1. 第13章 机械波
§13.1 机械波的产生和传播
§13.2 平面简谐波
§13.3 波的能量和能流
§13.4 波的干涉
§13.5 驻波
§13.6 多普勒效应

2. Interference of wave§13.4 波的干涉
两列波在空间相遇，某些点的振动始
终加强，另一些点的振动始终减弱。
干涉现象
产生干涉现象的波 相干波
CAI
Coherent condition相干条件
⑴频率相同 ⑵振动方向相互平行 ⑶相位差恒定
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3. P
r2
r1
S1
S2
)cos( 11010 ϕω += tAy
)cos( 22020 ϕω += tAy
)cos( 1111 krtAy −+= ϕω
)cos( 2222 krtAy −+= ϕω
21 yyy += )cos( ϕω += tA
ϕ∆cos2 21
2
2
2
1
2
AAAAA ++=
( )2121 rrk −−−= ϕϕϕ∆
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4. P
r2
r1
S1
S2
ϕ∆cos2 21
2
2
2
1
2
AAAAA ++=
ϕ∆cos2 2121 IIIII ++=
( )2121 rrk −−−= ϕϕϕ∆
πϕ∆ n2=
21 AAA +=
…±±= ，，， 210n
干涉加强 (干涉相长 )
2121 2 IIIII ++=
πϕ∆ )12( += n
21 AAA −= 干涉减弱 (干涉相消)
2121 2 IIIII −+=
…±±= ，，， 210n
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5. ( )2121 rrk −−−= ϕϕϕ∆
12 ϕϕ =
( ) ( )1212
2
rrrrk −=−=
λ
π
ϕ∆
P
r2
r1
S1
S2
波程差
…±±==− ，，， 21012 nnrr λ波程差
212121 2 IIIIIAAA ++=+= 干涉加强
( ) …±±=+=− ，，， 210
2
1212 nnrr
λ
波程差
212121 2 IIIIIAAA −+=−= 干涉减弱
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6. Geometrically, how can the minima and maxima be
located?
For maxima:
L210 ,,,nnL ±±== λ∆
θ∆ sin12 dLLL =−=
Here, S1 and S2 are the sources, and P is
either a maximum or a minimum.
The difference in path lengths can be
written in terms of the angle ,
assuming that R>>d .
θ
d
n
λ
θ =sin
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7. d
n
λ
θ =sin L210 ,,,n ±±=
00 =→= θn 中央极大
For minima:
( )
2
12
λ
∆ += nL
L210 ,,,n ±±=
θ∆ sin12 dLLL =−=
d
n
λ
θ )
2
1
(sin +=
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8. Two coherent sources are 3.0 cm apart and make
harmonic ripples of the same frequency. Consider
the ripples along a straight line parallel to the
line that connects the sources and 40.0 cm away
from line . If the distance between the central
maximum at and the next maximum on is 8.0
cm， what is the wavelength of the ripples?
1
L
2
L
2
L
1
L 1
L
The angle of the next maximum
is given by
L
D
=θtan
cm040
cm08
.
.
=
= 0.20
o
311.=θ 退出返回

9. d
n
λ
θ =sin
For the next maximum：
= d sinθλ
= (3.0 cm) sin 11.3°
= 0.59 cm
在均匀介质中沿直线传播的波在遇到另外一种介质时，
会发生反射和折射现象。
vZ ρ= 介质的特性阻抗
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10. undulatory thinner mediummallersvρ 波疏介质
largervρ undulatory denser medium波密介质
Incident wave
Reflected wave
π反射时相位突变
phase jump
half-wave loss
波疏介质 波密介质
半波损失
CAI 退出返回

11. Standing waves§13.5 驻波
具有这种波形特征的波
驻波 standing waves
两列振幅相同的相干波在同一直线
上沿相反方向传播时叠加
一种特殊的干涉现象 CAI
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12. 没有波形的推进，参与波动的各
个质元处于稳定的振动状态。
各振动质元的振幅各不相同，但
却保持不变，有些点振幅始终最
大，有些点振幅始终为零。
波腹 antinode 波节 node
CAI
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14. Two harmonic waves of the same amplitude and wavelength
travel in opposite directions along a stretched string
Their interference with each other produces a standing wave
CAI
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15. 2A
t = 0
y
0 x
0
t = T/ 8 x
x
0t = T/2
0 xt = T/4
波节波腹 λ /4-λ /4
x0
2A
-2A
λ/2
振动范围
xt = 3T/8 0
CAI
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