BT Sóng cơ_LTĐH

LOẠI I : ĐẠI CƯƠNG VỀ SÓNG CƠ HỌC     l = = Trong đó: λ   !"#$% $&'$%λ ()$ !* +,'-. . /01ω 2ϕ +,''3456.4 1,7 !89$ !"#  2: !"# ;1'#<$ !=.7 * 5 /0 5 1ω 2ϕ+ 7 (π λ   2: !"# ;1'#>4 !=.7 * 5 /0 5 1ω 2ϕ2 7 (π λ  ?@AB9'C''34D4 !89$ !"#E64 1F G7  7 7 (  ∆ ∆ ∆ϕ = ω = π λ 2''34<1H9 GI (J G7 K= ⇒ = 2''34<1H9 K GI ( J G7 (  ( = + ⇒ = + Ví dụ 15 -$L<1'#1E ;19$ !*7/1MJ 2JN(O1F6 P  !89$ !"#'C''344E ,'69> Q !14R' !SAB94 JN( AET4*4/U @MM4N Ví dụ 2,''34: !84V "8 W-<1'#1E ;19$ X' O' Y4V * EB- >4,'('345YZ6T4 !8S X'[:AR <1\9']   !"# !84V AE^M4NE <1-'6 !% !11F _`a]a`*4 <1-U @/Ta Ví dụ 3'3 & ,'4 '34D4 !8<>"1bc'/a' ? π    ÷   4dE1Ae Y/?4Yf"E1 S''34YT *A'bDb1'8U @/? ? 4 Ví dụ 45 $\ !"3 ;19$.7'f  (M4NY'FQ !"#''b'8 Rg','.<19$ !*   `1` 44= π ,' S''34   A' ,''34.AE  ?44= E'F4hec'3456.4 1,</`M4iA'AEb1'8U 5 -96  ,'.<,  01 4= ω 1b'8Rg''A !"# @'345 !84V 6.4 Qb,' S''34bDY(TA<1YA' <1 ,'5AE(4'8<1 0 (4  ( (4  (4 j ` (4 (  k '4R k '8 l 4 !84m k > n A1 l 1 n 4R k R o <1R k $ n ' > o R n (MY  k 1!1 n R l ' k  !84m k > n A1 l p; n T$ k AR o 'A'8 '8 n 9 !84R k 9$ !"8 o 1 n Y$ l 8 o 4R k 9q n 1$ n 'R o Y$ k   n > n  n  $ k   n m4MYT4R n R k  !"8 o 1 n A o 0(4N T4N ?M4N j(T4N ?5 -96 <,  01 4 ` π = 1  !"#Rg','4 '34 6-4 1F<YAB9<1 ,'c' S''346 MY(∆ = AE 0 MYMTπ  MY(Tπ  MYaπ j MY(`π `@04 \'<>"m\AE41<1 ;19$\'<>"'c% !r>bD'] <1Ya:MY? *<1 !"#<L ;1\'<>"\Y(4<1E" AE 0?Y(4 aY`4 (YT4 jT4 TO'>4 !"# _4R' !SRrE14R' !S * 0 R "g' bR "g' b'F4 j m a: !"# _4]<L4 9$ !"#'bΛ/(M4 *41F6</5Z b'] !D ,'Z !s9$ ,'5AE ? π  0</T4 </(?4 </?M4 j</(M4 t5 \b'3<'sbc'9$ !*/ 7 ^' (J  (M ( é ù ê ú + ê ú ë û 4Y'1F6$%AE4Y S''$%AE'>"O] AfE1>"AEeU 0 AE(M4Ndf  !"#AE M J 4N  '8AE`4jAE( ^,'4 '34. !84V "8 W-<1'#1E ;19$ X&'  TMO' !84V * EB !u- >4.,'''340ED46v4 !8S X'[.AR<1H9''] !Df  !"# "g' !1 1F _tM4N]^M4Ndf  !"# !84V AE 0tT4Nt`4N^T4Njt(4N vZ-c.<1' MY<1 !"#''f MY`4N !89$." !8 9$E"('34)Ew ;1 & x)w/T41b'8/4Eb'8R "g''  !"#Z] ,' S''34E1)A'4 *A' ,'wAE 04 +4 M j(4 M5 -.<1'   / TM  ,1! !84V b'8?41'Rg' ' !"#''] 1F6'Ct\A-'A'8 ']9AEv4@'345D4 !84V 6- .1,bDT4L /M AEAe9 Q ,'.'