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We will start by first defining waves, and then move on to other terms referred in the question, which refer to different characteristics of waves.
Waves is a kind of movement of energy through matter without movement of matter it self. For example, we see that waves in a see exert a force in the direction of movement of waves, making clear that energy is being carried forward with the movement of sea waves. It appears to us that water is also moving forward along with waves. But in reality the water is not moving forward it is just oscillating up and down in vertical direction.
The waves are generated on or inside some material. This material is called the medium. Medium of sea waves, which travel on surface of the medium is sea water, and medium of seismic waves which travel within the medium is the earth. There are many other types of waves which impact our lives. For example the sounds we hear are because of waves which occur in air. Light and all other electromagnetic radiations are also waves. But these waves travel in vacuum. Such waves travelling in vacuum are assumed to travel in a hypothetical medium called ether.
The speed with which the waves travel, which is same as the speed with which the energy in the waves travels, the speed with which the the waves apparently travels depends only on the characteristics of the medium through which it travels.
Having covered the basics of waves, we will now move to describing the terms in the question.
The waves create a pattern of oscillating upward and downward movement in the medium. Some type of waves create a pattern of expansion and compression of the medium. In such up and down movement of medium the highest point reached is called the crest, and the lowest point reached is called trough. The wavelength is the distance between to immediately following crests or troughs.
Frequency of wave is the number of times a particle in the medium completes the cycle of its movement from crest to trough and back to crest. Incidentally, for a given type medium, wavelength multiplied by frequency is constant and is equal to speed of the wave.
In general terms amplitude is like height of waves. It is defined as the distance between mean position of a particle in the medium and its crest or trough.
in most of the waves the medium appears to move forward in the direction of the waves. These are called progressive waves or travelling waves. In another kind of waves the energy of the waves is restricted to a small section of the medium. For example when the string of a musical instrument is plucked, the waves generated within the string are confined to the two fixed end of the string. Waves of this kind are called standing waves.
Wave is a sort of disturbance.The propagation of disturbance from a region to another region in a medium is called wave motion. A wave which travels continuously in a medium is called a progressive wave,
Wave length is the distance between the two consecutive particles in the medium which are in the same state of vibration.
Frequency of a wave is the number of oscillations executed by a particle of the medium in one second.
Amplitude of a wave is the maximum displacement of a particle of the medium from its equilibrium postion.
Frequency f of the wave , the wave lenth L and the velocity c of the wave are related by the relation: f=c/L
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