongly doubted by almost all physicists and is incompatible with the Standard Model of physics.[citation needed]

References

1. ^Erhard Winkler (1997), Stone in Architecture: Properties, Durability, p.55 and p.57, Springer Science & Business Media
2. ^Michael Allaby (2008), A Dictionary of Earth Sciences (3rd ed.), Oxford University Press
3. ^Dean A. Stahl, Karen Landen (2001), Abbreviations Dictionary, Tenth Edition, p.618, CRC Press
4. ^Francine Milford (2016), The Tuning Fork, pp.43–44
5. ^Weisstein, Eric W., "P-Wave". Eric Weisstein's World of Science.
6. ^ abDavid J. Griffiths, Introduction to Electrodynamics, ISBN 0-13-805326-X
7. ^John D. Jackson, Classical Electrodynamics, ISBN 0-471-30932-X.
8. ^Gerald E. Marsh (1996), Force-free Magnetic Fields, World Scientific, ISBN 981-02-2497-4
9. ^Heaviside, Oliver, "Electromagnetic theory". Appendices: D. On compressional electric or magnetic waves. Chelsea Pub Co; 3rd edition (1971) 082840237X
10. ^Corum, K. L., and J. F. Corum, "The Zenneck surface wave", Nikola Tesla, Lightning Observations, and stationary waves, Appendix II. 1994.
11. ^Lakes, Roderic (1998). "Experimental Limits on the Photon Mass and Cosmic Magnetic Vector Potential". Physical Review Letters. 80 (9): 1826–1829. Bibcode:1998PhRvL..80.1826L. doi:10.1103/PhysRevLett.80.1826.

• Varadan, V. K., and Vasundara V. Varadan, "Elastic wave scattering and propagation". Attenuation due to scattering of ultrasonic compressional waves in granular media - A.J. Devaney, H. Levine, and T. Plona. Ann Arbor, Mich., Ann Arbor Science, 1982.
• Schaaf, John van der, Jaap C. Schouten, and Cor M. van den Bleek, "Experimental Observation of Pressure Waves in Gas-Solids Fluidized Beds". American Institute of Chemical Engineers. New York, N.Y., 1997.
• Krishan, S.; Selim, A. A. (1968). "Generation of transverse waves by non-linear wave-wave interaction". Plasma Physics. 10 (10): 931–937. Bibcode:1968PlPh...10..931K. doi:10.1088/0032-1028/10/10/305.
• Barrow, W.L. (1936). "Transmission of Electromagnetic Waves in Hollow Tubes of Metal". Proceedings of the IRE. 24 (10): 1298–1328. doi:10.1109/JRPROC.1936.227357.
• Russell, Dan, "Longitudinal and Transverse Wave Motion". Acoustics Animations, Pennsylvania State University, Graduate Program in Acoustics.
• Longitudinal Waves, with animations "The Physics Classroom"
Sours: https://en.wikipedia.org/wiki/Longitudinal_wave

Acoustics and Vibration Animations

Another example of waves with both longitudinal and transverse motion may be found in solids as Rayleigh surface waves (named after John W. Strutt, 3rd Baron Rayleigh who first studied them in 1885). The particles in a solid, through which a Rayleigh surface wave passes, move in elliptical paths, with the major axis of the ellipse perpendicular to the surface of the solid. As the depth into the solid increases the "width" of the elliptical path decreases.

Rayleigh waves in an elastic solid are different from surface waves in water in a very important way. In a water wave all particles travel in clockwise circles. However, in a Rayleigh surface wave, particles at the surface trace out a counter-clockwise ellipse, while particles at a depth of more than 1/5th of a wavelength trace out clockwise ellispes. This motion is often referred to as being "retrograde" since at the surface, the horizontal component of the particle motion is in the opposite direction as the wave propagation direction. I have identified two particles in orange in this animation to illustrate the retrograde elliptical path at the surface and the reversal in the direction of motion as a function of depth.

The Rayleigh surface waves are the waves that cause the most damage during an earthquake. They travel with velocities slower than S waves, and arrive later, but with much greater amplitudes. These are also the waves that are most easily felt during an earthquake and involve both up-down and side-to-side motion.

