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SÓNG CƠ HỌC
I/ TÍNH CHẤT CỦA SÓNG CƠ.
CHUYÊN ĐỀ 1: BƯỚC SÓNG VÀ VẬN TỐC TRUYỀN SÓNG.
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CHUYÊN ĐỀ 3: PHƯƠNG TRÌNH TRUYỀN SÓNG.
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5
Th.s Trn Quc Dng -_0909959462
CễNG DUY - !" #$#%
&'()*)+,)-#./- ./ Ti Liu LTH
Cõu 15:#/#+,/+,8fH#U)C615
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a +./CYw)
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CHUYấN 2: S IM, S NG CC I V CC TIU TRấN ON THNG NI 2 NGUN.
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Y
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5
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Y
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Cõu 2:+f1u
Y
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s)*/>#/29+u
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4 j i k
Cõu 5:Hai nguồn sóng kết hợp S
1
,S
2
cách nhau 13 cm dao động với cùng phơng trình u = A cos( 100
t), tốc độ truyền
sóng trên mặt chất lỏng là 1 m/s. Giữa S
1
S
2
có bao nhiêu đờng hypebol tại đó chất lỏng dao động mạnh nhất
4 Y YS Yk Yi
Cõu 6+f>D)#XH4=8.U.# #+,F,@X)-+/:;)#'/H#@7)*B#
Y
a4./CSw)Q.T=8
S
a4./CQSw)|wTQ.T)*Ee))#/U.`+)#1 rn)=<;)H#d+.`+:@3)*)*^..`+4@3)+)#A=1
(%.> : g+ :V .6 4 } a YS=8=1 (%. Q>|jTQ.L,/W =G =1 (%.>T : g+ :V .6
4}ajk 5M:V.^.:W+/)#/+)*E:/W4,8
4 YS Yj YY Yi
Cõu 7*Ee)@G.I+)W#+:V5
Y
5
S
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Y
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Cõu 8QRS!T~(<e);).#A),[.6#+fH#U)C6>D)#XH5
Y
=85
S
.U.##+S. +f8-+/
6
Th.s Trần Quốc Dũng -_0909959462
CÔNG DUY - !" #$#%
&'()*)+,)-#./- ./ Tài Liệu LTĐH
:;)#'/H#@7)*J:K.6H#@7)*B#,F,@X),8
Y
a./Ciπ)QT=8
S
a./CQiπ)|πTQT M.:;)*<
C6)*Ee).#A),[,8b.\C 5M:V-+/:;=G(E:;.^.:W)*E:/W)#J5
Y
5
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Câu 9+fC6.L(E:;.L)FCM=8@X.H#+ D>#/2.U.#9+#+f,84aYkS…)#BCM
:V:KE=8CM:V-+/:;=G(E:;.^.:W)*E:/W4,F,@X),8
4 jS=8jj ji=8jj jj=8jS jj=8ji
Câu 10 *E e) @G. .6 #+ f >D) #XH 4 .U.# #+ YQ.T -+/ :; )#'/ .U. H#@7 )*B#
Y
aS./CQw)|wT.=8
S
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.^.:W=8.^.)V)*E:/W4
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Câu 11QRSYT */;))#d#=<+/)#/+C6@G.#+fC6>D)#XH-+/:;.LH#+)W#+
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@G.-+/:;=G(E:;.^.:W,8
4 Y YY YS !
Câu 12:)@X+/)#/+C6)*Ee)@G.=G#+f
SY
55
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.Yj55
SY
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+
5
Y
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5
Y
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55
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C
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5
Y
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Y
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5
Y
g+g+#
Y
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C+/.#/
5
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SY
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55
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i 5M=1+/)#/+.^.)Vg+CU):@X.)*E:/W5
Y
5
S
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4 Yj Y YY !
CHUYÊN ĐỀ 3: SỐ ĐIỂM, SỐ ĐƯỜNG CỰC ĐẠI VÀ CỰC TIỂU TRÊN ĐOẠN THẲNG KHÔNG ĐỒNG THỜI NỐI 2
NGUỒN.
Câu 1:*Ee)@G.#+f>D)#XH4.U.##+i.,?-+/:;.LH#+.6(@G.C6k. +:V
I)*Ee)@G.84,8;)#B#.#9#%)4aj. 5M:V.^.:W=8:KE)*E:/W,F,@X),8
4 =8k =8k Yj=8YS YY=8Y
Câu 2: */;))#d#+/)#/+C6)*Ee)@G..6#+f>D)#XH4=8-+/:;.LH#+=G)FCM
oaSl.U.##+b. M.:;)*<C6)*Ee)@G.=aj.\C 0=8,8#+:V)*Ee)@G.C+/.#/
4,8#B#=? 5M:V-+/:;=G(E:;.^.:W)*E:/W,8
4 YY ! j
Câu 3 : */)#d#+/)#/+C6@G.#+=E(#[5
Y
5
S
]s.F*.U.##+S.=8.#W#†=8/e)
@G. #.F*-+/:;)#'/H#@7)#J:K=G)FCMoaYl)#B)W/*+C6)*<)*Ee)@G.=G=%)M.
=ak.\C ;):VI)*/<+/)#/+=8.U.#5
Y
5
S
.U.>#/2-
Y
aSi.-
S
aYS. rU.:q#CM:V-+/
:;=G(E:;.^.:W)*E:/W5
Y
Q>#?>Vs5
Y
T
4 k b
Câu 4:#/SfC6>D)#XH:fH#+-+/:;=G.#>OaSC)*Ee)@G.>#/2.U.#9+Sf
5
Y
5
S
aS %)M.)*<C6)*/?)*@3,8i\C +:V)W/=G5
Y
5
S
#B#.#9#%)5
Y
5
S
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5
Y
5
S
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Y
aY *E5
S
Q>#?>Vs5
S
T.6CM:V.^.:W+/)#/+,8
4 iY iS i j!
Câu 5:*Ee)@G.I+.6#+fC6>D)#XH.LH#+4=8.U.##+k.(@G.C6…aY. rn)
:V .6 4a. aY. 5M :V -+/ :; =G (E :; .^. )V)*E:/W Q>#? >V s T,8
4 k ! b
Câu 6: +f>D)#XH4.U.##+Yk.:+.L-+/:;=?6.=Ge)@G.)#'/H#@7)*B#
ca+./C
π
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+/)#/+.^.:W D)4aYS. aYjk. 5M=1+/)#/+.^.:W:g+.W#4,8
4 Yk:@3 k:@3 :@3 .b:@3
Câu 7:*/)#d#+/)#/+C6)*Ee).#A),[#+f4-+/:;@X.H#+#+=G)FCMoaSl
=%)M.)*<C6)*Ee).#A),[=ai.\C +:V)*Ee).#A),[.64aYb.aYi.
