Bài tập giao thoa sóng cơ

SỞ GIÁO DỤC VÀ ĐÀO TẠO VĨNH PHÚC
CHUYÊN ĐỀ:
BÀI TẬP GIAO THOA SÓNG CƠ
VẬT LÝ 12
Phạm Thị Toản
Giáo viên
Trường THPT Phúc Yên
Lớp 12
 !!4 tiết
22
GIAO THOA SÓNG CƠ
CƠ SỞ LÝ THUYẾT
I. Lý thuyết cơ bản về giao thoa sóng cơ :
"#$$#%##&'(#)#*& !'+
,
-+
.
#*
/0 $1l
23.* !'*
,
45
,
$6
,
t
ω ϕ
+
7-*
.
45

.
$6
.
t
ω ϕ
+
7-
2389/:($;#$$#& $1<*=>
,-

.
?(@&$*
,-
*
.
(*AB<:
*
,:
45
,
$6
,
,
.
d
t
ω ϕ π
λ
+ −
7

*
.:
45
.
$6
.
.
.
d
t
ω ϕ π
λ
+ −
7
?(@&C'D:*
:
4*
,:
E*
.:
1. Độ lệch pha của hai sóng từ hai nguồn đến M là:

. , , .
.
6 7
M M M
d d
π
ϕ ϕ ϕ ϕ
λ

∆ = − = − +∆

F<
. ,
∆ = −
ϕ ϕ ϕ
2. Biên độ dao động tổng hợp
;'''18G(HH=9*I3J*#A5
,-
5

>5KL#&
Biên độ dao động tổng hợp:
5
.
45
,
.
E5
.
.
E.5
,
5
.
$6
. ,
, .
.
d d

ϕ ϕ π
λ
−
− +
7
a. Biên độ dao động tổng hợp cực đại545
,
E5
.

$6
. ,
, .
.
d d
ϕ ϕ π
λ
−
− +
74,
⇔
. ,
, .
.
d d
ϕ ϕ π
λ
−
− +
4 .

π


, .
6 7
.
d d k
ϕ
λ λ
π
∆
→ − = +

b. Biên độ dao động tổng hợp cực tiểu: 5=
, .
5 M5

$6
. ,
, .
.
d d
ϕ ϕ π
λ
−
− +
74M,
⇔
. ,
, .

.
d d
ϕ ϕ π
λ
−
− +
4
.k
π π
+
23
:
+
,
+
.

,

.
, .
,
6 7 6 7
. .
d d k
ϕ
λ λ
π
∆
→ − = + +


3.Phương trình sóng tại điểm M khi hai nguồn cùng biên độ A

, ,
5$6 7u t
ω ϕ
= +
>
. .
5$6 7u t
ω ϕ
= +
E?(@&D:$#&)#*(*AB<

,
, ,
5$6 . 7
M
d
u t
ω π ϕ
λ
= − +
>
.
. .
5$6 . 7
M
d
u t

ω π ϕ
λ
= − +
E?(@#$$#&D:u
M
= u
1M
+ u
2M

, . , . , .
. $ $
. .
M
d d d d
u Ac c t
ϕ ϕ
ϕ
π ω π
λ λ
− + +
∆
   
= + − +
   
   
ENO80#$80D:
. ,
.K K $6 7
.

M
d d
A A c
ϕ
π
λ
− ∆
= +

E8D#$$#5
:/#P
4.K5 
, .
6 7
.
d d k
ϕ
λ λ
π
∆
− = +
E9*#$$#5
:/
4Q 
, .
,
6 7 6 7
. .
d d k
ϕ

λ λ
π
∆
− = + +
R!*#*#$80;'#
MF(S8D#$$#
.
T
,
4 U6 4QVW,VW.XK7
6Y89/#$80<O808D=>Y89//>*88%#
#&)*(*AB<Zsố nguyên lần bước sóng7
MF(S9*#$$#
.
T
,
46 E
,
.
7U6 4QVW,VW.XK7
6Y89/#$80<O809*=>Y89//>*88%#
#&)*(*AB<Zsố bán nguyên lần bước sóng7


24
8D
 4M[ 4M. 4M, 4Q 4, 4. 4[
8[8.8,8Q8,8.8[

 4M[ 4M. 4M, 4Q 4, 4.