Update (Aug. 5, 2016): Thanks to Dongyao Li (graduate student at the University of Illinois, Urbana-Champaign) who asked questions resulting in a much improved version of this animation.

Sours: http://www.acs.psu.edu/drussell/Demos/waves/
Different Types of Waves : Longitudinal \u0026 Transverse Waves - Mechanical Wave - Physics

In physics, waves refer to disturbances in a medium carrying energy without a net movement of particles. The two most common types of waves are electromagnetic and mechanical waves. Both transmit information, energy, and momentum, but they do not transfer particles in the medium.

A mechanical wave is a vibration in matter, which transfers energy through a substance. However, an electromagnetic wave (such as light) can travel through a vacuum.

Mechanical waves can be further categorized based on the ways they propagate. The three propagation types are transverse, longitudinal, and surface waves. In this article, we will focus on longitudinal waves.

What are longitudinal waves?

In a longitudinal wave, particles move in a medium in the same dimension as the direction of movement of the wave. In other words, the displacement of the particle is parallel to the direction the wave is moving.

Figure 1

A simple example of such waves is compressions moving along a slinky. One can generate a longitudinal wave by pushing and pulling the slinky horizontally.

When traveling through a medium, these waves create compression and rarefaction.

• Compressions are high-pressure regions where wave particles are close together.
• Rarefactions are low-pressure regions where particles are spread further apart.

As you can see in figure 1, compressions travel from left to right, and energy is transferred in the same direction. However, not even a single particle is transported along the longitudinal wave. Instead, they all move forward and backward between compression as the wave travels through a medium.

The distance between the centers of two consecutive regions (between compressions or rarefactions) determines the wavelength of the longitudinal wave. It can be produced in any medium, including solid, liquid, and gas.

To better explain this phenomenon, we have listed some of the best examples of longitudinal waves that people see in their everyday life.

9. Vibrating Tuning Fork

Form: Sound waves

A tuning fork clearly illustrates how a vibrating object can generate sound. It contains a handle and two prongs made of elastic metal (generally steel). When you hit the tuning fork with a rubber hammer, its prongs start to vibrate, producing disturbances of nearby air molecules.

As the prong stretches outward from its normal position, the surrounding air contracts, creating a high-pressure region (compression) next to the prong. As the prong then moves inward, it expands the surrounding air molecules into a large region of space, which creates a low-pressure region (rarefaction) next to the prong.

As long as prongs vibrate, they create an alternating pattern of high and low-pressure regions. These regions travel through the adjacent air molecules, carrying sound signals from one place to another.

8. Diagnostic Sonography

Sonogram of a fetus in the womb | Wikimedia

Form: High-frequency sound waves

Sonography uses ultrasound waves to create images of internal body parts, such as blood vessels, muscles, joints, tendons, and internal organs. These sonograms (also called ultrasonic images) are formed by transferring ultrasound pulses into tissue using a probe. The pluses echo off tissues with distinct reflection characteristics and are processed and converted into a digital image.

Unlike other medical imaging techniques, ultrasound provides pictures in real-time. The instruments are portable, less expensive, and do not use harmful ionizing radiation. However, they offer a limited field of view and require a skilled operator.

7. Windows Shake When Thunder Strikes Nearby

Form: Sound waves

During a thunderstorm, discharges of lightning produce powerful and fast pressure waves that propagate for very long distances. When these waves reach your office/home, they cause window panes to vibrate in the same manner our eardrum vibrates in response to sound waves.

Based on the attributes of the office/home and its windows (such as level of insulation, the structure of window frames, and thickness of glass), vibrating window panes can create their own distinctive noise. Most of the time, it sounds like rattling or buzzing.

6. Tsunamis

Form: Water waves (or surface waves)

Tsunami is not something that you see every day, but still, we have included this in our list to cover every aspect of longitudinal waves. Tsunami is very different from tidal waves: it is caused by an earthquake underwater.

Unlike typical ocean waves, tsunami waves are created when water moves under the influences of gravity and radiates across the ocean like ripples on a pond. While normal waves only involve the movements of the upper layers of the water, tsunami involves motions of the entire column from the seafloor to the surface.