4aY.ajY. 5M:@3-+/:;.6(E:;.^.:W9+#+:V,8
4 !:@3
Y:@3 YY:@3 b:@3
Câu 8 :W#+:V)*Ee)@G..6#+fH#U)C64=8.6H#@7)*B#
a+./CQiπ)TQ.T=%)M.)*<C6,8Q.\CT4=8.U.##+YYQ.T
0,8:V)*Ee)@G..64aYQ.T=8aQ.T 5M:V-+/:;
.^.:W)*E:/W4Q>#?>Vs4T,8
4 k S ! .
7
C
A B
Th.s Trần Quốc Dũng -_0909959462
CÔNG DUY - !" #$#%
&'()*)+,)-#./- ./ Tài Liệu LTĐH
Câu 9 : W#+ :V 4 )*E e).#A) ,[.6 #+ f H#U) C6-+/ :;:< #z+ )#'/ H#@7 )*B#
Y
a
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a+./CQYπ)TQT 4aYj.;):V)*Ee).#A),[.U.#:V;)>#/2aYj.=8#XH=G4
;)6.YS
)M.:;)*<C6)*Ee).#A),[,8Y\C *E.W#4Q>#?>Vs4T.6CM:V-+/:;=G(E
:;.^.:W,8
4.YY Yj ! Y
Câu 10 :W#+:V5
Y
=85
S
)*Ee)@G..U.##+SQ.T.6#+fH#U)C6-+/:;)#'/H#@7)#J:K
=G.U.H#@7)*B#,F,@X),8
Y
aS./CQπ)TQ.T=8
S
aj./CQπ)vπTQ.T)M.:;)*<C6)*Ee)@G.,8
YQ\CT V)*Ee)@G..U.##+fC65
Y
5
S
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:W)*E:/W5
S
,8
4 i k
Câu 11:
+f>D)#XH.LH#+u
Y
u
S
.6…a.:V.U.#fu
Y
,8jY..U.#u
S
,8Yb. V
.U.#fu
Y
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S
,8ij. */>#/2CM:V-+/:;=G(E:;.^.:W.^.)V,8
4. •k
• k• k•b
Câu 12: WS:V4)*Ee).#A),[.U.##+Yk..6SfH#U)C6>D)#XH-+/:;)#'/H#@7)*B#
Y
a+./CQjπ)T
S
a(./CQjπ)|π\ST M.:;)*<C6)*Ee)@G.,8j.\C 0,8S:V)*E:/W4C+/
.#/4aaS. 5M:V-+/:;=G(E:;.^.)V)*E:/W,8
4.YS YY Y Yj
Câu 13QRSYT~e))#/U.`+;).#A),[.6#+fC6>D)#XH4=8.U.##+S.-+/:;)#'/
H#@7)#J:K=GH#@7)*B#
4
aS./Ciπ)=8
aS./CQiπ)|πTQ
4
=8
)d#(I))d#(ICT D))M.
:;)*<C6)*Ee).#A),[,8j.\C rn)#B#=?4)#;.e))#/U.#A),[ 5M:V-+/:;=G
(E:;.^.:W)*E:/W,8
4 Y! Yb S Y
CHUYÊN ĐỀ 4: SỐ ĐIỂM, SỐ ĐƯỜNG CỰC ĐẠI VÀ CỰC TIỂU TRÊN ĐOẠN THẲNG VUÔNG GÓC VỚI ĐƯỜNG
THẲNG NỐI 2 NGUỒN.
Câu 1: se))#/U.`+;).#A),[.6#+f>D)#XH4=8.U.##+SQ.T-+/:;)#'/H#@7)#J:K
=GH#@7)*B#
S Qi TQ T
A
U cos t mm
π
=
=8
S Qi TQ T
B
U cos t mm
π π
= +
D))M.:;)*<C6)*Ee).#A),[,8
jQ.\CT rn)#B#=?4)#;.e).#A),[ 5M:V-+/:;=G(E:;.^.:W)*E:/W4,8
4 ! b k
Câu 2:~e))#/U.`+;).#A),[.6#+fC6>D)#XH4=8.U.##+S.-+/:;)#'/H#@7)#J
:K=GH#@7)*B#
4
aS./Ciπ)=8
aS./CQiπ)|π\STQ
4
=8
)d#(I))d#(ICT D))M.:;)*<
C6)*Ee).#A),[,8j.\C rn):/W)#JaYS.)#;.e))#/U.#A),[=?6.=G4I
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4 S j i
Câu 3 :WS:V4.U.##+Yj.)*Ee)@G..6SfC6:f(;)W/*+C6e)@G..6(@G.C6,8
YS. ,8:V)*Ee)@G..U.#4=8,F,@X),8YS.=8. :McK=Gg+4 5M#H'*(/,.^.:W.])