[.,,.[
9*
R\$1Y##8D$]#9*=O!'=>U^.
\$1Y#/08D>/09*=O!'=>U^_
II. Tìm số điểm dao động cực đại, số điểm dao động cực tiểu giữa hai nguồn:
R+8D
, . , .
. .
S S S S
k
ϕ ϕ
λ π λ π
∆ ∆
− + < < +
6
k Z
∈
7
R+9*
, . , .
, ,
. . . .
S S S S
k
ϕ ϕ
λ π λ π
∆ ∆
− + − < < + −
6
k Z

∈
7
=> Số giá trị nguyên của k thoả mãn các biểu thức trên là số đường cần tìm.
III.Tìm số điểm dao động cực đại, dao động cực tiểu giữa hai điểm M, N bất kì:
+8D>9*(O8$D`#89/:>($;&#$
$#=>(%# 6 ∈ a7SH$#*6 S#
*7
R+8D
. , . ,
. .
S N S N S M S M
k
ϕ ϕ
λ π λ π
− −
∆ ∆
+ ≤ ≤ +

k Z
∈

R+9*
. , . ,
, ,
. . . .
S N S N S M S M
k
ϕ ϕ
λ π λ π
− −

∆ ∆
+ − ≤ ≤ + −
6b*c+
.
:T+
,
:d+
.
T+
,
7
RL(':-8P<#*J*#89/e=>
(*89/%#+
,
+
.
@fS8D-9*Y##89/:e(g.K
IV. Bài toán liên quan đến đường trung trực
$#*+
,
 +
.
 #*;#$808B*h#<'(@
*
,
4*
.
45K$6i7K"j=>#$89/%#8(*(>#*+
,
+

.
K
L(O8(*(89/:-<:kjlK
M ?(@#$80%#:
*
:
4.5K$
. d
t
π
ω
λ
 
−
 ÷
 
M 28:j:j4
.
.
, .
_
S S
d −
EB* 89:#$80;'#<#*
.
.
d
k d k
π
π λ

λ
= → =
/>
, . , .
. .
S S S S
d k
λ
≥ → ≥
R:j
/
 
/
8&
.
.
, .
/
6 K 7
_
min min
S S
d k MI k
λ λ
= → = −
25
:
+
,
+

.

,:

.:



,

.
M
d
d
I
S
1
S
2
EB* 89:#$80;<#*
. , ,
6 7. 6 7
. .
d
k d k
π
π λ
λ
= + → = +
/>

, . , .
,
. . .
S S S S
d k
λ
≥ → ≥ −
R:j
/
 
/
8&
.
.
, .
/ /
, ,
6 7 6 7
. . _
min
S S
d k MI k
λ λ
 
= + → = + −
 
 
M N>$P889/#$80;'#<*($8$D:j

, .

.
S S d
k
λ λ
≤ ≤
($8&
.
.
, .
.
S S
d MI
 
= +
 ÷
 
M N>$P889/#$80'#<*($8$D:j

, .
, ,
. . .
S S d
k
λ λ
− ≤ ≤ −
($8&
.
.
, .
.

S S
d MI
 
= +
 ÷
 
BÀI TẬP VẬN DỤNG
Dạng: Xác định số cực đại, cực tiểu giao thoa
Bài 1: m#*&+
,
>+
.
(O/]l=n#*.Q/#$
80H$'(@ 
tuu
π
_Q$_
.,
==
6/-7-=#(*AB($/(
<804, /^K
,^2389/(O8$D`+
,
<+
.
K
#KLS $1Y##89/=O!'&O808Do
KL(O+
,
+

.
&#$O*89/#$80<O808D-9*o
.^2389/:+
,
 $1,./>+
.
 $1,p/K28
88D-9*8J*#8$D+
.
:o
Giải :
1 a/ Khoảng cách giữa hai điểm liên tiếp có biên độ cực đại:
Bước sóng
λ
= v.T =v.2
π
/
ω
= 6 (cm)
Khoảng cách giữa hai cực đại liên tiếp:
[6 7
.
cm
λ
=
b/ Số điểm dao động với biên độ cực đại trên S
1
S
2
:

+8D(O+
,
+
.

