Download 020140411072652428707EDEC029BFCF81DA670857C105C2A

Chapter 13&14
Mechanical Waves
Wave is everywhere in nature!
13-1 Creation and Propagation of Waves (p326)
1. Conditions of a Mechanical Wave
(1) A Wave Source
(2) Medium in which
a mechanical wave
propagates.
2.The Feature of wave’s propagation:
1 2 3 4 5 6 7 8 9 10 11 12 13
t=0
1 2
3
t=T/4
2
t=T/2
4 5 6 7 8 9 10 11 12 13
3 4 5
1
6
7 8 9 10 11 12 13
6
t=T
7
1
2
8
10 11
12
13
34 5
Wave is propagation of oscillatory state
(oscillatory phase ).
3. The Characteristic Quantities of wave:
(1) The wavelength  reflects the periodic property in
space. It depends on both source and medium.
(2) The period T of wave reflects the periodic property in
time. It depends on the source only.
(3) The wave speed is the phase speed (波速v 即相速).
It depends on medium only.
Relationship:

v  f
T
13-2
Wave Types
(P327)
Classification According to Oscillation Types
1. Transverse Waves:
The direction of oscillation of medium elements
is perpendicular to the motion of the wave.
crest
trough
Mechanical transverse waves propagate in solid only.
2. Longitudinal Waves:
The direction of oscillation of medium elements is
parallel to the motion of the wave.
Mechanical longitudinal waves can travel in
solid, liquid and gas.
Any complex wave can be considered as
being composed of transverse and longitudinal
traveling waves.
13-4 Mathematical Expression of a Traveling wave (P332):
1. Simple Harmonic Wave (简谐波）:
The wave source and the medium elements are all at
SHM .
For a Simple Harmonic Wave traveling in + x direction
yo (t )  Acos(t  0 )
x
t 
yP ( x, t )  A cos[ (t  t )  0 ]
v
x
y ( x, t )  A cos[ (t  )  0 ]
v
y
v

o
P
x
x
P点在t 时刻的位
移相当于O点在
t-∆t时刻的位移。
2. Equivalent expressions
Using
2
 2 f
relationships:  
T
  vT
and k 
2



v
(where k is angular
wave number,角波数)
we have equivalent expressions for SH wave equation:
x
y ( x , t )  A cos[ ( t  )  o ]
v
t x
y ( x , t )  A cos[2 (  )  o ]
T 
x
y ( x , t )  A cos[2 ( f t  )  o ]

y ( x , t )  A cos( t  kx  o )
The consistent forms in our textbook :
x
y ( x, t )  A sin[  (  t )   'o ]
v
x
t
y ( x, t )  A sin[ 2 (  )   'o ]
 T
y ( x, t )  A sin[ 2 (
x

 f t )   'o ]
y ( x, t )  Asin( kx  t   o )
'
All motions in which the variables x and t enter
in combination t±kx are traveling waves.
3. The Physical Meaning of Wave Equation:
(1) Fixed x= xo, corresponding to the oscillating curve (振动曲线)
of medium element at position xo , i.e. y(t, xo).
y
波具有时间周期（T )
A
t
o
盯住一点拍电影
T
(2) Fixed t =to, corresponding to the wave pattern
curve
y (波形曲线) at time to.
波具有空间周期（ )
x1
A
o
x2

x 广镜头拍照片
(3) The phase of element x2 is behind of x1:
x2
x
x  x1
)  0 ]  [ ( t  1 )  0 ]  2 2
v
v

x  x2  x1 : wave-path difference (波程差)。
  [ ( t 
  
then
2

x
** Three types of periods (三类周期 )
Period for phase
位相周期
Period in space
空间周期

2

2
T
Period in time
时间周期
T
x

＝

x
2
  
x
t
x

t
＝
T
2
  
t
x
(4) For varying t and x, it relates to the propagation of wave.
y
wave pattern at t+t
o

x x

x
v
宽银幕电影
x  vt
wave pattern at t
x
(5) If the wave moves along -x axis y ( x, t )  A cos[ (t  )  0 ]
v
(6) If the source of wave is at x0 , the general expression is
x  x0
y ( x, t )  A cos[ (t 
)  0 ]
v
(7) The oscillatory speed of a particle at position x is
y
x
u
  A sin[  (t  )  0 ]  A sin[ kx  t  0 ]
t
v
Note the difference between v ( wave speed ) and
u (oscillatory speed of a particle )
EXAMPLE:
A SH wave travels in -x direction with speed
v=20m/s as Fig. If yA(t) = 3cos4 t , (1) write the
equation for it about origin A (2) how about origin B;
Solution:
(1)
(2)
x
y  3 cos 4 ( t 
) m
20
x5
y B  3 cos 4 (t 
)
20

or  f 
 2 ( Hz)
2
v

5m
 
B A

x
m
v 20
  
 10m
f
2
The phase of B is behind of A:
2
2
 
AB 
5  

10
x
Wave function about origin B: y  3 cos[4 ( t 
)  ]
20
m
•Questions (思考题）
•P347 1; P347 2; P347 4
•Problems (练习题）
• P349 20; P349 24 ; P34926