:/W,8
4 j S i
Câu 4:WS:V4.U.##+Yj.)*Ee)@G..6SfC6>D)#XH@X.H#+)W/*+C6)*Ee)@G..6
(@G.C6,8YS. ,8:V)*Ee)@G..U.#4=8,F,@X),8YS.=8. :McK=Gg+4 5M:V
-+/:;=G(E:;.^.)V)*E:/W,8
4 j S i
Câu 5: #+f>D)#XH5
Y
=85
S
M#+5
Y
5
S
ab.oaYQlT =%)M.)*<C6S.\C +:V=8)*E
e)@G.85
Y
5
S
=?6.=G.])5
Y
5
S
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S
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CHUYÊN ĐỀ 5: SỐ ĐIỂM, SỐ ĐƯỜNG CỰC ĐẠI VÀ CỰC TIỂU TRÊN ĐƯỜNG TRÒN, ELIP, HÌNH CHỮ NHẬT,
HÌNH VUÔNG…
Câu 1:*Ee)@G..6#+fC6@G.4M#)#+.U.##+;)>#/2
ibAB
λ
=
*E:@3)*z
I)*Ee)@G..6)1,8)*:Vu.`+:/W4.6(U>d#
R
λ
=
C{.6CM:V-+/:;=G(E:;.^.:W
,8 4 ! Yk Yb Yi
8
Th.s Trần Quốc Dũng -_0909959462
CÔNG DUY - !" #$#%
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Câu 2:+fC6>D)#XHM#)#+:@X.:e).U.##+;)>#/2.U.#c)*E:@3>d#.`+;)=z)*z
(U>d#QcˆT=8:McKg+)1.`+=z)*z D)*I€f:<H#U)C6.6(@G.C6 …=8cak…
5M:V-+/:;.^.:W)*E=z)*z,8
4 Sk Si . SS S
Câu 3:*E(<e).#A),[#+f-+/:;=GH#@7)*B#)@7K,8
cmtucmtu
AA
T
j
Y./CQ •TY./CQ j
π
ππ
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{:@3)*z)1(U>d#S.CM:V.^.:W-+/:;)*E:@3)*z,8
4 Yk YS Yb Yi
Câu 4:~e)@G..6#+fC6.74=8.U.##+Y.-+/:;:<#z+.L)FCM.LH#+)#'/H#@7
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Câu 5: *E(<e).#A),[.#/Sf-+/:;=?6.=G(<e).#A),[.6H#@7)*B#-+/:;
4
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:W)*E:@3)*z8,8
4 k b i
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C6S. 5M:V-+/:;.^.:W)*E:@3',dH)#;.e)@G.#%4,8)E:V,8
4 Yk j Sb Yi
Câu 7.*/)#d#+/)#/+C6)*Ee)@G.#+f4.U.##+Yi.-+/:;@X.H#+ V
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4 Sk Sb Yb Yi
Câu 8:*Ee)@G.#+f>D)#XH4.U.##+i.,?-+/:;.LH#+.6(@G.C6k. +:V
I)*Ee)@G.84,8;)#B#.#9#%)4aj. 5M:V8:@3#H'(/,.^.:W=8:@3#H'(/,
:KE+/#+=G#B#.#9#%)4,8
4 =8k =8k Yj=8YS Sk=8Sb
Câu 9: */;))#d#+/)#/+C6)*Ee)@G..6#+f>D)#XH4=8-+/:;@X.H#+=G)FCM
oaSl.U.##+b. M.:;)*<C6)*Ee)@G.=aj.\C 0=8,8#+:V)*Ee)@G.C+/.#/
4,8#B#=? 5M:V8:@3#H'(/,.^.:W=8:@3#H'(/,:KE:g+#B#.#9#%)4,8
4 S=8SS =8k Yj=8YS Sk=8Sb
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H#@7=?6.=Ge)@G. VI)*E4.U.#)*:Vu,8Y.,8:VFu#A),?-+/:;
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:W,8
4 Yb Yk jS Y
Câu 11:*/)#d#+/)#/+C6)*Ee)@G.#+f4.U.##+Y.-+/:;@X.H#+ V
)*E4F)*:V‡.`+4#A).U.#‡,8Y.,?-+/:;.^.:W 5M:V-+/:;.^.:W)*E:@3',dH
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4 Yk j Sb Yi
CHUYÊN ĐỀ 6: SỐ ĐIỂM DAO ĐỘNG VỚI BIÊN ĐỘ CỰC ĐẠI, CỰC TIỂU TRÊN ĐOẠN THẲNG NỐI 2 NGUỒN
VÀ CÙNG PHA HOẶC NGƯỢC PHA VỚI 2 NGUỒN.
Câu 1 :+fC6>D)#XH)*Ee)@G..U.##+;):/W5
Y
5
S
a!λH#U)*+-+/:;.LH#+#+ *E:/W
5
Y
5
S
CM:V.6(E:;.^.:W.LH#+=G#+=8.LH#+=GfQ>#?>V#+fT,8
4 YS k b Y
Câu 2 :*Ee).#A),[.6#+fC6>D)#XHH#U)*+#+-+/:;
Y
a+./Cω)•
S
a+Cω) >#/2.U.#9+
#+f,85
Y
5
S
ajSλ [)*E:/W5
Y
5
S
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Y
#0:UHCM:$
4 :V S:V j:V i:V
Câu 3: *Ee).#A),[.6#+fC6>D)#XHH#U)*+#+-+/:;
Y
a+./Cω)•
S
a+Cω) >#/2.U.#9+#+
f,85
Y
5
S
ajSλ [)*E:/W5
Y
5
S
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2
#0:UHCM:$
4 j:V i:V :V k:V
9
Th.s Trần Quốc Dũng -_0909959462
CÔNG DUY - !" #$#%
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Câu 4*Ee).#A),[.6#+f>D)#XH5
Y
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Y
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aS… *E:/W5
Y
5
S
CM:V-+/:;=G(E:;.^.:W=8.LH#+=G
Y
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4 j:V i:V :V k:V
Câu 5: +fC6>D)#XH)*Ee)@G..U.##+;):/W5
Y
5
S
a!…H#U)*+-+/:;a+./Cω) *E:/W5
Y
5
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4 b ! Y Yk
Câu 6 : +fH#U)C6>D)#XH4=8)*Ee).#A),[-+/:;)#'/H#@7)*B#
4
a+./CQYπ)T•
a(./CQYπ)T M.:;)*<C6)*Ee).#A),[Y\C ‡,8)*:V.`+4 ,8:VI)*E:/W4‡,8
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,8 4 i k
Câu 7:~e).#A),[.6#+fC64.U.##+Y!.-+/:;)#'/H#@7)#J:K=GH#@7)*B#,8
4
a
a+./CSπ)Q=G))d#(ICT M.:;)*<C6.`+e).#A),[,8i.\C 0,8:Vse).#A),[
F4#A)C+/.#/H#F)_.#A),[)W-+/:;=G(E:;.^.:W=8.LH#+=Gf4 #/2.U.#4,8
4 . S. i. S
S
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CHUYÊN ĐỀ 7: VỊ TRÍ GẦN NHẤT HOẶC XA NHẤT CỦA ĐIỂM M DAO ĐỘNG VỚI BIÊN ĐỘ CỰC ĐẠI, CỰC
TIỂU NẰM TRÊN ĐƯỜNG THẲNG VUÔNG GÓC VỚI S
1
S
2
.
Câu 1QRSYST */#)@X+/)#/+C6@G.#+f-+/:;)#'/H#@7=?6.=Ge)@G.