λλ
.,.,
SS
k
SS
<<−
→
[[-[[[-[ <<− k

→&789/#$80<O808DK
26
+9*(O+
,
+
.

.
,
.
,
.,.,
−<<−−
λλ
SS
k

SS
→
q[ q[-[ <<− k

→&689/#$80<O809*K
2/ Số đường cực đại, cực tiểu đi qua đoạn S
2
M
&+
.
:T+
,
:4_/V+
.
+
.
T+
,
+
.
4M.Q/
+8Dn#/r
. . , . . ,
[-[[ Q-pp
S S S S S M S M
k k
λ λ
− −
< ≤ → − < ≤
blA( 4QVM,VM.VM[FsA(O+

.
:f&_8DK
+9*n#/r
. . , . . ,
, ,
[-q[ Q-,p
. .
S S S S S M S M
k k
λ λ
− −
− < ≤ − → − < ≤
blA( 4QVM,VM.VM[FsA(O+
.
:f&_9*K
Bài 2: LD#89/5>N(O/]l=n#*,Q/&#*
'& !'#$80H$'(@*
,
4#$6,Qπ7-*
.
4$6,QπE
π7KL80(*AB&(O/]l=n.Q6/^7KL@/8D-9*
(O8$D5No
Giải: N<&λ4
.
Kv
π
ω
4.Q^t4_6cm)
+8Dn#/r

, . , .
,Q ,Q
. . _ . _ .
S S S S
k k
ϕ ϕ π π
λ π λ π π π
∆ ∆
− + < < + → − + < < +
. [k
→ − < <
blA 4QVW,V.sA&_8DK
+9*n#/r
, . , .
, , ,Q , ,Q ,
. . . . _ . . _ . .
S S S S
k k
ϕ ϕ π π
λ π λ π π π
∆ ∆
− + − < < + − → − + − < < + −
t tk→ − < <
blA 4QVW,VW.sA&t9*K
Bài 3 (ĐH 2009): uB/]/0l=n&#*'& !'+
,
>
+
. 
#*.Q/Km#*>A#$80H$'`8&

'(@=k==>*
,
4t$_Qv6//7V*
.
4t$6_QvEv76//7>80
(*AB&(O/]l=n=>qQ/^K+89/#$80<O808D
(O8$D`+
,
+
.
=>
A. ,,KB. wKC. ,QKD. qK
Giải:
27
S
1
:

N5
N<&λ4
.
Kv
π
ω
4_6/7
+8DY##*=>(%# n#/r
, . , .
. .
S S S S
k

ϕ ϕ
λ π λ π
∆ ∆
− + < < +
.Q .Q
_ . _ .
_-t t-t QV ,V .V [V _Vt
k
k k
π π
π π
→ − + < < +
↔ − < < → = ± ± ± ±
4d+89/#$80<O808D=>,QĐáp án C
Bài 4 (ĐH 2013): L($/0S/B#$$#&<-#*
& !'#$80;'#D#89/5>N#*,p/K+&
(*AB(O/]<<<&[/KL(O8$D5N-89//>D8&'k
x<#$80<O808D=>
5K,Q NK,, K,. Kw
Giải:
l l
k
λ λ
−
< <

,p ,p
QV ,V .V [V _V t
[ [
k k

−
< < => = ± ± ± ± ±
Đáp án B
Bài 5 (ĐH-2010): u/]$%#/0l=n&#*& !'5
>N#*.Q/-#$80H$'`8<'(@
tu
A
π
_Q$.=
>
7_Q$6.
ππ
+= tu
B
6*
5
>*
N
SZ//-SZ7KN!
80(*AB&(O/]l=n=>[Q/^K23@*5:N*0
/]$l=nK+89/#$80<O808D(O8$DN:=>
A. ,wKB. ,yKC. .QKD. ,qK
Giải:
N<&λ4K
ω
π
.
4,-t/
+8D(O8$DN:n#/r