As waves travel through the water, particles move in a circular pattern. The radius of these circles decreases as the depth into the water increases. This means, at the greater depth, water waves act as longitudinal waves. And near the surface, water waves behave as transverse waves.

5. Non-Destructive Testing

Form:  High-frequency sound waves

Non-destructive testing is a wide range of examination techniques used in the science and tech industry to assess the properties of a system, component, or material without damaging it.

One of those frequently used techniques is ultrasonic testing, which relies on the propagation of ultrasound waves in the material or object being tested. Very short ultrasonic pulses with frequencies between 0.1 and 50 MHz are transmitted into components to find internal flaws or material properties.

Since ultrasound waves have high sensitivity and high penetrating power, they allow the detection of extremely small flaws hidden deep in the parts. The technique provides immediate results, so engineers can make spot decisions. It is mostly used on metal alloys and concrete.

Form: Low-frequency sounds

Subwoofers are designed to reproduce low-pitched audio frequencies ranging from 20 to 200 Hz for consumer products and less than 100 Hz for professional live audio systems. They are never used alone; instead, they augment the low-frequency range of speakers that cover higher frequency bands.

When you play a song, you can see small movements in the woofer cone. It actually moves in and out, and if you try to cover its mouth, you can feel the air pressure on your hand. That’s because woofers produce longitudinal waves by moving air particles in and out.

3. Seismic P-Waves

P waves (arrows in yellow) can penetrate through the mantle and core | Image credit: Byron Inouye

Form: Seismic waves

Seismic waves travel through the layers of Earth. They are produced by volcanic eruptions, earthquakes, large landslides, magma movements, and large human-made explosions. There are two types of seismic waves that travel through the Earth’s interior: Primary (P) and Secondary (S) waves.

Primary waves (also called pressure waves) are longitudinal in nature. They travel faster than other waves (up to 8 km/s in Earth’s mantle and core, and 6 km/s in Earth’s crust) and thus are the first signals detected on seismographs.

P-waves can travel through solid rocks and fluids (liquid layers) of the Earth in a special pattern. Some animals can hear the P waves generated from an earthquake. Cats and dogs, for example, start acting strangely minutes before the earthquake. In contrast, humans can only sense the bump and rattle of these waves.

2. Sonic Weapons

A Long-Range Acoustic Device on the USS Blue Ridge

Form: Powerful sound waves

Sonic weapons use high ultrasound frequencies to incapacitate, injure, or kill opponents. While they are used by military and police forces, several types of sonic weapons are currently in the research and development phase.

These weapons produce longitudinal sound waves that can cause humans to experience discomfort or nausea. They are often used to disperse protestors and rioters in crowd control efforts.

Weapons using high-power sound waves can destroy opponents’ eardrums, causing severe pain or disorientation. Studies show that exposure to high-intensity ultrasound (700 kHz – 3.6 MHz) causes intestinal and lung damage in mice.

Read: 11 Different Types Of Energy With Examples

1. Acoustic Microscopy

A scanning acoustic microscope

Form: Ultra high-frequency ultrasound

Acoustic microscopes can penetrate most solid materials, revealing their internal features such as cracks, voids, and delaminations. They operate in frequencies ranging from 10 MHz to 500 MHz.

Scanning acoustic microscopes, for example, are often used in biological and medical research. They provide data on the elasticity of tissues and cells, which gives invaluable information on the physical forces holding structures in specific positions and the mechanics of structures like the cytoskeleton.

Read: 14 Best Examples Of Radiation And Their Effects

Over the last decade, several acoustic microscopes based on picosecond ultrasonics systems have been demonstrated operating in GHz frequencies. They are increasingly being applied to nanostructures, quantum wells, as well as a single biological cell to probe its mechanical properties.

Sours: https://www.rankred.com/best-examples-of-longitudinal-waves/

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I love you. Or maybe not. I'm still good. - Masha tried to joke, getting out of the car and thinking that maybe everything will work out. Her last words had an effect on Kirill like a red rag on a bull.

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