12 PHYSICS 6. Superposition of waves

 12 PHYSICS   

 6. Superposition of waves

Wave motion:-

The vibratory distribution in the particle of the  medium is called wave . Various types of waves is being observed by us in our day to day life e.g. water waves , sound waves , light waves , mechanical waves, electromagnetic waves etc.

Mechanical Waves:- Mechanical wave is a disturbance produced in an elastic medium due to periodic vibrations of particles of the medium 

about their respective mean positions. 

• In mechanical waves energy, and momentum are transferred form 

     one particle to another, there is no transfer of matter or particles of the medium in which the wave is travelling.

• Mechanical wave required material medium for their propagation.

• Mechanical waves are of two types

• i) Transverse and ii) Longitudinal 

• Electromagnetic Waves :-

• Electromagnetic waves are those waves which do not require any material medium for their propagation. They are produce due varying electric and magnetic field.

  Ex. Light waves are electromagnetic waves.

  Consider a long cylindrical tube closed at one end. It consists of an air column with rigid boundary at one end. When a vibrating tuning fork is held near the open end of the closed pipe, sound waves are sent by the fork inside the tube. Longitudinal waves traveling along  a pipe of finite length are reflected at the ends as transverse waves are refelcted at the fixed ends of a string.

At the closed end there is least freedom for motion of air particles. Thus, there must be a node at the closed end. The particles little beyond the open end are most free to vibrate. As  a  result,  an antinode must be formed little beyond the open end. The length l of pipe and length L of air column are shown separately in all the figure. 

In a pipe open at both ends boundary conditions are such that an antinode is present at each open end.

Comparison of sound vibrations produced in open and closed pipe :

Sound produced by an open pipe contains all harmonics whereas only odd harmonics are present in closed pipe.

Quality of sound in open pipe is richer than that produced by a closed pipe.

Fundamental frequency of vibration of air column in an open pipe is double that of the fundamental frequency of vibration in a closed pipe of the same length.

Practical Determination of End Correction:

An exact method to determine the end correction, using two pipes of same diameter but different lengths l1 and  l2 is as follows.

For a pipe open at both endFor a pipe closed at one end:

Explain the vibrations produced in a string when stretched between two rigid supports