λ
ABBB
−
E
π
ϕ
.
∆
z 
λ
AMBM
−
≤
E
π
ϕ
.
∆
π
π
π
π
.t-,
.Q Q
.t-,
.QQ
+
−
≤<+
−

→
k
M, qz 
≤
p-Q.V@ ∈{O s,w(-$8&(ON:&,w8DK
28
Bài 6: L($S/#$$#&(O/]<-m#* !'5
>N;'#KLD89/:(O/]<5>N=k==>
,
4_Q/
>
.
4[p/#$80&O808DK$!s(*AB&=>4
_Q/^-Y#:>8(*(%#5N&/08D K
,^LSk&K
.^LD89/(O/]<5>N=k==>
,
4[t/>
.
4_Q/
#$80&O80!>$oL(O8$D`D*&)8!
8(*(%#5N&#$O*89/#$80<O808Do
G iải :
1/ Tần số sóng :
LD:&8DO
λ
kdd =−
,.
617
"Y#:>8(*(&/08D →

.=k
6Hay k = -27627
FsA)617>627→
=
−
=
.
[p_Q
λ
./V\!J*1: |
==
λ
v
4.QmaK
2/ Số cực đại trong đoạn NI 6F<j=>#$89/%#8`*&)
8!8(*(%#5N7
Q t
BI AI BN AN
k k
λ λ
− −
≤ ≤ → ≤ ≤
blA 4QV,V.FsA)8!j&[8D
Bài 7. m#*'& !'5-N(O/]$%#/0l=n#$
80H$'(@
pK $6.Q 76 7V pK $6.Q ^ .76 7
A B
u c t mm u c t mm
π π π
= = +

K$O
80& 1/H$ $1-80&
[Q6 ^ 7v cm s=
K\$1
Y##*
.Q6 7AB cm=
K
,KLS89/8AO>89/#$80<O808D(O8$D5No
2.m=>(*89/%#5N-89/8AO(O8$D5Nkml>P#m
lm/08$DZ#$O*o
3. m#89/ 
, .
VM M
 ;Z/(O/0H='s5-N=>/O*89/&
, ,
[6 7AM BM cm− =
>
. .
_-t6 7AM BM cm− =
KLD89/
,
>$8&-=80%#:
,
=>2(mm7, S=80%#:
.
D89/8&o
29
G iải :
EN<&
[Q

[6 7
,Q
v
cm
f
λ
= = =
,K+89/#$80<O808D

.Q ^ . .Q ^ .
. . [ . [ .
AB AB
k k
ϕ ϕ π π
λ π λ π π π
∆ ∆
− + < < + → − + < < +

p-_ p-w QV ,KKKK pk k→ − < < → = ± ±
FsA&,[8D
E+89/#$80<O809*

, , .Q ^ . , .Q ^ . ,
. . . . [ . . [ . .
AB AB
k k
ϕ ϕ π π
λ π λ π π π
∆ ∆
− + − < < + − → − + − < < + −


p-w p-_ QV ,KKKK pk k→ − < < → = ± ±
FsA&,[9*
.KLD89/:*08$D5N(*89/m/08$Dx-&*88%#
#&=>
, .
.d d x− =
E9/:*08$D5N8AO$1/r

, .
, ,
. 6 7 6 7K
_ _ .
d d x k x k
λ
λ
− = = + → = +
6,7<
pVKKKVpk = −
E$8&
#P
/
, [
6p 7K w-[yt6 7
_ .
, [
6Q 7K Q-[yt6 7
_ .
m
x cm

x cm

= + =




= + =


[K?(@#$80C'D:5-NY8$D
,
>
.
=>

, . , .
,.K $ 6 7 K $ 6 7 6 7
_ _
M
u c d d c t d d mm
π π π π
ω
λ λ
   
= − + + + +
   
   
Em#89/:
,

>:
.
8B**0/0H='s5-N=>/O*89/O

, , . .
AM BM AM BM b+ = + =
+*A(#'(@#$80%#:
,
>:
.
=>

,
,
.
.
K
,.K $ K[ K $
[ _ _
,
K
,.K $ K_-t K $
[ _ _
M
M
M
M
b
u c c t
u

u
b
u c c t
π π π π
ω
λ
π π π π
ω
λ

   
= + + +

   
    