.L(E:;.LH#+.L)FCMl:@X.:e))W#+:V5
Y
=85
S
.U.##+Y. M.:;)*<C6)*Ee)
@G.,8.\C rn).U.:V)*Ee)@G.)#;.:@3)*z)15
Y
(U>d#5
Y
5
S
:V8H#F)_)W:6-+/:;=G
(E:;.^.:W.U.#:V5
S
;):/W]#A)(I
4 b Y Y b!
Câu 2: *E(<e).#A),[.6#+f>D)#XH4.U.##+i.-+/:;.LH#+ D)C6-/€fH#U)
*+.6)FCMoaYQlT=%)M.)*<C6SQ\CT 0Q,8;):VI)*E:@3=?6.=G4)W:V4T
-+/:?=G(E:;.^.:W /W4.6U)*q,G#A),8
4 S. j. i. .
Câu 3: *E(<e).#A),[.6#+f>D)#XH4.U.##+Y.-+/:;.LH#+ D)C6-/€f
H#U)*+.6)FCMoaYQlT=%)M.)*<C6jQ\CT 0Q,8;):VI)*E:@3=?6.=G4)W:V
4T-+/:?=G(E:;.^.:W /W4.6U)*q#[#A),8
4 Sb. Yk. YS. j.
Câu 4: */;))#d#+/)#/+=G#+fH#U)C6M
#+)W4=8)*Ee)@G. #/2.U.#4aYk. +C6
)*<:.6(@G.C6…ai. *E:@3)#JccŠC/C/=G
4.U.#4;)>#/2b.0,8+/:V.`+ccŠ=G
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-+/:;=G(E:;.^.)VI)*EccŠ,8
4 SS. Y. SY. YiS.
Câu 5: +:V4=8)*Ee)@G..U.##+YS.H#U)*+#+C6>D)#XH.6H#@7)*B#
TQi./C
SY
cmtauu
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==
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#/2.U.#,G#A))x:D4C+/.#/)*E:/W.#P.6:V-+/-;=G(E:;.^.:W,8
4 Yk. i. !S. kb.
Câu 6: +/)#/+C6@G.=G#+fM#)#+4.U.##+S..6)FCMl M.:;)*<C6)*E
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:W.U.#:@3)#Jg+4;):/WF#A),8
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Câu 7:*Ee))#/U.#A),[)W4=8.U.##+S.@3)+(M)*d#+f
:f(;.6)FCMSl M.:;)*<C6)*Ee))#/U.#A),[=a.\C B#
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4 YS. Sb. S. j.
Câu 8: +f5
Y
5
S
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Y
a
S
a+./CSw) 56C#*+)*<=G)M.:;b\C V)*Ee).#A),[
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Y
5
S
=8F5
Y
5
S
#A).6H#@7)*B#,8
4
aS+./CQSπ)vYSπT
aS‹S+./CQSπ)vbπT
10
d
2
d
1
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M
C
A B
x x’
d
2
d
1
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A
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Th.s Trần Quốc Dũng -_0909959462
CÔNG DUY - !" #$#%
&'()*)+,)-#./- ./ Tài Liệu LTĐH
a‹S+./CQSπ)vbπT
aS+./CQSπ)vbπT
Câu 9: #/#+fC65
Y
=85
S
.U.##+b. <;)H#d+.`+5
Y
5
S
,A)#E#+:V5
j
=85
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j
5
i
ai.
=8#XH)#8##B#)#+.15
Y
5
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5
j
5
i
D)(@G.C6
Ycm
λ
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)*E5
j
5
i
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4
S SQ Tcm
j Q Tcm
iQ Tcm
k SQ Tcm
Câu 10: D)4=8,8SfC6@G.M#+.U.##+i. ,8;):V)*Ee)@G.C+/.#/
ABAC
⊥
U)*q,G#A).`+:/W4:VI)*E:@3.^.:W+/)#/+,8iS. @G.C6.6U)*q(I(+/#E
4 Si. jS. Yk. b.
Câu 11QRSYjT*/;))#d#=<+/)#/+C6@G.#+fC6>D)#XHu
Y
=8u
S
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Y
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I
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S
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C+/.#/6.u
S
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(E:;.^.:W.U.#;):/W,8
4 YY. ji. S. S.
CHUYÊN ĐỀ 8: VỊ TRÍ, SỐ ĐIỂM DAO ĐỘNG CÙNG PHA HOẶC NGƯỢC PHA VỚI 2 NGUỒN TRÊN ĐOẠN
THẲNG VUÔNG GÓC VỚI 2 NGUỒN.
Câu 1:*Ee)@G..6SfC6M#)#+4=8.U.##+;)>#/24aSi. @G.C6
λ
aS.
+:V=8)*Ee)@G..L.U.#:<)*:V.`+:/W4;):/WYk.=8.L.U.#:<SfC6
=84=8 5M:V)*E:/W-+/:;.LH#+=GSf,8
4 b k !
Câu 2 *Ee)@G..6#+f>D)#XH4.LH#+.U.##+;):/WYS.:+-+/:;=?6.=Ge)
@G.)W/*+C6=G(@G.C6Yk. 0,8;):V)*Ee)@G..U.#:<#+f=8.U.#)*:Vu.`+
:/W4;)>#/2b. [)*E:/WuCM:V-+/:;.LH#+=Gf,8
4 S j i
Câu 3*Ee)@G..6#+f>D)#XH4.LH#+.U.##+;):/WYS.:+-+/:;=?6.=Ge)
@G.)W/*+C6=G(@G.C6Yk. 0,8;):V)*Ee)@G..U.#:<#+f=8.U.#)*:Vu.`+
:/W4;)>#/2b. [)*E:/WuCM:V-+/:;@X.H#+=Gf,8
4 S j i
Câu 4*Ee)@G..6#+fC6M#+4=8.U.##+>#/24aYSQ.T:+-+/:;=?6.
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4 j Y k
Câu 5W#+:V4=8)*Ee)@G..U.##+;)>#/2Yk..6#+fC6>D)#XH-+/:;:<#z+=G
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4 Yk Y Yi Y
Câu 6: *Ee)@G..6SfC6+.L)FCMSl.LH#+=8.U.##+jS.)M.:;)*<C6
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:V)*E-+/:;.LH#+Sf,8
4 Y k Yj j
Câu 7: *Ee)@G..6#+f>D)#XH5
Y
5
S
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S
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tau
π
S./C
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QT M.:;)*<C6)*Ee)@G.,8i\C=8(E:;C6>#?:p)*/gU)*B#)*< VF#A)-+/
:;@X.H#+=G.U.fI)*E:@3)*)*^..`+5
Y
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S
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Y
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4 k. S. j
S
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Câu 8: +fC6>D)#XH:e))W4=8.U.##+S.-+/:;)#'/H#@7)*B#a+./CQ‰)T)*Ee)@G.