[% !r>bD ;1'#<$,' S''34  A"<1 ,'5bD(4h"<1 ,'5E1 S''34 ( ) (  / 2(YM  bDb1'8U 0(4 +(4 M4 j+YT4 py 4  !"# ;19$.7) ,'5<,/T' J (J7 ( ? 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Hai nguồn dao động cùng pha ( (  M∆ϕ = ϕ − ϕ = ) }@'34<1x,'<  z< ( /λ∈~ Þ :S1V'34 − ≤ ≤ l l k λ λ }@'34<1x '3<  z< ( /(2 ( λ ∈~ Þ :S1V'34   ( ( − − ≤ ≤ − l l k λ λ 2. Hai nguồn dao động ngược pha:( (  ∆ = − = ϕ ϕ ϕ π ) }@'34<1x,'<  z< ( /(2 ( λ ∈~ Þ :S1V'34   ( ( − − ≤ ≤ − l l k λ λ }@'34<1x '3R<1<  z< ( /λ∈~ Þ :S1V'34 − ≤ ≤ l l k λ λ Chú ý:d'bE' 16 *4S<1x,'ER<1'C''345YZ6'-A A\ AE< 5 Y< (5 Y< Z Y< (Z  @V ∆< 5 /< 5 +< (5 ∆< Z /< Z +< (Z E'FQ∆< 5 •∆< Z  2'-<1H9 • x,'∆< 5  £ <  z< ( /λ £ ∆< Z • x '3∆< 5  £ <  z< ( /(2 ( λ £ ∆< Z 2'-<1\9 • x,'∆< 5  £ <  z< ( /λ £ ∆< Z • x '3∆< 5  £ <  z< ( /(2 ( λ  £ ∆< Z :'6 !%"8 1F4€6b'3 & !8AES *4 Ví dụ 1!1 r'B4'1 1 !84V (-y \9:  Y: ( <1' /M ,''3456: Y : ( AA\ AE<  /a4Y< ( /M44 x,'|'C5ES ! !x:  : (  'x,'*4  !"# @(M4N Ví dụ 2 !84V '-] \9:  Y: ( 6(4<1'9$ !* /(1^MJ 4 '] 9$ !* ,'56:  Y: ( AA\ AEM4Ea4Yb'] /MY^4N b *4'34ZD4 !8:  Y: ( #9r: ( E: ( P D41E'1F:  : ( <1H9':  : ( U @ 5 /`1^MJ +^J4b(4 Ví dụ 3!1 r'B4'1 1 !84V (-y \9:  Y: ( <1' /M ,''3456: Y : ( AA\ AE<  /a4Y< ( /M44 x,'|'C5ES ! !x:  : (  'x,'*4  !"# (M4N Ví dụ 4 !84V '-] \9:  Y: ( 6(4<1'9$ !* /(1^MJ 4 '] 9$ !* ,'56:  Y: ( AA\ AEM4Ea4Yb'] /MY^4N b *4'34ZD4 !8:  Y: ( #9r: ( E: ( P D41E'1F:  : ( <1H9':  : ( U @ ⇒  5 /`1^MJ +^J4b(4 Ví dụ 5@•(MMv‚b#4V 4 P A{'-96 ] \9:   Y: ( 6(M4' -E"<1 X&9$ !*AA\ AE  /T1`MJ 2J44E ( /T1`MJ 44  !"# !84V P A{AE^M4N:'34<1'b'8x,' !8:   : ( AEb1 '8U @M Ví dụ 6!1 r'B4'1 1 !84V '-] \9: Y : ( 6M4Y<1' K/(4*4'34x,'Yx '3 !81F:  : ( E"!"9;b1AA-'EAƒ4 @v\A-'T"9;b1AA-'M\Aƒ4"!T"9;b1AAƒ4 '-] \9YH9Yb'80/(4Y'1 11„' !84V 1' b'8Rg''A !"#!1H'1 1YC'344E'BS' _' -96 ]bD (  ` λ +  *b'8<1 g\9 ,'AE 0 ( (4  (4 M j`4 (‚b#4V P A{'-96 ] \9:  E: ( 6(M4'-E"<1 ;1 9$ X&9$ !*AA\ AE   T1 `M 44= π E (  T1`M 44= π + π  !"# !84V P A{AE^M4N:'34<1'b'8x,' !81, X:  : ( AE 0v ^ M j ?'-] \90E' !84V  16P A{<1' ^Eb'8/ 44{[x4P 46 mA\' !"#Yf  !"# !84V  16AE(4N@'34 5D4 !84V  1660EC1F05/tYM4Y5/aY(T4<1'b'8 0M4 YM4 YT4 j(YM44 `!84V  16P A{(-] \90EY9$ !