Wave:

Definition:     "A wave is a disturbance of some kind that propagates through a medium from one place to another"

                                                                             (OR)

"Wave is a mechanism, which is used to transfer energy and momentum from one place to another without transporting matter"

Examples:

i.               A large amount of heat energy from the sun reaches us in the form of waves.

ii.            Sound (energy) reaches our ears by means of waves in the air around us.

Explanation:

In the above definition of wave, the word 'medium' means a substance or material which carries the wave. Some waves required medium for their propagation, while some waves do not required medium for their propagation.

The nature of the wave may be different, but the mechanism by which it transports energy is the same.

Characteristics of wave motion

All the waves have some common Characteristics which are given below.

  1.        Wave Speed
  2.        Frequency of waves
  3.        Time period of waves
  4.       Wavelength
  5.       Amplitude of wave
  6.       Intensity of wave

Let us discuss these Characteristics one by one.

1)      Wave speed (v):

Definition:       “The distance travelled by a wave per unit time is called speed of wave”.

The speed of a wave depends upon the type of wave as well as the properties of the medium.

It is denoted by ‘v’.

SI unit of speed of wave is m/s.

For example, the speed of a transverse wave pulse in an elastic stretched string or spring is given by:


Where, ‘M’ is the mass, ‘L’ is the length of the string respectively and ‘T’ is the tension in the string. If ‘m’ is the mass per unit length of the string, then above equation becomes:


  =                ∵  

Thus the speed of transverse wave in a well stretched and thin string is greater as compared to a loosely and thin one.

 The speed of compressional or longitudinal wave depends upon the modulus of elasticity E and density  of the medium, which is given by:


Hence longitudinal waves travel more slowly in gases then in solid because gases are more compressible and hence having a smaller elastic modulus ‘E’.

1)     Frequency of Waves (f):

Definition:      “The number of waves passing through a certain point in unit time is called frequency of the wave”.

As a wave progress, each particle of the medium oscillates periodically with the frequency and period of the source. So the frequency ‘f’ of the wave is equal to the frequency of the simple harmonic oscillating source.

SI unit of frequency is cycle per second or Hertz ‘Hz’.


1)   Time period (T):

Definition:      "The time during which a wave passes through a certain point is called the time period of the wave”.

It is equal to the reciprocal of the frequency.

SI unit of time period is second ‘s’.

        Time period   =   

1)      Wavelength (λ):

Definition:      The distance between the two successive particles which are exactly in the same state of vibration is called wavelength.

It is denoted by Greek letter ‘λ’.

SI unit of wavelength is meter ‘m’.

 In the given figure the point ‘A’ and ‘C’ or point ‘P’ and ‘Q’ or point ‘B’ and ‘D’ are in the same phase because they are in the same state of vibration.

1)      Amplitude of Wave (A):

Difinition:       "The maximum displacement covered by a vibrating particle from its equilibrium position on either side is called amplitude".

It is denoted by Xo.

SI unit of amplitude is meter ‘m’.

2)      Intensity of Wave (I):

Definition:       "The amount of energy transmitted per second per unit area placed perpendicular to the direction of propagation of waves is called intensity of waves".

It is denoted by letter ‘I’.

Mathematically:    

Intensity of a wave is proportional to the square of the amplitude of the wave i.e. I ∝ A2

SI unit of intensity is Watt/m2.

Relation between Speed, wavelength and frequency of wave:

A very important relation exists between frequency and wavelength.

One wavelength of a wave is sent out by the wave generating source as it completes one vibration. The time for one vibration is called time period ‘T’. The wave cover distance ‘λ’ in the time period ‘T’ and we find the speed ‘v’ of the wave as:

  =             ∵ x = λ  &  t = T

 = 

The above equation shows the relationship between speed, frequency and wavelength and is valid for all waves.