Wave and Wave Motion

Wave    매질이 평형상태에서 벗어난 상태가 이동해 가는 

현상    종파     변형 방향이 진행 방향과 나란한 파동   

  횡파    변형 방향이 진행 방향과 수직인       

        Examples: http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html　

Mathematical Foundation for the (traveling) wave formula　　        Let's use to denote the deviation from the equilibrium.                           

                                 

Let's move this graph by +3 and see what we need to incorporate proper changes in coordinates.

The original function still retains its functional shape in the new coordinate system. That is,

Since   x' = x -3.  in  the old coordinate system,  the equation for the now-translated function becomes 　

25( 3)( ) xx e Conclusion:  In order to move a graph by +a, replace the variable by (x-a) in the original

function.  　     Exercise : Find the expression for the function when it has moved -5 units.

What happens if we replace the x with x - 3 t ?   That is,       　　 동영상 파일What is the physical meaning of "3" in the above expression?

25( 3 )( ) x tx e

Harmonic Waves　

Waves that behave according to Sin or Cos functions are called harmonic waves.　　   

    

The function that produced this graph is  

      

      

            

  Review of the Sin function

2k                      

Now, we move this function as             

Let's take an example. l = 1 m,   v= 0.5 m/s.

 http://www.kettering.edu/~drussell/Demos/rad2/mdq.html

의 시간 특성 분석

계산 편의를 위해  x=0, A= 10를 가정해 보면 위 식은 다음과 같아진다 .2 1

(0, ) sin sin 2 sin 2t A vt A tv

A t

v

v

1(0, ) sin 2t t

TA

1

fT

2 2( , ) sin sinx t A kx vt A kx t

파동의 일반적 표현

A :  진폭      Amplitudek:    각 파수   Angular Wavenumber   :  각 진동수   Angular Frequency 

2 2,k

Tkv

( , ) 12.5 sin 7.5 2.5x t x t

0.5 1 1.5 2 2.5

-10

-5

5

10

0.5 1 1.5 2 2.5

-10

-5

5

10

T = 0 T=1