# Nature of Waves essay

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A wave's phase velocity refers to the rate at which the given phase of that particular wave tends to propagate in space. This refers to the speed at which the particular phase of any single frequency component of the associated wave travels.  In this component, any existing phase of the wave like the crest will look just like travelling at the phase velocity. It is also notable that the phase velocity's unit is the wavelength λ (lambda). The period's symbol is T.

The relationship relating the velocity, wavelength and the period is:

dx/dt = vp = λf.

This may also be given in terms of the wave's angular velocity ω and also the wave number k;    intrinsic property of the medium determines the phase velocity for a wave. Phase velocity of electromagnetic waves rely upon the medium. Phase velocity in vaccum too depend upon the permettivity and permeability of the vaccum. Phase velocity may also depend upon the mode of the wave propagation. Dispersion is an phenomenon that determines the speed of different waves of different frequency  this phenomenon affect the speed of the signals.

The phase velocity varies with frequency  and its not a must like group velocity of the wave in the dispersive medium. Group velocity mostly deals with changes in amplitude known as wave's envelope propagate..

Phase velocity of electromagnetic radiation exceeds the speed of the light in the vaccum under anomalous dispersion without indication of superluminal information. When a solid substance is sliding on either right or left, the phase velocity is the speed at which the real outer or physical parts are moving. Imagine a certain quantity (x) is in the transverse axis and then many  small particles are each oscillating vertically. In this situation the propagation of the wave is to the right together with the associated phase velocity. This shows that the phase of the wave in motion may or may not show any correspondence with a particular physical entity. It's totally possible for a wave to pass through a serial of material, none of which is moving in the direction of the wave. This is similar to the phenomenon of aliasing in signal processing. (Brillouin, 1960).

What is perceived as a rational wave may in fact be simply a serial of causally disjoint processes like the individual spring-mass systems that happen to be aligned temporally, either by design or chance, such that their totaled behavior show a wavelike pattern, even if there is no actual propagation of information and energy along the sequence. (Main, 1988)

Since a general wave or wavelike phenomenon need not include the causal flow of any physical effects, obviously there is no upper limit on the possible phase velocity of a wave. However, even for a real physical wave, that is a chain of consecutive dependent events, it is not vital for the phase velocity to correspond to the speed at which energy or information is propagating. This is partly a semantically issue since in order to disseminate information, a signal may not be a simple periodical wave, so is must to consider non-periodic signals; hence the overall perception of phase dynamics is unclear. If the wave fails to re-occur, then it may be said that the period of the signal is the entire signal. On this grounds, it may be said that the velocity of the signal is uncertainly equal to the phase velocity, but in this context the phase velocity could only be defined as the speed of the leading edge of the overall signal.

On the other hand, the group velocity of a given wave refers to the actual velocity with which the entire shape of the wave's amplitudes referred to as modulation or envelope of that particular wave, tends to propagate in space. So as to comprehend this, one should imagine the behavior the waves propagated by a stone when it is thrown into the center of a still pond.

The group velocity is always thought as the velocity where energy and information is communicated through the wave.Sometimes the group velocity may be seen as a signal velocity unless the wave is going through an absorptive medium. It  has been found that  group velocity can  at times exceed the light speed in vacuum.  It is possible to reduce the group velocity to zero,or have negative group velocity hence making the pulse to propagate backwards. Group velocity is usually thought as velocity that transmit the  energy or information waves. In several cases it is always true and hence called signal velocity.

There are some abnormal cases such as case of anomalous dispersion. The index reflection changes with respect to wavelength hence changes in sign. It is possible for the group velocity to exceed the speed of light. Sometimes anomalous dispersion where wavelength of the light is near the reverberation of the medium. Group velocity ceases to be a signal velocity when the dispersion is anomalous but instaed the signal travel at the speed of wavefront.

Today it has become possible for the group velocity to be even negative where a medim can be exited by a pulse before it enters. Still, in this case signal travel less than the speed of the light.  Group velocity is a function of the frequency of the wave. This leads to group velocity dispersion which makes the light's short pulse to spread in time as a result of different velocities.

Normally dispersive medium gives a result of higher frequency component to travel slower than the lower frequency component once the light pulse is propagated through this media. This pulse become positvely chirped. The oppposite is also true, that is once light pulse is propagated through an anomalously dispersive medium the high frequency medium travel faster than the lower frequency component.

Energy or information  propagation  in a wave always occurs due to changes in the wave. The most common example is changing wave from being absent to making it appear present,which propagates at the speed of the leading edge of a wave train. Mostly commonly the modulation of the frequency or the amplitude of the wave is needed for the message or information to be transmitted and understood. This modulation is there to represent what is in the signal. Hence the actual speed of content in the situation described above is Dw/Dk. This shows the phase velocity of the wave's amplitude , bearing in mind that each amplitude wave contains a group of internal waves, this speed may still be used to describe the the group velocity.

Group velocity show correspondences to the real signal velocity only under conditions of normal dispersion or under conditions where the group velocity is more less than the phase velocity. In some other situations, the group velocity is not a must to represent the actual propagation speed of any energy or information. For example, in the case of anomalous dispersion, which means decrease in refractive index and increasing in the number of wave.some formulae shows that what is called the phase velocity is less than what is called the group velocity. In such cases where group velocity is greater of phase velocitry, the group velocity no longer represents the speed at which information or energy propagates.

Group velocity may not represent the actual speed of the energy or  information. Both  group and phase velocity play a great role in transmission of signal as method of communication. This give it a great importance oif their incorporation in the study of the wave. It is through wave that we are able to hear and convey effective communication to all the people. It is through the wave that we receive information through radio, television any many more.