./(E:;>#?:p(@G.C6λaj. 0u,8)*:V.`+4 ;):VI)*E:@3)*)*^.4-+/
:;.LH#+=G.U.f4=8.U.#4#/e.;):/W#[#A),8
4 YS. Y. Yj . Y.
Câu 9:
*Ee)@G..6#+f>D)#XH5
Y
5
S
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S
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tau
π
S./C
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QT M.:;)*<C6)*Ee)@G.,8i\C=8(E:;C6>#?:p)*/gU)*B#)*< VF#A)-+/
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Y
5
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Y
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11
Th.s Trần Quốc Dũng -_0909959462
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CHUYÊN ĐỀ 9: VỊ TRÍ, SỐ ĐIỂM DAO ĐỘNG CÙNG PHA HOẶC NGƯỢC PHA VỚI ĐIỂM M BẤT KÌ TRÊN ĐOẠN
THẲNG VUÔNG GÓC VỚI ĐƯỜNG THẲNG NỐI 2 NGUỒN.
Câu 1: L;)1)#/+.6)FCM*oaYl@3)+)W/*+#+:V5
Y
5
S
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:;.LH#+ 5
Y
5
S
ajS. M.:;)*<C6,8i.\C ‡,8)*:V.`+5
Y
5
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q##9:V-+/:;.LH#+=G
‡ d#>#/2)x‡:D:V8F‡#A)-+/:;.LH#+=G‡=8I)*E)*)*^.5
Y
5
S
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4 YbY. YjY. YS. YSk.
Câu 2:+fH#U)C6>D)#XH5
Y
5
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Y
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4
k
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k
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Câu 3: ~e).#A),[.6#+fC64.U.##+Yk.-+/:;)#'/H#@7)#J:K=GH#@7)*B#
)./C+
4
π==
Q=G))d#(ICT M.:;)*<C6se).#A),[,8.\C 0u,8)*:V.`+4
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H#+=GH#F)_)Wu #/2.U.#u,8
4
Y
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Si
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Sk
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Câu 4: ~e))#/U.`+;).#A),[.6#+fC6>D)#XH5
Y
=85
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:K=GH#@7)*B#aS./Ciπ)QT D))M.:;)*<C6)*Ee).#A),[,8i.\C #F)_u)#;.(<e)
.#A),[,8)*:V.`+5
Y
5
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V)*Ee).#A),[)#;.)*)*^..`+5
Y
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.U.#u:/W
4 kk. bS. YS. Yk.
Câu 5: +:V4)*Ee)@G.,8j:P#.`+)+U.:<.6.W#(Ib.)*/:64=8,8SfH#U)C6
M#+.6(@G.C6b. V)*E:@3)*)*^..`+4-+/:;.LH#+=G:V=8F#A))#B
H#2.U.#;)>#/2(+/#EZ
4 !i. bY. !Y. bi.
Câu 6: +fC6>D)#XH4=8)*Ee).#A),[-+/:;)#'/H#@7)*B#
4
a+./CQYπ)T•
a(./CQYπ)T
M.:;)*<C6)*Ee).#A),[Y\C ‡,8)*:V.`+4 ,8:VI)*E:/W4‡,8:VI)*E
:/W‡ D)‡a.=8‡ak. 5M:VI)*E:/W.6(E:;.^.:W=8.LH#+=G‡,8
4 i k
Câu 7: +:V4)*Ee)@G.,8(+:P#.`+)++.:<.6.W#S.)*/:64=8,8#+fH#U)C6
.6H#@7)*B#
TTQS./CQS
SY
cmtuu
π
==
C6)*<)*Ee)@G.>#?C2=8.6=%)M.SQ.\CT )*
:V.`+4 5M:V-+/:;@X.H#+=G:V)*E:/W,8
4 i k j
Câu 8: +:V4)*Ee)@G.,8(+:P#.`+)++.:<.6.W#Yk.)*/:64=8,8#+fH#U)C6
.6H#@7)*B#
TTQS./CQS
SY
cmtuu
π
==
C6)*<)*Ee)@G.>#?C2=8.6=%)M.SQ.\CT
)*:V.`+4 5M:V-+/:;.LH#+=G:V)*E:/W,8
4 i S j
CHUYÊN ĐỀ 10: VỊ TRÍ, SỐ ĐIỂM DAO ĐỘNG VỚI BIÊN ĐỘ BẤT KÌ.
Câu 1: *Ee)@G.)W#+:V5
Y
5
S
.U.##+b.@3)+:e)#+fC6.7>D)#XH-+/:;:<#/8)#'/
H#@7)#J:K=GH#@7)*B#
4
ak./Ciπ)=8
ab./CQiπ)TQ
4
=8
)d#(I))d#(ICT D))M.:;
)*<C6)*Ee)@G.,8i.\C./(E:;C6>#?:p>#)*<: 5M:V-+/:;=G(E:;Y.)*E
:/W)#J5
Y
5
S
,8
4 Yk b Yi
Câu 2:
~e))#/U.`+;).#A),[.6#+fC6>D)#XH4=8.U.##+Y.-+/
:;)#'/H#@7
)#J:K=GH#@7)*B#
4
a
j./Ci
w
)=8
a
i./CQi
w
)
TQ
4
=8
)d#(I))d#(ICT D))M.:;
)*<C6)*Ee).#A),[,8j.\C [)*E:@3+*+(/,.6:P#‡I)*E:@3)*)*^..`+4
.U.#u;):/WY.=8:g+4.6(+/#E:V-+/:;=G(E:;(IQu,8)*:V.`+
4T
4 Yj S Sk Sb
12
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CÔNG DUY - !" #$#%
&'()*)+,)-#./- ./ Tài Liệu LTĐH
Câu 3: *Ee)@G.)W#+:V5
Y
5
S
.U.##+b.@3)+:e)#+fC6.7>D)#XH-+/:;:<#/8)#'/
H#@7)#J:K=GH#@7)*B#
4
ak./Ciπ)=8
ab./CQiπ)TQ
4
=8
)d#(I))d#(ICT D))M.:;