*<1 ,'0YAE 0  /' … 4   /' … 2 J 4,'.AE !'340b'8 0DM (4 4 j†4 T,'''340Y !84V P A{6T4'-96 ] \9<1 ;1 9$ !*  /1`Mπ 4E ( /b1`Mπ 2π4 !"# !8b#4V P A{AE `M4N|L'‡YˆAE('34 !81,0110‡/‡ˆ/ˆ*4x,' !8‡ˆ 0T a ` jt aN!84V '-'0EY61F0/(4<1 R'4V  ,1!bλ/Ya4EjAE''346 !84V Y 6#'-E6 !'34.04 1F^4:'34<1H9'-c !81,jAE 0? M T ja tN!84V '-'0EY'-H9Y61F0/M4 <1R'4V  ,1!bλ/MYT4EjAE''346 !84V YjR'0 ,'51150/?45/5j/`4:'34<1x,' !8jAE 0? ` T  ja ^!1 r'B4'11 !84V Y <1'-0YAETMYf  !"8  !84V AE`M4Npy 4 '345 !84V 05/v4E5/t4'<1 ,' 5<1' !"# _0E]AE'<1 0H9 \9 R9 jAB94  π N? v,'4V D4Y'-] \90E<1 ;19$ X&'9$ !* AA\ AE  /  '`MJ 2JNa4Y ( / ( '`MJ 2JN(4'- 6A84V  ,'' '340E6^4'] f  !"# !84V /(M4N|L'EjAE''34 4V 110jAE*R:'34<1'b'8x '3 !81,jAE 0` ? ( j M,'''340Y !1Rr6MY`4Y'-96 >4 \9H9YH b'8Y ^MM']   !"#>4 !1RrAE/?`M4NE1'b'BRg' !11F0:'34R;\>4 !11F0AE 0 ( ? j` '-96 '345YZ6M4<1\9YHb'8AET44E ,1 !4 B>'1 1 !84V df  !"#AEMY`4NAE(M:6'34b'8 T44 !8S''-AE 0M ( (M j (‚4V  164 P A{'-] \90E6(M4Y<1 ;1 9$ X&'9$ !* 0 /(1`Mπ E  /(1`Mπ 2π 0 E   rbD44Y  r bD']   !"# !84V P A{AE?M4Npy *R05Z 4V  16P A{:'34<1'b'8x,' !81,5AE 0v ^ (M jt ?N'->4.  Y. ( 1'AE'-'346`4Y96 ] \9H `(TYH b'84EH9bbDRf  !"#>4AE?`M4N:'34<1'b'8 4c !11F'C.  . ( AE 0^ v ^ j(M `N'-] \90Y6a4H<1R'4V  ;19$ !* 7/1TM π 4AE4 '34 !84V  >'1 1x '3Y'CE ! !x0 4 >'1 1x,''] 0/tY(4/?Ya4:>'1 1x,''[,0AE 0aS aS tS j^S TN!84V '-'0YV 6(4<1R'4V  ,1!bYa4|L'AE'34 !84V 6#'-E6 !'34. 04 1F^4:'34<1\9'- !81,.AE 0( ? ` jT aN'4‰'L:  Y: ( 6^4YŠc4 !\V 1,4‹E14V P A{Y ,1!'-9$ !*/01(MM J  !"# !84V P A{AE/MY^4N @'345 !84V P A{ ,1! 4'65:  : ( #)$ !*<1'345AE 0 5 /(01(MM π   5 /(01(MM π + π   5 /(01(MM π 2 π  j 5 /(01(MM π 2 ( π  tN!84V P A{Y ,'0E6v4'-<1] \9  0 /  /MYT1MMπ 4df  !"#/MM4N@'34x,''1 15 !8SR '0 ,'0AE'340P O1F6 _5]0AE 0YMa(T4 YMM(T4 (YMa(T4 j`YMa(T4 ^N‚4V  164 P A{'-] \90E6(M4Y<1 ;1 9$ X&'9$ !* 0  (1 `M = π E ( )   (1 `M = π + π  0   E    rbD44Y  r bD']   !"# !84V P A{AE?M4N@'34x '3'1 15 !8SR '0 ,'5R !HAE'34P O1F6 _5]07P97ŒAE 0(MYMMa4 ?M4 `M4 jT4 LOẠI III : SÓNG DỪNG Một số chú ý }@%1V<1{AEe  }@ x<1AEb= }''34'7&'[e AR<1\9 }''34'7&'[b=AR<1H9 }6'34 !8<>"#<1'b'8Rg'⇒mA\R !"