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Wave Motion and Relation of Wavelength with Velocity and Frequency

What is Wave?

A wave is a disruption in the medium which causes the particles of the medium to undergo vibratory motion about their mean position in equal intervals of time.

wave-length

Waves play an essential function in our everyday life. It is due to the fact that waves are a carrier of energy and information over big distances. Waves transport energy without carrying matter. The energy transportation is carried by a disruption, which expands from a source. We are well acquainted with various kinds of waves such as water waves in the ocean, or little ripples on a still pond due to raindrop.

When a musician plucks a guitar-string, sound waves are created which on reaching our ear, produce the sensation of music. Wave disruptions might also be available in a focused package like the shock waves from an aeroplane flying at supersonic speed. Whatever might be the nature of waves, the mechanism by which it carries energy is the same.

The wave is created by an oscillation in the vibrating body and propagation of a wave through the area is by means of oscillations. There are 2 categories of waves:

  1. Mechanical waves
  2. Electromagnetic waves
1.Mechanical waves

The waves which propagate by the oscillation of material particles are known as mechanical waves.

2.Electro-magnetic waves.

Waves which do not require any medium for their propagation are called electromagnetic waves.

Electro-magnetic-waves

For Instance: Radio waves, tv waves, X-rays, heat and light waves are some examples of electro-magnetic waves.

Types of Mechanical or Progressive Waves

A wave, which transfers energy by moving far from the source of disturbance, is called a progressive or travelling wave. There are two kinds of progressive waves – transverse waves and longitudinal waves.

Longitudinal waves

In longitudinal waves, the particles of the medium move back and forth along the direction of propagation of wave.

Longitudinal-waves

Longitudinal waves can be produced on a spring (slinky) placed on a smooth floor or a long bench. Fasten one end of the slinky with stiff support and hold the other end into your hand. Now provide it a normal push and pull rapidly in the direction of its length.

A series of disruptions in the form of waves will begin moving along the length of the slinky. Such a wave includes regions called compressions, where the loops of the spring are close together, alternating with regions called rarefactions (expansions), where the loops are spaced apart.

In the regions of compression, particles of the medium are more detailed together while in the regions of rarefaction, particles of the medium are spaced apart. The range in between two consecutive compressions is called the wavelength. The compressions and rarefactions move backwards and forward along the instructions of motion of the wave.

Transverse waves

In transverse waves, the vibratory motion of particles of the medium is perpendicular to the direction of propagation of waves.

Transverse-waves

A big and loose spring coil (slinky spring) can be utilized to show the result of the motion of the source in generating waves in a medium. It is better that the spring is laid on a smooth table with its one end fixed so that the spring does not sag under gravity.

If the totally free end of the spring is vibrated from side to side, a pulse of a wave having a displacement pattern will be created which will move along the spring. If the end of the spring is returned and forth, along the direction of the spring itself, a wave with back and forth displacement will travel along with the spring. Waves in which displacement of the spring is perpendicular to the direction of the waves are called transverse waves.

Relation between Velocity, Frequency and Wavelength

Wave is a disruption in a medium which travels from one place to another and for this reason, it has a specific velocity of travelling. This is called the velocity of the wave which is specified by

Velocity = distance/time

v= d/t

If the time taken by the wave in moving from one point to other is equal to its time period T, then the range covered by the wave will be equal to one wavelength, for this reason λ we can say that:

v= λ/ T

But time period T is reciprocal of the frequency f, i.e., T = 1/f.

So, v= fλ.

Waves as a Carrier of Energy

Energy can be moved from one place to another through waves. For instance, when we shake the stretched string up and down, we offer our muscular energy to the string. As a result, a set of waves can be seen travelling along the string. The vibrating force from the hand interrupts the particles of the string and sets them in motion. These particles then transfer their energy to the nearby particles in the string. Energy is thus moved from one location of the medium to the other in the form of a wave.

The quantity of energy brought by the wave depends on the distance of the extended string from its rest position. That is, the energy in a wave depends on the amplitude of the wave. If we shake the string faster, we offer more energy per second to produce a wave of higher frequency, and the wave delivers more energy per second to the particles of the string as it moves forward. Water waves likewise move energy from one location to another.