)*<C6)*Ee)@G.,8i.\C./(E:;C6>#?:p>#)*<: *E:/W)#J5
Y
5
S
:V-+/:;=G
(E:;Y.=8.U.#)*:V.`+:/W5
Y
5
S
;):/WF#A),8
4 S. . . Y.
Câu 4: ~(<e);).#A),[.6#+fH#U)C6>D)#XH5
Y
=85
S
.U.##+S. +f8-+/:;)#'/
H#@7)#J:K.6H#@7)*B#,F,@X),8
Y
a./Ciπ)QT=8
S
a./CQiπ)|πTQT M.:;)*<C6)*E
e).#A),[,8b.\C rn).U.:V)*E5
Y
5
S
0‡,8)*:V.`+5
Y
5
S
•I.U.#‡;):/Wj.C{-+/:;
=G(E:;
4 Y S
Câu 5: *Ee)@G..6#+fH#U)C6>D)#XH4.6.L(E:;+aSQ.T.L)FCMoaSQlT@X.H#+
#+ /(E:;C6>#?:p=%)M.C6=abQ.\CT E:;-+/:;)p#XH)W:V.64aYSQ.T
aYQ.T,8
4 iQ.T SQ.T
22
Q.T
Câu 6: +fC6>D)#XH,?@X.H#+.6.L(E:;41*+)WC^+/)#/+=G(E:;S4 D)t)F
CM-+/:;.`+#+f,ES,F)#B(E:;-+/:;)W>#8,8
4 4 4
S
S4
Câu 7: +fC6>D)#XH4=8.L)FCM.L(E:;=8.LH#+ /(E:;C6>#?:p V
4)#'/)#K)^)#J#8(D)}4a4v D(E:;-+/:;)p#XH)W.6U)*q,8k)#B
(E:;-+/:;)p#XH)W.6U)*q
4 #@+:`-9> j k
j j
.
Câu 8: +C6@G.:@X.)W/(s.U.f4.6(@G.C6#@#+=8(Ib €C6*E()1*+)W
.U.#4;):/W-
Y
aj=8.U.#;):/W-
S
a-+/:;=G(E:;(I4 D-+/:;)W.U.f@X.
H#+#+)#B(E:;-+/:;)W-/.2#+f1*+,8
4 4 S4 j4
Câu 9: +fC6>D)#XH4)*Ee))#/U.#A),[-+/:;)#'/H#@7)*B#
i /CQY T
A B
u u c t mm
π
= =
/
(E:;C6>#?:p)M.:;C6
Y \v cm s
=
+:V
Y S
M M
.LI)*E;)',H#%4,8)E:V.6
Y Y
YAM BM cm
− =
=8
S S
j AM BM cm
− =
W)#3:V,:;.`+
Y
,8
jmm
)#B,:;.`+
S
)W)#3:V:6,8
4
j mm
j mm
−
j mm
−
j j mm−
Câu 10: ~e))#/U.`+;).#A),[.6#+f>D)#XH4.U.##+Y.-+/:;)#'/H#@7)#J:K
=GH#@7)*B#,F,@X),8
4
aj./CQiw)|w\kT.•
ai./CQiw)|Sw\jT. #/(D))M.:;)*<C6,8i.\C
;):@3)*z.6)1,8)*:V.`+4I)*Ee)@G..6(U>d#ai. 5M:V-+/:;=G(E:;
..6)*E:@3)*z,8
4 j jS ji jk
Câu 11: *E e)@G. .6 #+ f 4 -+/:; ,F ,@X))#'/ H#@7 )*B#
Q TQ T
S
A
U a cos t cm
π
ω
= +
=8
Q TQ T
B
U a cos t cm
ω π
= +
/=%)M.=8(E:;C6>#?:p)*/gU)*B#)*<C6 U.:V)#;.e)@G.
I)*E:@3)*)*^..`+:/W4C{-+/:;=G(E:;
4
Sa
S+ +
Câu 12: +fC/>D)#XH4=8-+/:;)#'/H#@7)*B#
tau
A
ω
./C=
=8
T./CQ
ϕω
+= tau
B
D):V
>#?-+/:;F)*:V‡.`+4#A);):/W
j\
λ
B
ϕ
4
k
π
j
π
j
S
π
j
i
π
Câu 13:~(<e);).#A),[.6#+fH#U)C6>D)#XH5
Y
=85
S
.U.##+S. +f8-+/:;)#'/
H#@7)#J:K.6H#@7)*B#,F,@X),8
Y
a./Ciπ)QT=8
S
a./CQiπ)|πTQT M.:;)*<C6)*E
e).#A),[,8b.\C rn).U.:V)*E5
Y
5
S
0‡,8)*:V.`+5
Y
5
S
•I.U.#‡;):/Wj.C{-+/:;
=G(E:;
4 Y S
Câu 14:~e))#/U.#A),[.6Sf>D)#XH4.U.##+Y.-+/:;)#'/H#@7)#J:K.6H#@7
)*B#,F,@X),8
A
aj./CQi
π
)|
π
\kT=8
B
ai./CQi
π
)|S
π
\jT #/=%)M.)*<C6,8i.\C @3)*z.6
)1‡,8)*:V4I)*Ee)@G..6(U>d#ai. 5M:V-+/:;=G(E:;..6)*E:@3)*z,8
13
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CÔNG DUY - !" #$#%
&'()*)+,)-#./- ./ Tài Liệu LTĐH
4 Yb b ! Yk
III/ SÓNG DỪNG.
CHUYÊN ĐỀ 1: SỐ BỤNG, SỐ NÚT, SỐ BÓ SÓNG TRÊN DÂY, TRÊN ĐÀN VÀ ỐNG SÁO.
Câu 1QST*E;)CX-1.6.#<-8l#+:F.M:q#:+.6C6-x *E-1.6;)(NC6 D)
=%)M.)*<C6)*E-1,8=>#?:p FCM.`+C6,8
4 =\l =\S l S=\ l =\i l
Câu 2QSYT ;)CX-1.#<-8Œ.t+#+:F.M:q# *E-1:+.6C6-x=G(NC6)M.