→ = −

   

= + + +
   

   

LD89/
,

, .
.6 7 .6 7
M M

u mm u mm= → = −
30
Bài 8:  L(OB/]l=n$#*#$80*&<B/]
l=n&'(@#$80*
5
4[$,Qπ6/7>*
N
4t$6,QπE
π^[76/7KL80(*AB&(OgA=>4tQ/^K5N4[Q/K$89/
(O8$D5N-5 $1,q/>N,./KF}h(h8 S
,Q/-g/DK+89/#$808D(O8(h=>o
5KyNKpKqK_
Giải: N<&
 tQ
,Q
| t
cm
λ
= = =
.
9S8D(O8(h@#S
8D(O8 S:(g.@/~
8D(O:}•8(hD.89/
$D().89/:>f•8(hD/089/K€'
π
π
π
π
π
ϕ

λπ
ϕ
λ
.
[^
,Q
,[,y
.
[^
,Q
.[y

+
−
≤≤+
−
→
∆
+
−
≤≤
∆
+
−
k
MAMB
k
NANB

,VQtp-Q_-, −=→≤≤−→ kk

⇒
&.8D(O:
⇒
&_8D(O8(h
Dạng: Đường trung trưc
Bài 1 L#$$#&(O/]<<#*+
,
V+
.
;'#-
#*,./KN!<&%#&(O/]<=>U4[/KL(O
8(*(%##*&89/:-:(*89/j%##*
q/Kmn(O:j&#$O*O*89/#$80;'#<.*o
5K_89/BK.89/Kp89/K[89/
Giải
[
qp
[K.
,.
.

,.,
+
≤≤→≤≤ k
MS
k
SS
λλ

[V.[-[. =→≤≤→ kk

NK
Bài 2 (ĐH 2011):u/]l=n&#*&5-N#*,q/-
#$80H$'`8<'(@=>*
5
4*
N
4#$tQπ6<
SZ7KL80(*AB&%#/]l=n=>tQ/^K"e=>(*
89/%#5N-89/:•/]l=nZ/(O8(*(%#5N>k
31
A
B
C
M
N
j
:

+
.
+
,
el#$$'kxl=nD:#$80;'#<'kxl=n
DeK\$1:e=>
5K,Q/K NK
. ,Q
/KK
. .
/K K./K
Giải: N<&

. .
K tQK .6 7
tQ
v cm
π π
λ
ω π
= = =
?(@#$80%#e*
Q
4.5K$
. d
t
π
ω
λ
 
−
 ÷
 
4.K5$6iMwv7K
F@e'#<*O:‚'#<*K
&
,q
_-t
. _
AB
k
λ
≥ = =

KFsA
/
4t
:e
/
4
. .
.
.
, .
/
, , ,q
6 7 6t 7. . ,Q6 7
. _ . _
S S
k cm
λ
   
+ − = + − =
   
   
chọn B
Dạng: Biên độ dao động tổng hợp
Bài 1: 
LD

#

89/


5

>

N

(O

/]

<

&

.

*

&;'#-

O

80
=
k==>_/>./
-

<

&


=>,Q/K
 
9/

:
(O/]<


5
.t/>

N
[
Q/

}

#$

80

<

O

80

=>
A. ./ B. _/ C. p/ D. q/

Giải : A
:
.
45
,
.
E5
.
.
E.5
,
5
.
$6
. ,
, .
.
d d
ϕ ϕ π
λ
−
− +
7
L#A5
.
4_
.
E.
.
E.K_K.$6

[Q .t
.
,Q
π
−
74_
FsA5
:
4./

Chọn A
Bài 2: u/]$%#/0l=n&#* !'5-N#*,Q
/-  #$  80  H$  '  `  8  <  '  (@  =k  =  =>
*
5
4[$6_QπEπ^p76/7V*
N
4_$6_QπE.π^[76/7K$!80(*AB
&=>_Q/^K:08(h&g/=>(*89/%#5N-Z/(O/]
32
I
<-& Sƒ4_/K+89/#$80<O80t/&(O8
(h=>
A. [QB. 32C. [_ D. [p
Giải:
NO80&C'D:=>
5
.
45
,

