# Wave Motion

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### Concept of Wave:

• Wave in medium may be defined as the disturbance moving through the medium without change of form.
• e.g. ripple in water formed due to dropping a stone in water.
• When a tone is dropped in water, it transfers part of its kinetic energy to the particles of water with which it comes into contact. These particles are set into vibration.
• Now these vibrating particles give their energy to the neighbouring particles. Thus neighbouring particles are set into vibrations.  Thus each particle receives energy from previous particle and passes it to the next particle. Thus wave transfer energy from one point to the another.

#### Wave Motion:

• Wave motion is a mode of transfer of energy or a form of disturbance travelling through an elastic medium due to the repeated oscillations of the particles of the medium about their mean positions.

#### Characteristics of Wave Motion:

• The particles of the medium are not carried along the waves.
• It is the disturbance which moves and forms the wave.
• All the particles of the medium perform S.H.M. about their mean positions, with the same amplitude and period.
• As the disturbance reaches different particles successively, each succeeding particle lags behind the previous particle in a phase.
• Wave motion is both periodic in space and periodic in time. Hence it is a doubly periodic phenomenon.
• The wave velocity is different from particle velocity. The velocity of a wave is constant in a given medium, whereas the velocity of the particles changes, being maximum in the mean position and minimum at the extreme position.
• The wave travels from one medium to another, the wave speed and wavelength change but the frequency remains the same because the frequency is determined by the source.

#### Wave Motion as Doubly Periodic Phenomenon:

•  The time taken by a wave to complete its one cycle is called the time period of a wave. Thus, the wave motion repeats after a fixed interval of time. Thus the wave motion is periodic in time.
• The distance between two consecutive points which are in the same state of motion i.e. they are in the same phase is always constant and this constant distance is called the wavelength of a wave. Thus, the wave motion repeats after a fixed interval of distance. Hence wave motion is periodic in space.
• Thus, wave motion is a doubly periodic phenomenon, periodic in time and periodic in space.

#### Properties of the Medium Necessary for the Propagation of Mechanical Waves:

• For propagation of mechanical waves, the medium should possess following properties.
• The medium must be elastic so that it regains its original condition after the wave passes through it.
• The medium must possess inertia (mass) so that it can store energy and transfer in the form of waves.
• The frictional resistance of medium should be negligible. so that the medium can travel without loss of energy.

#### Terminology of Wave Motion:

• Period of a Wave:
• A time taken to complete one cycle or oscillation is called as the period of the wave.
• it is denoted by ‘ T ‘. Its S.I. unit is second.
• Frequency of a Wave:
• The number of cycles or oscillations performed by a wave in one second is called as the frequency of the wave.
• It is denoted by ‘ f ‘ or ‘ n ‘. Its S.I. unit is hertz (Hz).
• Amplitude of a Wave:
• The maximum displacement of medium particles from their mean positions is called amplitude of a wave.
• It is denoted by ‘ a ‘. Its S.I. unit is metre.
• Velocity of a Wave:
• The distance travelled by a wave in one second is called as the velocity of the wave.
• It is denoted by ‘ v ‘. Its S.I. unit is m/s.
• Wave Length of a Wave:
• The distance between two successive particles of a wave in the same phase is constant and is called the wavelength of the wave.
• It is denoted by ‘ λ ‘. Its S.I. unit is metre.
• Wave number of a wave:
• The number of waves passing through a unit distance is called as wave number of the wave. or  Reciprocal of a wavelength is called as the wave number of the wave.
• It is denoted by ‘ ν’. Its S.I. unit is m-1.

### Classification of Mechanical waves:

• Depending on the motion of wave in a space the waves are classified into three types
• One-dimensional waves: The wave which moves in a straight line is called a one-dimensional wave. e.g. transverse wave set in a rope.
• Two-dimensional waves: The wave which moves in a plane is called a two-dimensional wave. e.g. ripple in the water.
• Three-dimensional waves: The wave which moves in a space is called a three-dimensional wave. e.g. Radio wave from transmitting tower.
• Depending upon the direction of the vibration of medium particles w.r.t the direction of the propagation of the wave, mechanical; waves are classified into two types a) transverse waves and b) longitudinal waves.

#### Transverse Waves:

• A progressive wave is a wave in which the medium particles are vibrating in the direction perpendicular to the direction of propagation of the wave is called as a transverse wave.
• e.g. the wave produced in a rope by tying the rope at one end to a rigid wall and jerked at the other end.

• Crest: The convex part formed by the wave due to upward displacement of the particles of the medium, is called crest.
• Trough: The convex part formed by the wave due to downward displacement of the particles of the medium, is called trough.

#### Characteristics of Transverse Waves:

• When transverse waves pass through a medium, the medium gets divided into alternate crests and troughs.
• A crest and trough form a transverse wave.
• The crests and troughs follow each other in rapid succession i.e. crests and troughs are produced alternatively at the same point of the medium.
• Every particle of medium performs S.H.M. of the same amplitude and period.
• Every particle lags behind the previous particle in a phase.
• The distance between two successive particles in the same phase is constant and it is called wavelength of the wave.
• Consecutive crest and trough constitute one cycle of a transverse wave.
• The transverse waves are produced in a medium, which undergoes a change of shape. Hence transverse waves can be propagated only through solids.

#### Longitudinal Waves:

• A progressive wave is a wave in which the medium particles are vibrating in the direction parallel to the direction of propagation of the wave is called as a longitudinal wave.
• e.g. sound wave

• Compression: The region where the particles of the medium are crowded together is called the compression. Sometimes compression is also referred as the condensation. At compression, the density of the medium is higher. Similarly, the pressure at the compression is more than the normal pressure of the medium.
• Rarefaction: The region where the particles of the medium are widely separated is called the rarefaction. Sometimes rarefaction is also referred as the extension. At rarefaction, the density of the medium is lower. Similarly, the pressure at the rarefaction is less than the normal pressure of the medium.

#### Characteristics of Longitudinal Waves:

• When Longitudinal waves pass through a medium, the medium gets divided into alternate condensations (compressions) and rarefactions (relaxation).
• A compression and rarefaction form a Longitudinal wave.
• The compressions and rarefactions follow each other in rapid succession i.e. compressions and rarefactions are produced alternatively at the same point of the medium.
• Every particle of medium performs S.H.M. of the same amplitude and period.
• Every particle lags behind the previous particle in a phase.
• The distance between two successive particles in the same phase is constant and it is called wavelength of the wave.
• Consecutive compression and rarefaction constitute one cycle of a Longitudinal wave.
• The Longitudinal waves are produced in a medium, which undergoes a change in volume and pressure. Hence Longitudinal waves can be propagated through solids, liquids and gases.

### Relation Between Velocity, Frequency and Wavelength:

• Let ‘ λ ‘ be the wavelength, ‘v’ be the velocity, ‘n’ be the frequency and ‘T’ be the time period of the wave.
• The wave travels a distance equal to its wavelength in one period. Hence the velocity of the wave is given by

Velocity = Distance / time

v = λ /T

But 1/T = n

Hence   v = n λ

This is the relation between the wavelength, frequency and velocity of wave

 Science > Wave Motion > You are Here