:;)*<C6)*E-1,8= #/2)#3+9+#+,F,E)DHCX-1-€)#J,8
4 =\Œ =\Œ Œ\S= Œ\=
Câu 3QRSYST*E;)CX-1.6C6-x=G(@G.C6,8… #/2.U.#9+#+$)C6,<><,8
4 …\S S… …\i …
Câu 4QRSYST#6=<C^H#2cW.`+C6.7)*E=%).2.M:q#H#U)(V8/C+:1:$Z
4 FCM.`+C6H#2cW,?,G#7)FCM.`+C6)G
56H#2cW,?@X.H#+=GC6)Gs:VH#2cW
FCM.`+C6H#2cW,?#[#7)FCM.`+C6)G
.56H#2cW,?.LH#+=GC6)Gs:VH#2cW
Câu 5: #J:q#8/C+:1,8sai
4 M=GC6-x>#/2.U.#9+S(N#/e.S$),E)DH(I;)_+(@G.C6
*/+/)#/+C6(E:;C6)p#XH.^.:W>#:;,.#H#+(ICM.#•π
*/+/)#/+C6(E:;C6)p#XH.^.)V>#:;,.#H#+(ICM,•_+π
5^)*<C6,8C^)*<t,@X=8t,@XH#N)#;.(E:;-+/:;C6
Câu 6: #J:q#8/C+:1,8sai
4 +/)#/+,8C^)p#XH.`+S#+#<C6
56-x,8C6)p#XH.`+C6)G=8C6H#2cW)*E.LH#@7)*<
GC6-x.U.$),8#9:V.M:q#
U.C6>D)#XH,8.U.C6.6.LH#@7.L)FCM#CMH#+>#?)#+:p)#'/)#3+
Câu 7;)C6-xc2*+)*ECX-1#+:F.M:q#=G)FCMo D)t)FCM,ESo)#B
4 Ž.6C6-x.U.$)C6(+:F)*s)#8#(NC6
Ž.6C6-x.U.(NC6(+:F)*s)#8#$)C6
#?.6C6-x9+
Ž.6C6-x.U.(NC6(+:F,$.8=Ž,8(NC6
Câu 8:*E;)CX-1-8S:+.6C6-x=G)FCMl@3)+)#A/8#+:F-1.M:q#.z.6j
:V>#U.,?:KE %)M.)*<C6)*E-1,8
4 i\C \C b\C k\C
Câu 9:;)-14-8Yb.t)#JI+:F.M:q#:F4]=8/;)(2*)FCMYl #(2
*#/W):;@3)+)#A)*E-1.6C6-xfk(6C6=G4c'#@;)$) d#(@G.C6=8=%)M.
)*<C6)*E-14
4 λaj•=ak\C λak•=ak\C λaj•=aj\C λak•=aYS\C
Câu 10:*E-14-8S.6C6-x.6#+(NC6:F4M=Gf-+/:;Q./,8;)$)C6T:F
.M:q# B)FCM-+/:;.`+f(D)=%)M.C6)*E-1,8S\C
4 Sl Sl l Yl
Câu 11:;)-1:8#f4-8k..6:F.M:q#:F4].=8/;)#U#1)#/+:+-+/:;=G)FCM
oal #1)#/+*)*E-1.6C6-x=Gj(NC6 %)M.)*<C6)*E-1,8
4 =aY\C =aSb\C =aS\C =aS\C
Câu 12*ECX-1u4:F4.M:q#=8:Fu-+/:;:<#/8=G)FCMSl)#B)*E-1.6$) M)*E-1
*)#8#S(NC6)#BsuH#2-+/:;=G)FCM
4 il YSl l Yl
Câu 13"+CU))*E;)CX-1)#A.6C6-x=G(E:;.`+(NC6,8+ W:V)*ECX-1.U.#(N
C6;)H#F)@(@G.C6.6(E:;-+/:;(I
4 +\S +\i +
Câu 14:#.6C6-xc2*+)*E-1-8b.6S:F.M:q#)#Bg+CU))#A.6:VF#@>#?-+/:;
Q>V.2#+:F-1T @G.C6)W/)#8#)*E-1,8
4 k b Y i
14
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CÔNG DUY - !" #$#%
&'()*)+,)-#./- ./ Tài Liệu LTĐH
Câu 15: ;)CX-1 laY:@X..M:q#:F4.z:F:V)^-/H#2-+/:;=G(@G.C6(I(+/#E:V.6Y
$)Q>V.24T)*/#B#2#C6-x.`+CX-1Z
4 SY. SSSS. Y!. >D)g2>#U.
Câu 16:+@3:K.U.##+i=8,8.#/CX-1I9+#0-+/:; [(@G.C6,G#A).`+C6-x
8#+@3.6)#V)W/E,8
4 Yk b i S
Câu 17: ;)CX-1 laY:@X..M:q#sS:F4-+/:;=G)FCMl=%)M.)*<C6=a\C 6(+/#E
$)=8(NC6)*/#B#2#C6-x)*E
4 (N•k$) Y(N•YY$) Y(N•Yk$) S(N•SY$)
Câu 18: ;)CX-1 laY:@X..M:q#:F4.z:F:V#s-+/:;=G(@G.C6(I(+/#E:V.6Y(N
C6)*/#B#2#C6-x.`+CX-1Z
4 Skk. Yjb. YS!. >D)g2>#U.
Câu 19: ;)CX-1AB.t+=G:FAB.M:q# #:FA:@X.)*<-+/:;=G)FCMHz)#BC6-x
)*E-1.6Y(NC6 VC6-x)*E-1.#P.6(NC6=8=%)M.)*<C6=Ž>#?)#+:p)#B:FA
H#2:@X.)*<-+/:;=G)FCM
4 YHz SHz Hz Hz
Câu 20: *E;)CX-1:8#f.t+.6C6-x,8;)(NC6.z,8;)$)C6 D))*/
>#/2.6j(NC6akj.)FCM.`+C6oaSl @G.C6=8=%)M.)*<C6)*E-1,8
4
λ
ajk.•vaS\C
λ
ajk.•vaS.\C
λ
ajk.•vaS.\C
λ
ajk.•vaS\C
Câu 21: ;)+:.6-z:c/+.#<)FCMl:g+ e)+.#1:H#d+)*E;)-1)#nH4.t
+=G#+:F.M:q#.#<-8CX-1k. +)#A)*E-1.6C6-x=GS(6C6 d#=%)M.C6)*<
)*E-1Z
4 k\C k.\C k\C k.\C
Câu 22: ;)CX-12#-8S.:F)^-/=8:F4-+/:;=G)FCMo M.:;)*<C6)*E-1,8
i.\C <>=<)FCM:Vc2*+#)@XC6-x)*E-1,8
4 oaYkQ>|Y\ST oabQ>|Y\ST oab> oaYk>
Câu 23: ;)MCU/#s#+:F)W/*+C6-x.#/1=Gj$) #/2.U.#9+S$),E)DH,8S. #<-8
.`+MCU/,8
4 b. k. YS. j.