#' }O1F S'''C'A\'<>"m69 Q'[dAEQN( 2. Điều kiện để có sóng dừng trên sợi dây dài l : }'AEe  } A   Z  ( λ = ∈ :b=/b/ :e /2 }5 AEe u4 AEb= A (   Z ` λ = + ∈ :b"8/ :b=/e /2 3. Phương trình sóng dừng trên sợi dâyvới đầu C cố định hoặc dao động nhỏ là nút sóng }@%e  +)$ !* 'E9F7, ,'   01(  = π E   • 01(  01(  = − π = π − π +)$ !* 'E9F7, ,'564 1F<AE 5 <  01(  ( = π + π λ E 5 <  • 01(  ( = π − π − π λ )$ !*<_ ,'5 5 5 5    •= + 5 < <  (01( 1(   (0'( 1(   ( ( ( π π π = π + π − = π π + λ λ '8<19 Q ,'5 5 < < 0 (0 1(  (0 '(  ( π = π + = π λ λ Ví dụ 15 <>"1mY4 ŠE1%Y'ŠE1>4 1<1'  /`M!8<>"* EB<_-4te R3'e 'Y<>"<E'4 Y*4  !"# !8<>" bY1>4 1<1'ŽbDb1'83 !8<>"Te 3F'e ' @M4Nb(M Ví dụ 25 <>" !;1A$AQY0ŠŠE1>4 1<1' /MMYA$AQ  '] 1F6 _0]e  &?AET4 *4  !"# !8<>"U b *4{6 _]6e Y6b= !8<>"]'#<E'<>"AE(4*4b=Y e [6 \ !8<>"U @`4Nb< 5  (  = + n "! ∈ •MYY(Y•YM‘e  Ví dụ 3!8<".0Y0%Y.<1'#1E' /(M * !8<>"Te  5 !8<>"! E'b= *.9F'<1' bDb1'8U @M :<_7F"! !8<>"0/(M4'%YbbD^4 * !8<>" 0Tb=YTe ab=Yae ab=YTe jTb=Yae  (5 \'<>"m0<E'(4%Y0AE4 -<1*'* NTMZS' ]4\ _0]Te 01'AE4 e Z]4<>"0! E(e  *  <1AEb1'8 0T  TM (YT jtT ?!84 \'<>"'#<E'AY(%<_!8<>"b='] f  !"# !8<>"AERg'AE 0N(A N`A (NA jNA `5 <>"<E'(4Ym X5 Š'4 '34%Y4 Š'46"! MM O'1, Y  P" !8<>"<_-4Tbdf  !"# !8<>"  ^M4N bTM4N  `M4N < aT4N T5 \'<>"<E' (l m= Y'%ZS' r r3<_7P 'B !8<>" <E'P bD 04 (4 `4 jMYT4 a5 \'<>"0<E'A/vM4 x<1Y0''46"! /TM!8<>" <_E]4\`b"8df  !"# !8<>"AE 0/(`MM4N /aMM4N /^MM4N j/(MMM4N t5 61<E'^M4Yc(Y ,1!4 <_ !161'>4x,'c(!1 1F'C61(e >4AE 0(M4 `M4^M4 jaM4 ^:<_ !84 \'<>"<1x-P ' !"# ;1'#\  / M '7+ … E ( / M '72… '3 &E1>"b'3 %<_ !8<>"P" 0/ M '71…  /( M 17'…  /( M '71…  j/( M '7+…  v5 <>"0<E'Y^M4m XD4Y%Y0ŠE14 bF! MM O'bF!1, YS'  P" !8<>"<_-4abY'07;44 e r bEf  !"# !8<>"0 0K/MY?M4/?M4N K/MY?M4/aM4N K/MYaM4/aM4N jK/Y(M4/(M4N LOẠI IV: SÓNG ÂM S>4 ’ ) “/ / : : d'’”Y)’AEmA\YRP 96 >4-:4 ( AE<'B r4V R'9$ !"#>4với sóng cầu thì S là diện tích mặt cầu S=4πR 2  (5&S>4 M “ h A “ = 1V M “ h< MA “ =  ( 0   0   0 0 “ • • h h MA MA (MA “ • •   ⇒ − = = =  ÷   d'“ M /M +( ’N4 ( c/MMMS>4– ?}<1E96 !'<>"%⇒'AEe       Z} (A = ∈ —'/⇒>496 !