Wave and Motion

Wave
          A mechanism by which energy can transfer from one region to another region through medium without the actual movement of the medium itself.
Basically waves are classified into two main groups.
       1) Mechanical wave
       2) Electromagnetic wave
Mechanical wave
  Such wave which need medium for their propagation. Like sound wave, water wave, string wave.
  Mechanical waves are divided into two types.
       1) Transverse wave
       2) Longitudinal wave or Compressional wave
Transverse wave
Such mechanical wave whose particles are perpendicular to the way of propagation. Like water wave or string wave.
Longitudinal wave or Compressional wave
                                 Such type of mechanical wave in which the particles of the medium is parallel towards the propagation. Like sound wave. It moves due to compression and rare faction. At the region of compression pressure is high where as the region of rare faction the pressure is low. So due to this P.D the wave moves.
Electromagnetic wave
            Such wave which don't need medium for their propagation, like light wave and radio wave.
Electromagnetic waves are transverse waves.
Characteristics of wave
      There are some characteristics associated with the wave motion.
           1)   Wave length
           2)   Amplitude
           3)   Time period
           4)   Frequency
           5)   Velocity
Wave length
  The distance between two consecutive crest or trough is known as wave length. It is denoted by (l). The unit used to measure wave length is meter (m).
Crest
  The portion of the wave above the equilibrium position is called crest.
Trough
  The portion of the wave below the equilibrium position is called trough.
Vibration
  A complete round trip of wave is called one vibration or one cycle.
Amplitude
  The peak value of wave on either side of the equilibrium position, or the maximum height of the wave from equilibrium position is called amplitude.
Time Period
  Time of one vibration or time interval needed for a wave to complete one vibration or one cycle. Time Period is denoted by (T) and its unit is second (s).
Frequency
  The number of vibration passing a point in unit time is called frequency. It is denoted by (f) the unit used to measured the frequency is hertz (Hz), cycle/second (c/s) or Vibration/second=vib/sec or the reciprocal of time period
Hook's Law
  Hook's Law is applied on elastic object like spring or rubber..... This is stated as, if the spring (elastic object) are stretched or compressed by external force (Fext). Due to external force object displaced or produce displacement (x) in the spring. So the external force has done work.
So the work is done and store is the spring in the form of elastic restoring force (Fr) and the elastic restoring pull back the spring to its original position. The magnitude of restoring force is directly proportional to the displacement and opposite in direction to that displacement.
Mathematically:
  Fr a -y
  Fr=constant (-x)
  Fr=k(-x)
  Fr=-kx
Simple Harmonic Motion (S.H.M)
  It is a type of vibrating motion in which the acceleration produced due to elastic restoring force (Fr) and it is directly proportional to the negative of the displacement (X) which is produced due to external force (Fext) and always directed towards the mean position
Conditions for S.H.M
     1)      The system must have restoring force.
     2)      The system must have inertia (m).
     3)      The plane over which attached to spring moving must be frictionless  
               and at the point of spring and firm support.  
Characteristics or feature of S.H.M
             Any system executing S.H.M have the following main characters or Features.
1)     At extreme position the P.E is maximum. Because displacement (X) is
         Maximum and K.E is zero. Because velocity is zero.
2)     At mean position the K.E is maximum. Because velocity is maximum  
         while the P.E is zero. Because displacement(X) is zero.
3)     The acceleration always directed towards the mean position and it is  
         directed in the direction of restoring force(Fr).  
4)      Displacement and acceleration are always in opposite direction.
Pendulum
Definition
                Simple pendulum is consisting of bob (hard steel sphere), inextensible string and firm support. One end of spring attached with bob and the other end with firm support. These three components are from the system of simple pendulum.
Explanation
              If the bob is displaced through displacement (X) by an external force (Fext) from point (O) to point (B) against the gravitational field. So the work done by external force stored in the pendulum in the form of gravitational potential energy. When the applied external force release and the bob moves towards the mean position, Due to change of G.P.E into K.E the bob do not stay to point (O.) due to inertia (mass) the bob moves to other G.P.E side of the mean position at point (A) and again don't stay there. and moves to point (O) and then to point (B) and the bob repeats its movement about the mean position in the regular interval of time. The acceleration produce and it is always directed towards the mean position and directly proportional to the displacement (X) produce due to external force. Therefore the Simple Pendulum also executes S.H.M like mass attached to spring.
It is experimentally proved the time period of simple pendulum as
  T=2pl/g
Where T=time period of pendulum
L=length of the string of pendulum
g=gravitational acceleration.
Properties of waves
           Basically any types of wave exhibit (to show) four basic properties which are as follows.
            1)    Reflection
            2)    Refraction
            3)    Diffraction
            4)    Interference
Reflection
              When the transmitted waves (water waves, light waves, sound waves-------) strike any plane surface.(In the case of light waves on plane mirror)with the some angle after stricking with the plane it bounce back to the same medium from which it transmitted in this case is known as reflection.
Refraction
                       The banding of waves when it enters from one medium to another medium is known as refraction. The waves bend towards normal when it enters from rare medium into dense medium to the reduction is the speed of the waves.
Diffraction
        The bending of waves around the corners of objects or obstacles is known as Diffraction.
Interference
               When two (or more than two) waves each gives own displacement to the same particle of medium. The resultant displacement is equal to some of all the individual displacement. This phenomenon is known as Interference of waves.
Constructive interference
                    When two identical waves (same amplitude, same wave length, and same frequency) moving along the same direction propagation along the same medium. If both waves are in phase when they interact and they produce Constructive interference pattern (arrangement) and the resulting waves are with individual waves reinforce each other.
Destructive Interference
                          When two identical waves generated in same medium propagating in same direction, If waves are out of phase. When they interact they produce interference pattern. Which is destructive in nature and they cancel the effect of each other and the resultant waves is zero (The medium through which wave generated came into its undisturbed level).

Stationary Waves or Standing Waves
              When two identical waves (same amplitude, same frequency, same wave) generated in the same medium but propagating in opposite direction, If both waves are out of phase when they interact with each other. They formed standing waves or stationary waves. Both waves lock each other and form Loops. The 1st loop is known as the 1st Harmonic or Fundamental harmonic, 2nd is called 2nd harmonic and so on.
Fandamental or 1st Harmonic
The frequency (f) of the standing wave divided by number of loops