Câu 24: ;)CX-1:8#f-8.6;):F)^-/:F>+M=G;)#U#1)#/+*=G)FCMbl %
)M.)*<C6)*E-1,8jS\C )*E-1.6C6-x d#CM(6C6E#B#)#8#)*E-1
4 k j i
Câu 25: 14a!..6:F4.M:q#:F)^-/ #)FCM)*E-1,8Yl)#B)*E-1.6b$)C6-x
+Td#>#/2.U.#)x4:D$))#K4 S bi Ykb b
(TD.M:q#=8)M.:;)*<C6>#?:p8M.6C6-x)*E-1)#BH#2)#+:p)FCMo;),@X
#[#A)(I(+/#EZ 4 Y\jl bl kl Yjjl
CHUYÊN ĐỀ 2: PHƯƠNG TRÌNH SÓNG DỪNG.
Câu 1: V)#K.C6)p#XH.`+C6)G=8C6H#2cW)W;):V.U.#:F.M:q#>#/2c.#/(s
( )
2cos .sin 20
4 2
x
u t
π π
π
= +
÷
Q.T )*/:6c)d#(I.=8))d#(IC U.:V$).U.#:F.M:q#>#/2
4 S>Q.T j>Q.T i>Q.T S>|•Q.T=G>aYS•
Câu 2: #.6C6-x)*E-1:8#f)#BH#@7)*B#:;-3.`+-1)#'/)0+:;c=8)#3+)#@C+
5cos 4 .cos 10
2 2
u x t
π π
π π
= + −
÷ ÷
)*/:6c)d#(I.=8))d#(IC U.:V(NC6-x)*E-1
:@X.cU.:q#(s
4 caS>|YQ.T caQ>|YTQ.T caS>|YQ.T caSQ>|•TQ.T
Câu 3: #@7)*B#C6)f#XH.`+C6)G=8C6H#2cW)W;):V.U.#:F-1H#2cW;)>#/2c.#/
(s
( ) ( )
8cos 40 .cos 10u x t
π π
=
.)*/:6c)d#(I=8))d#(IC B(@G.C6)*<)*E-1
4 . S. S
Câu 4: *E-1:8#f.6C6-xc2*+ #@7)*B#:;-3.`+-1)#'/)0+:;c=8)#3+).#/(s
5cos 0,05 .cos 8
2 2
u x t
π π
π π
= + −
÷ ÷
)*/:6c)d#(I.=8))d#(IC M.:;)*<C6)*E-1,8
4 S.\C Yk\C Y\C i\C
15
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CÔNG DUY - !" #$#%
&'()*)+,)-#./- ./ Tài Liệu LTĐH
Câu 5;)C6-x)*E-1.6-W
S./CQ T./CQS T
i S S
d
u t mm
π π π
π
= + −
)*/:6,8,:;)W)#3:V).`+
H#F)_)*E-1.U.#:F.M:q#.`+-1;)>#/2,8-Q.T %)M.)*<C6)*E-1,8
4 b.\C Y.\C k.\C i.\C
Câu 6: *E:/W-1:8#f4.6C6-xc2*+ V)#K.C6)p#XH.`+C6)G=8C6H#2cW)W;)
:V.U.#:FH#2cW;)>#/2c.#/(s
( ) ( )
0
cos 10 .cos 5u u x t
π π
=
)*/:6c)d#(I=8))d#(I
C
,8#ICM-@7 W.U.#;):/WY\j..6(E:;-+/:;,8 U)*q.`+
,8
4 . S. Y. Y.
Câu 7: *E-1.6C6-x,:;-+/:;)W:V)*E-1.6)0+:;c=8/,$.),8
( ) ( )
cos .cosu a bx t
π
=
)*/:6+(,8.U.#ICM-@7c)d#(I))d#(IC M.:;)*<C6)*E-1,8S\C ICM((I
4 jYi
vY
S
vY
Y
vY
kSb
vY
Câu 8: V)#K.C6-x)W;):V.6)0+:;c=8/,$.))*E-1.#/(s
( ) ( )
2cos .cos 10u x t
π π
=
Q.T)*/
:6c)d#(I=8))d#(IC B=%)M.-+/:;.`+H#F)_)*E-1QcaS.T=8/,$.)aY\iC,8
4 vjYi.\C kSb.\C Si.\C vYi.\C
Câu 9: ;)C6-x)*E;)CX-1.6-WaiCQS
π
cT./CQ
ω
)TQT)*/:6,8,:;)W)#3:V).`+;)
:V)*ECX-18=q)*d.1(I.`+6.U.#M.)0+:;u:/WcQc)d#(In)):/(ICT #/2)#3+
]#A)9+#+,F,E)DH:V;).#A):V)*E(NC6.6:;,G,:;(I(E:;.`+:VQ.U.#$)
C6Y.T,8YSC M.:;)*<C6)*ECX-1,8
4 jS.\C Yk.\C b.\C Y.\C
CHUYÊN ĐỀ 3: CÁC ĐẠI LƯỢNG ĐẶC TRƯNG CỦA SÓNG DỪNG.
Câu 1: ;)CX-1.t9+#+:V.M:q#.U.##+. @3)+)W/C6-x)*E-1 +)FCMF#+
#A).L)W/*+C6-x)*E-1,8Yl=8Sl FCM#[#A))W/*+C6-x)*E-1:6,8
4 Yl YSl l l
Câu 2: ;)CX-1:8#f:@X.)*'/)#J:K=8/;):V.M:q#:F-@G.`+-1:V)^-/ @3)+)W/C6
-x)*E-1=G)FCM(n#A),8o
Y
V.6C6-x)*E-1H#2)t)FCM)M)#V:DU)*qo
S
PCMo
S
\o
Y
,8
4 Y S S j
Câu 3: +C6#B#C.L(@G.C6
λ
.L(E:;+)*<@X..#<#+)*E;)CX-1.L=%)M.
S.\C)W/*+C6-x D)S)#3:VF#A)8-1-€)#J,8C U)*q(@G.C6
λ
,8
4 S. Y. . Y.
Câu 4: ;)CX-1.t9+#+:V.M:q#.U.##+b. +C6.6)FCMF#+,E)DH.L)W/*+C6
-x)*E-1,8o
Y
al=8o
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Th.s Trần Quốc Dũng -_0909959462
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