Wave Motion

1. Wave motion (Travelling Wave)

What  happened  if you throw a stone into a pool of water ? circular waves form and move out word.

Water waves and waves on a cord / rope are examples of waves motion. It’s are  The mechanical waves. The mechanical wave need medium to move.

A wave is not matter. Although it may move in matter.

§  A wave consist of oscillations that move without carrying matter with them

§  Wave carry energy from one place to another. All form of wave motion transport energy.

A.    Kind of wave motion : (Types of waves) be based on a medium :

1.      a mechanical wave à with medium

2.      a electromagnetic wave à without medium

B.     Vibration direction :

1.      a transverse wave à vibration and motion direction are perpendicular

2.      a longitudinal  wave à vibration and motion are the  same direction.

Frequency : is the number of wave per unit time

Period : is the time needed for travelling one wave length

   or     

Wave velocity : is the velocity at which wave crests appear to move (Wave crest travels a distance of one wave length in one period)

 or

A.    Amplitude

a.       Stationer wave (Standing wave) à amplitude change

b.      Travelling wave à a is constant

c.       Wave walks / spread from O to P (by velocity u )if the point O has vibrated t second, so if the point P, wave has vibrated  because wave need time for move from O to P , so the equation of deviation of wave motion is :

yp = A Sin wtp

     = A Sin w (t - )

     = A Sin (wt -  )

= A Sin

Just the opposite :

Wave spread from P to O :

If the point O has vibrated t s, so in the point P, wave has vibrated tp =

yp = A Sin tp = A sin w

     = A Sin (wt + kx)

n  General Equation of Wave Motion :

       Y = A sin (wt ± kx)                

§  Vibration direction and spread direction of wave :

-          If vibration direction upward so A is +

-          If vibration direction up down so A is –

-          Spread direction from x – axis to x+ axis the equation use –

-          Spread direction from x+ axis to x – axis the equation use +

            = A Sin    à vibration from x axis hey to pos

n  Velocity of particle vibration at P point :

Vibration velocity and wave motion velocity vibration of the particle can be gotten from first differential of displacement bto time :

y   = A Sin (wt – kx)

v   =

v   = A w cos (wt – kx)

motion velocity of wave can be gotten from relation v and k

n  Vibration acceleration / Acceleration of particle vibration at P point

Vibration acceleration is first differential of vibration velocity to time

n  Phase angle, Phase and Phase difference :

Example1 :

Wave motion move to direction positive X axis with velocity v = 5 m/s, frequency 10 Hz, and amplitude 2 cm. If vibration source  has vibrated during 2/3 second with first vibration direction to ward, determine:

1. General equation of wave motion
2. Velocity and accelerationof particle at point x = 0.5 m
3. Phase and phase angle of wave at point x = 0.5 m
4. D
   1. Stationer Wave
   Stationer/standing wave is a wave that formed from the result of interference two wave that A and f the same.
   A in stationer wave is not constant but change. There are A  max (Anti node) and A Min (Node)
   Stationer wave on free end of a fine wire string the free end of string is a  string by string the reflection end that can move free up/down which motion follow direction of wave vibration that come.
   On a spring by the end free, phase of come wave is the same by phase of reflection wave.
   a.      Fixed End
   In the point P :
   The equation of come wave is :
   Xp = (е – x )          y₁= A sin (wt – kxp)
                                     = A sin {wt – k(e – x)}
   ifference phase between point x = 0.25 m with x = 0.75 m