.
E5
.
.
E.5
,
5
.
$6
. ,
, .
.
d d
ϕ ϕ π
λ
−
− +
7
54
. .
. ,
6 7
.
[ _ .K[K_K $6 . 7
[ p
d d
c
π π
π
λ

−
+ + − +
4t
. ,
6 7
$6 . 7
.
d d
c
π
π
λ
−
→ +
4Q
\8&
. ,
.
6 7
.
d d
π π
λ
− −
74
.
k
π
π
+

$8&
.
T
,
4
.
λ
V:>Mq≤
.
T
,
≤q⇔Mq≤ ≤q&,y( K
LD#89/:>•#8k* S=>89/#$80<O80Zt/K
O89/#$80<O80t/=>n = 17x2 – 2 = 32. Chọn B
Dạng: Tìm điểm M dao động với biên độ cực đại hoặc cực tiểu thỏa mãn điều
kiện đề bài
Bài 1: L(OB/]l=n&#* !'5N#*_Q/#$
80;'#KN!&$/~*'(#&k|4,Q6ma7-s
(*AB&
.6/^7K":=>/089/Z/(O8*&<5ND5($8&:
#$80<O808DKĐoạn AM có giá trị lớn nhất=>
5K.Q/NK[Q/K_Q/KtQ/
Giải: L#&
.QQ
.Q6 7
,Q
v
cm
f
λ

= = =
K
$:=>/08D#$$#O898$D5:& giá trị lớn
nhất @ M phải nằm trên vân cực đại bậc 1 như@}>
n#/r
33
5
N
:
\4
Q
,
.
\4
,
A R = 4cm O B

. ,
,K.Q .Q6 7d d k cm
λ
− = = =

:] -$#/5:N=>#/*D5
O#&

. . . .
. ,
6 7 6 7 _Q 6.7AM d AB AM d= = + = +

. .

, , ,
_Q .Q [Q6 7d d d cm→ + − = ⇒ =
'N
Bài 2 : L(OB/]l=n&#* !'5N#*,QQ/#$
80;'#KN!&$/~*'(#&k|4,Q6ma7-s
(*AB&
[6/^7K":=>/089/Z/(O8*&<5ND5($8&:
#$8<O808DKĐoạn AM có giá trị nhỏ nhất=>
5Kt q/NK,Q-tp/K,./K[Q/
Giải: L#&
[QQ
[Q6 7
,Q
v
cm
f
λ
= = =
K
+g#$80<O80#$808D(O8$D5N
„#/r8B* 
,QQ ,QQ
[-[ [-[
[ [
AB AB
k k k
λ λ
− −
< < ⇔ < < ⇔ − < <
K

+*A(#
Q- ,- [k = ± ± ±
K
FsA898$D5:&(nl@:'1Z/(O88Ds[
(
/#P
4[7@}>n#/r
. ,
[K[Q wQ6 7d d k cm
λ
− = = =
6,7
:] -$#/5:N=>#/*D5O#&

. . . .
. ,
6 7 6 7 ,QQ 6.7AM d AB AM d= = + = +

L#A6.7>$6,7#8
. .
, , ,
,QQ wQ ,Q-tp6 7d d d cm+ − = → =
Chọn B
Bài 3:LD#89/5>N(O/]<#*q/&#* !'
#$80<'(@
, .
* * #$_Q 6/7= = π
-80(*AB&(O/]<
=>
[Q/ ^ 

K238$D`4_/(O/]<&*8(*(<
5NK\$1=<l)8!5N#$$(O8$Df&[89/#$
0<O808D=>
A. [-[/K B. p/K C. q-w/K D. w-y/K
34
5
N
:
\4Q
,
.
\4[
Giải : N<&U4^|4[Q^.Q4,-t/
\$1=<l)8!5N/>(Of&[89/
#$80<O808D D>*0g8D
s,6 4W,7
LD
.
T
,
4,-t6/76,7
\8&5:4./VN:4p/
L#&
,
.
4
.
E.
.


