What are Waves? And Wave Equation in Physics

 Waves 

"A wave is a kind of oscillation (disturbance) that travels through space and matter. Wave motions transfer energy from one place to another. This is because waves are a carrier of energy and information over large distances. Waves require some oscillating or vibrating source."

"A disturbance that carries the matter from one place to another one"

There are many different ways to understand or Define a Wave  and Wave Properties. but in starting, we can consider it as a disturbance that travels in medium. As we know that energy can be transferred by two ways......

1. By transfer of Matter
2. By Wave Motion 

Types of Waves 

There are two types of Waves called MECHANICAL WAVES  and ELECTROMAGNETIC WAVES 

Later on! we'll study about both kind of waves.

1. Mechanical Waves 

A mechanical wave is a wave that is an oscillation of matter, and therefore transfers energy through a medium. While waves can move over long distances, the movement of the medium of transmission of the material is limited. Therefore, oscillating material does not move far from its initial equilibrium position.

Of course Mechanical waves are one kind of disturbance that travels from one point of  a medium to another with a constant velocity of PERIODIC OSCILLATION .

or we can say that waves which's transportation needed a material medium having inertial and elastic properties called mechanical waves.

 Not all waves are like this. For example, electromagnetic waves such as visible light are not mechanical because they can travel through the vacuum of space to reach us from the sun. Mechanical waves include water waves, sound waves, earthquake waves, and many more. Like all waves, those of the mechanical variety have peaks, or crests, and troughs. They also have a frequency, which is the number of waves that pass by per second, and a wavelength, which is the distance from one peak to the next, or one trough to the next.

Water waves, sound waves, and seismic waves are all examples of mechanical waves.

  

Explanation:

A mechanical wave is any wave that uses matter as its mode of transportation. This includes both transverse and longitudinal (compression) waves.
Sound is a mechanical wave because it moves though air (or any material). This is why sound can't travel through space, as there is no medium there for it to travel though.
On the other hand, light is not a mechanical wave because it can travel though space and the absence of material.

Mechanical Waves: Production & Propagation

Now we discuss about How a Mechanical Wave Propagate and How a Mechanical Wave Produced or How is a Mechanical Wave Created?

1.Production of Mechanical Waves

The local excitation of a medium is not instantaneously detected at positions that are at a distance from the region of excitation. It takes time for a disturbance to propagate from its source to other positions. This phenomenon of propagation of disturbances is well known from physical experience, and some illustrative examples immediately come to mind. Thus an earthquake or an underground nuclear explosion is recorded in another continent well after it has occurred. The report of a distant gun is heard after the projectile has arrived, because the velocity of disturbances in air, i.e., the speed of sound, is generally smaller than the velocity of the projectile. More familiar manifestations of the propagation of disturbances are waves in a rope or propagating ripples on the surface of water. These examples illustrate mechanical wave motions or mechanical wave propagation. Mechanical waves originate in the forced motion of a portion of a deformable medium. As elements of the medium are deformed the disturbance is transmitted from one point to the next and the disturbance, or wave, progresses through the medium. In this process the resistance offered to deformation by the consistency of the medium, as well as the resistance to motion offered by inertia, must be overcome. As the disturbance propagates through the medium it carries along amounts of energy in the forms of kinetic and potential energies. Energy can be transmitted over considerable distances by wave motion. The transmission of energy is effected because motion is passed on from one particle to the next and not by any sustained bulk motion of the entire medium. Mechanical waves are characterized by the transport of energy through motions of particles about an equilibrium position. Thus, bulk motions of a medium such as occur, for example, in turbulence in a fluid are not wave motions.

There are two basic types of wave motion for mechanical waves: longitudinal waves and transverse waves.

Longitudinal Waves

In a longitudinal wave the particle displacement is parallel to the direction of wave propagation. The animation at right shows a one-dimensional longitudinal plane wave propagating down a tube. The particles do not move down the tube with the wave; they simply oscillate back and forth about their individual equilibrium positions. Pick a single particle and watch its motion. The wave is seen as the motion of the compressed region (ie, it is a pressure wave), which moves from left to right.

The second animation at right shows the difference between the oscillatory motion of individual particles and the propagation of the wave through the medium. The animation also identifies the regions of compression and rarefaction.

Transverse Waves

In a transverse wave the particle displacement is perpendicular to the direction of wave propagation. The animation below shows a one-dimensional transverse plane wave propagating from left to right. The particles do not move along with the wave; they simply oscillate up and down about their individual equilibrium positions as the wave passes by. Pick a single particle and watch its motion.

Water Waves

Water waves are an example of waves that involve a combination of both longitudinal and transverse motions. As a wave travels through the waver, the particles travel in clockwise circles. The radius of the circles decreases as the depth into the water increases. The animation at right shows a water wave travelling from left to right in a region where the depth of the water is greater than the wavelength of the waves. I have identified two particles in orange to show that each particle indeed travels in a clockwise circle as the wave passes.