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

*
.:
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

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 .

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

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
.

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.

∈
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
− −

.
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

.

,:

.:



,

.
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 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&
.
.
, .
.

.
&#$O*89/#$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
:

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+

, . , .
,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&

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
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Q t
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+ − = + − =
   
   
chọn B
Dạng: Biên độ dao động tổng hợp
Bài 1: 
LD
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#
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89/
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=>,Q/K
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Chọn A
Bài 2: u/]$%#/0l=n&#* !'5-N#*,Q
/-  #$  80  H$  '  `  8  <  '  (@  =k  =  =>
*
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N
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32
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(h=>
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Giải:
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λ
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nhất @ M phải nằm trên vân cực đại bậc 1 như@}>
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A R = 4cm O B
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
. . . .
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
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+*A(#
Q- ,- [k = ± ± ±
K
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. ,
[K[Q wQ6 7d d k cm
λ
− = = =
6,7
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
. . . .
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Chọn B
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#$80<'(@
, .
* * #$_Q 6/7= = π
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=>
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N#$80;'#-;k-#*5N4q/D$(##& !'
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$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&
,
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