.
.
4
.
Ep
.
L#A
,
>
.
>$6,7
. . . .
p . ,-t w-y6 7h h h cm+ − + = → =
Bài 4: L($S/#$$#(O/]<-#*& !'5>
N#$80;'#-;k-#*5N4q/D$(##& !'
&<&λ4./KL(O8`6∆7$$<5N>5N/0
$1=>./- $1•l)#$89/%#6∆7<8(*
(%#5N8!89/:#$80<O809*=>
A. Q-_[/K B. Q-t/K C. Q-tp/K D. Q-p_/K
Giải::#$809*klO:*09* 4Q
b…8&
,
T
.
46 E
1
2
7U4
1
2

U6,7
"P=> $1):8!
. .
,
 5j P :\= + +( )
V
. .
.
 Nj P :\= − +( )
#A>$6,7

. . . .
, .
  5j P :\ Nj P :\
.
λ
− = + + − − + =( ) ( )
L#A>$1'
. . .
, .
  _ P . _ P . , P Q tp/− = + + − − + = => =( ) ( ) ,

Bài 5: L(O/]<#*&5>N#$808B*$>H$'
*&</]<<'(@*
,
 4*
. 
4#$6.Qπ7KN!80
(*AB&_Q6/^7-O80& 8C (*AB8K:089/(O
35



.

,
:

5
N

/]<&* $18!#*5>N$1/r5MN4,Q
/K9/Z/(O88AOXK 9)(*(%#5N>B
XXXK
5K[M'S#5 NK.M'S#
K[M'S#N K.M'S#N
Giải: N<&λ4^|4_Q^,Q4_6cm)K
;
, .
.
6 7
N
d d
π
ϕ ϕ
λ
∆ = − + ∆
<∆ϕ4Q
.
K,Q Q t 6. ,7
_

M
k
π
ϕ π π
∆ = − = = +
4d 4.
FsA89/Z/(O88AO[69*[7B'S#N@
,
d
.
Bài 6: m#*+
,
>+
.
#$80H$'(@*
,
4#
,
$6qQπ7/-
*
.
4#
.
$6qQπEπ^_7/(O/]<K23B/0'S#8(*(%#
+
,
+
.
#lAgs8J*#89/:&*:+
,

M:+
.
4,[-t/>gs
E.6;=$D<g78J*#89/:†&:‡+
,
M:‡+
.
4.,-t/KL@/80
(*AB&(O/]<-g=>8D#A9*o
5K.t/^-9* NK,pQ/^-9*
K.t/^-8DK,pQ/^-8D
Giải236
,
M
.
74:+
,
M:+
.
4,[-t4λ
>6‡
,
M‡
.
74:‡+
,
M:‡+
.
4.,-t46E.7λ
#&.λ4.,-tT,[-t4q4dλ4_6/7sA4λK|4_K_Q4,pQ6cm/s)

;
, .
.
6 7
∆ = − + ∆
M
d d
π
ϕ ϕ
λ

<∆ϕ4π^_4d
.
K,[-t
_ _
∆ = +
M
π π
ϕ
4p-tπ46 EQ-tπ7
sAg=>9*
Bài 7 (ĐH 2012):L($#$$#&<-#*#$80
H$'*&</]<-;O80-;'#-;ktQ
ma88]D#89/+
,
>+
.
#*,Q/KL80(*AB&(O/]
36
<=>yt/^K2389/(O/]<*08(hg/+

,
- S
+
,
+
.
-89//>'kxD8&#$80<O808D89/+
.
/0
8$D•lZ
5Kqt//K NK,t//K K,Q//K Kqw//K
Giải
L#&U4^|4,-t/ˆ $1g&($x#/B#$$#=> z
λ
.,
SS
4
t-,
,Q
4p-pp
FsA89//>'kxD8&#$80
<O808DZ/(O8(h
g/+
,
+
.
/08#kl  4p
F<
,
M