>4$bF     (A = /(Y?Y`•61,>4bf( (  Ybf? ?  • }<16196 !4 b% rY4 3c⇒4 AEe Y4 AEb=   (   Z `A = + ∈ —'/M⇒>496 !>4$bF   ` v f l = /Y(Y?•61,>4bf? ?  YbfT  T  • Bài 15 ->496 !>4* !"#'' ;14L'EmA\>4\ bF1 1Ehe &6->44 1F<Y 'A,'- 84M4 *S >4;\ mA8P9`Ar1F6< @</(M4 Bài 45&S>4 m 84?M< *S>4 mA8b1'8AU @MMMA Bài 75&S4 >4AEh/`M<€" rS>4E" ;1$%’N4 ( 1b'] S˜;>4–AE“ M /M +( ’N4 (  @M +^ ’N4 (  Bài 8,'4 '340D4674 ->4Z1'4 -'344 1FZ0/4Y4& S>4AEh 0 /vM<1b'] ˜;>4–AE“ M /M +( ’N4 (  rS>4“ 0 >4 ,'0 brSE4&S>4>4 ,'D4 !8SZ0E6Z4 1,Z/M4 1'4R' !SAE1E 1ERP9 =>4 |'FQ->4E4R' !S#XrRP 96 >4-Z @M +? ’N4 ( bM +T ’N4 (  h  /tM<(YTa4’ !8S94&S>4AEh  /tM<Y !19u1\4&S>4AEh ( /`M< Œ“  N“ ( bD 0?MM MMMM ?MMM jMMM (5 ->4AE-'3496 >4X !1R'|'FxRxP9 =E9F 7,>4,'4 '346->4M4 *4&S>4AE^M<1b'] S>4'F4 ŒAB' b*9$1F6 '-,''346->44 *4&S>4bD 0MM< vM< M< j(M< ?5&S>4<1-:>"! ,''345AEhY'1: ']A,'54 1,a(4 *4& S>4 m 84t<O1F6 E:]5AE 0(4 (M4 (Mv4 j`(Yv4 `5  ']u'R R4&S>4(iS>4b1'8A> ']' 44&S >4(M< 0(`M ? M a M M jaM ? T5 >4 !"# !1Rr5&S>4 ,''345E ''34ZAA\ AE`M<E ^M<S>4 ,'ZA$S>4 ,'5 0MMMMA `MA MMMA j(A a5 ->47;4-'34Y96 >4 !14R' !SXERP9 =>4 Z˜;>4AE“ M /M +( ’N4 ( ,''340 1\4&S>4AEh/tM<S >4“ ,'0'6 !%AE 0tM’N4 ( M +t ’N4 ( M t ’N4 ( jM +T ’N4 ( tZ->4:96 !4 >4RP )Rg'Y !"#X#4L'9$,''3406 :4 1,• 0 /4Y4&S>4AEtM<|'FQ4R' !SRP9 =>45&S>4 ,' '346-4 1,M4AE 0?M< `M< TM< jaM< ^5 >4<,*\96 ! _4 -'34RP ’hP"J/?Y`E'FQ !D4R' !SRP9 =>4,''346-4S>4bD 0MY^’N4 (  MYM^’N4 (  MYM`’N4 (  jMY`’N4 (  vO'S>4 mP9MMA *4&S>4 m 0(M< MM< TM< jM< MN5&S>4 ,'''340YAA\ AE?M<E(T<:"!A'8B'CS>4 ,'0E ,'AE 0“ 0 /a“  NT “ 0 /T“  “ 0 /“  M j“ 0 /M“   N,'4 % !r !14R' !S !"#>4Y'S>4 mP9MA'6 !%S>4b *4&S>4 0'F4'M  m 84M  m 84M< j'F4'M< (N'34.Y0YHD4 !84 QS X7P 96  _.,'.V 4 -'3496  >4X!R'Y4R' !SRP9 =>45&S>4 ,'0AEaM<Y ,'AE(M <5&S>4 ,' !'3451,0AE 0(a< t< ?`< j`M< ?'34.Y0YHD4 !84 QS X7P 96  _.,'.V 4 -'3496  >4X!R'Y4R' !SRP9 =>45&S>4 ,'0AEaM<Y ,'AE(M <5&S>4 ,' !'3451,0AE 0(a< t< ?`< j`M< . LOẠI I : ĐẠI CƯƠNG VỀ SÓNG CƠ HỌC     l = = Trong đó: λ. :b=/e /2 3. Phương trình sóng dừng trên sợi dâyvới đầu C cố định hoặc dao động nhỏ là nút sóng }@%e  +)$