12 PHYSICS 7. Wave motion

 7. Wave motion 

    Introduction

 The wave motion has double periodicity. i.e. It is periodic in space & periodic in time.  

Wave can be defined as an oscillatory disturbance traveling through a medium without change of form. 

 There are two types of wave

(1) Transverse wave 

A wave in which particles of a medium vibrate in a direction perpendicular to the direction of propagation of the wave is called as Transverse wave. 

(2) Longitudinal wave

A wave in which particles of medium vibrate in a direction parallel to the direction of propagation of the wave is called as longitudinal waves.

For the propagation of wave through the medium, it must possess the following condition.

 (1)The medium should be elastic i.e. It can regain its original shape & size as soon as the wave passes through it.

(2)The medium should possess the inertia, so that it can store the energy & transfer in the form of waves.

(3)The frictional resistances of the must be very small, so that there no loss of energy.

Period of wave motion:- (T):-The time taken by any particle to complete one oscillation or vibrations is called as period of wave. 

 Frequency of wave (n):- The number of vibrations performed in one second is called as frequency of wave.   Here n =1/T.

Wavelength of the wave ( λ ):- The distance between two successive particles which differ in phase by 2π radian is called as wavelength .

Wave velocity (v):-The distance through  which a Wave can advanced in one second is called wave velocity. 

Amplitude of wave (a):- The maximum displacement of particle from its mean potion called as amplitude, denoted by which the wave advanced in one second is called wave velocity. 

Relation between wave velocity, frequency & wavelength: - In one second the distance covered by the wave is one wavelength (λ). Hence the magnitude of wave velocity is given as     V= Distance covered in one period /Time required for one oscillation.

  V= Displacement/Time= λ/T

              But   1/T=n  = frequency 

              Thus,   V=n λ 

Que. 1 : Obtain an equation of simple harmonic progressive wave and express it in different forms. write down the equation of  a progressive wave travelling along the negative direction of X- axis.

Ans: Simple Harmonic progressive waves:-  waves which continuously travel in a given direction is called as progressive waves. When these waves travel through a medium, the particles of the medium perform vibrations about their mean position. If vibrations are simple harmonic, the waves are called as simple harmonic progressive waves. Both transverse & longitudinal waves are simple harmonic progressive waves. 

Equation of simple harmonic progressive waves :-   

1. Let’s consider simple harmonic progressive  waves traveling in +ve direction of X axis 

2. Suppose y represent the displacement & x represent the position of particle in the medium, can be shown in fig. 

3. At any instant of time t the displacement of particle at the origin (x=0) is given as 

   1. Let us consider a particle A situated at distance x from the origin O. The particle A lags in phase behind the particle at the origin 

   2. A = Amplitude

   3. Displacement of particle ‘A’ at time “ t ” is  as 

                Y =A sin ( ωt  _  δ)……….(ii)

             Where δ is the phase difference between the points O & A, it depends on distance x   from origin.

   1. We know that wave motion repeats itself after a distance equal to wavelength λ. Hence the distance λ equivalent to phase difference of 2π. Therefore the distance x is equivalent to phase difference of δ = 2πx/ λ. Therefore