./
4 KU4pK,-t4w/
F@
,
4ƒ4+
,
+
.
4,Q/ˆ,QT
./
4w
ˆ
./
4,QTw4,/4,Q//Chọn C
Bài 8.m#/‚+
,
-+
.
#8k*#*q/••8k*/0k(*&
k|4,QQma-88]D/‰>$/]<KL80(*AB&(O/]
<=>4Q-q/^K
#^"„‰k(*$#89/+
,
-+
.
#$80H$'`8<
'(@D *45K$.v|KF!'(@#$80%#89/:
,
8B*+
,

-+
.
/0 $14q/K
^L@/(O8(*(%#+
,
-+
.
89/:
.
k:
,
l>#$80;
'#<:
,
o
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,
+
.
K9=DJ*#8
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,
+
.
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,
-+
.
&#$O*89/&

O808DK
$(Z &#$$#C8@#89/+
,
+
.
=>#89/&O809*K

Giải:
37
……
S
2
S
1
d
2min
k = 6
d
1
aKEU4
|

4Q-q/>
,
4
.
44q/
EL#&'(@#$80&C'D:
,



*
:,
4.5$






λ
+π
−π
λ
−π 76
.QQ$
76
.,,.

<
,
E
.
4,p/4.QU>
.
T
,
4Q-
#8*
:,

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bKm#89/:
.
>:
.‡
k:
,
#&
+
,
:
.
4EU4qEQ-q4q-q/
+
,
:
.‡
4TU4qTQ-q4y /
$8&j:
.
4
7/6q_-y_q-qj+:+

,
.
.,
=−=−
j:
,
4+

,
j
7/6w[-p[_[ ==
+*A(#:
,
:
.
4y-q_Tp-w[4Q-w,6/7
Lj:
.
‡
4
†. . . .
, . ,
+ : + j y _ t-ww6/7− = − =
 :
,
:
.
‡
4p-w[Tt-ww4Q-w_6/7
cKN#8k*#8r&+
,
+
.
4q/4,QU4.Q
.
λ

$sA#89/+

,
-+
.
=>#O*89/%#A'H$=>•(lk…PH/
k8…=>8D#$$#K
\&8rC8@#89/+
,
-+
.
=>#O*89/%#A'H$=>•
(lk…PH/k8…=>8AO-h(*89/j%#+
,
+
.
=*Z/
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$8&#&+
,
j4+
.
j4
_
7, .6
_.
λ
+=
λ
+
λ
4d+

,
+
.
4.+
,
j46. E,7
.
λ
4dfkŠ+
,
+
.
/0 $1
.
λ
4Q-_/K
\8&(O+
,
+
.
&.,89/&O808DK
BÀI TẬP TỰ GIẢI
Bài 1.L(O/]<&#*&#*5>N-#* $1
38
M
1
M
2'
M
2

S
1
I
5N4,.6/78##$80*&</]<D$(#&&<&
λ4,-p/K
#7L@/89/#$80<O808D-9*(O8$D5NK
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(*89/e%#5N/0 $1q6/7KL@/89/#$80;'#<
*•(O8$Do
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Bài 2. :] <&#*'& !'5-N#$80H$'
(@
t$6.Q 7
A
u t cm
π
=
>
t$6.Q 7
B
u t cm
π π
= +
K$O80& 8C-
80&=>pQcm/sK
#7F!'(@&C'D89/:5-NY8$D=>:54
,,cmV:N4,_cmK
7$5N4.QcmKm#89/-(O/]</>5N=>@Ys
<54,tcmKLS89/#$80<O808D(O8$D5N>
(O8$D5o

7m#89/:
,
>:
.
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89/>$8&s%#:
,
&(8D=>
scm^_Q−
K28(8D
%#s%#:
.
=…8&
o

ĐS#-
,QK$6.Q ^,,76 7K
M
u t cm
π π
= −
KL(O8$D5N&p89/8DKL(O5&t89/8D
Km!'(@&D:
,
-:
.
KLlA#89/:
,
>:
.

#$
80;O80'##*-O=…s%#:
,
&(8D=>M
_Q/^@s%#:
.
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Bài 11.L(O/]<&#*#*5>N#*,q/8#
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42