Một số phương pháp giải bài tập trắc nghiệm cơ học 12: Phần 2

Nối tiếp nội dung phần 1 tài liệu Phương pháp giải bài tập trắc nghiệm cơ học 12, phần 2 cung cấp cho người đọc phương pháp giải bài tập trắc nghiệm sóng cơ và sóng âm. Mời các bạn cùng tham khảo nội dung chi tiết.

PtiLiOng ph^p giai bai tgp tr^c nghigm Co hqc 12 - Trgn Trgng Hang

BAI TAP C d BAN

D a n g 1 C H U K I - T A N S O S 6 P 1 G

- Chu k i T cua song la chu k i dao dong cua mot phan tuf cua m o i trUdng c6

song truyen qua >

- T a n so cua song: f = •'•r•;^'•^•^r^''''r • '

V i du: M o t ngiTdi quan sat tha'y chiec phao tren mat niidc bien nho l e n cao

10 Ian trong 36s Chu k i cua song bien la: ' • ^ • i

- A T = 3,6s B T = 4,0s C T = 2,0s ' D T = 1,5s

Giai

Nu^dc bien ngay t a i phao dao dong khi c6 song truyen qua nen phao dao dong

theo Phao nho l e n cao 10 Ian tufc nu-dc bien tai d i e m do dao dong dat ciTc dai

10 Ian T h d i gian giiJa 10 Ian ciTc dai lien tiep la 9 chu k i (9T) V a y : 9T = 36

=> T = = 4 (s): do cung la chu k i cua song bien

Chon dap an IJ

D a n g 2 B U 6 c S 6 N G

- Bu'dc song X la quang diTcJng ma song truyen di diTdc trong mot chu k i

- Cong thufc: A = v.T = y , v d i v la van toe truyen song

- H a i phan ttf tren cting phUdng truyen song cac nhau m o t biTdc song X thi

dong pha

- Hai dinh song l i e n tiep each nhau mot bi/dc song X

i • • — • '

Vi du 1, M o t day dan hoi cang ngang Cho mot dau day dao dong theo phu'dng

thang du-ng v d i chu k i 2s thi tren day c6 song truyen d i Sau thdi gian 0,3s dao

dong truyen d i du^dc 1,5m Bu-dc song l a :

Cty TIMHH MTV DVVH Khang Vigt

dy 2 T r e n m a t nu-dc dang c6 song, ta thay khoang each giiJa hai gdn song

lien tiep la 10cm va chiec la nho tren mat nuTdc nho l e n l i e n tiep 3 Ian trong thdi gian 5s Toe do truyen song tren mat nu-dc la:

\ \ 4cm/s B V = 6cm/s C v = 8cm/s D v = 2cm/s

Giai

Khoang each each giffa hai gdn song l i e n tiep la bude song: X = 10cm

La nho nho l e n l i e n tiep 3 Ian iJng v d i 2 chu k i dao dong, vay 2T = 5

B i e t phu^dng trinh song tai O la: Uo = Aeoscot

- Phu-dng trinh song tai M each O khoang O M = x do song truyen tiT O t d i l a :

Vi du 1 M o t sdi day O A rS't dai cang ngang Cho dau O dao dong theo phU'dng

vuong goc vdi day PhiTdng trinh dao dong tai O la: U Q = 2eos

B i e t toe do truyen song tren day la 2m/s Phu-dng trinh song tai M each dau O khoang 50cm l a :

57Ct +

-4 (em)

Chon dap an B

V i d u 2 Song truyen tren phUdng x ' x tiY M N each nhau 40cm vdi hiidc son

X = 0,8m Bie't phUdng trinh song tai N la u ^ = 4eos

trinh song tai M la:

V i d u 3 Sdi day dan h o i Ox ra't dai Qang ggang Cho dau O dao dong dieu hoa

theo ph^dng thang duTng v d i bien dp 2cm, chu k i 0,5s L a y t = 0 la liic dau 0

dat l i dp cifc dai Toe dp truyen song tren day la 8m/s Phu'dng trinh song tai

M each O 50cm la:

A U M = 2cos4TCt ( c m )

C. U M = 2 cos 4 7 C t

-6 (cm)

B U M = 2cos

D U M = 2 C O S

47tt + —

2 (cm)

+ t = 0, u = A

A = Acoscp coscp = 1 - > ( p = 0

V a y : u,, = 2eos(47it) (cm)

196 I

Phu'dng irinh dao dpng truyen den M :

U M = 2cos4Tr t - • = 2cos47r t - 0 , 3 ^ = 2cos 47rt

4J (em)

Chpn dap an D

Yi d u 4 M o t song cd hpe du'de truyen theo phu'dng Ox v d i toe dp 20em/s Cho

rang khi truyen di bien dp song khong d o i B i e t phu'dng song tai O la

Phuang phdp gii'i b^i t$p tr^c nghigm Cp, hgc 12 - Tian !i:in(j Hifng

G i a i PhLTcfng t r i n h da c h o : u = 2cos l O O n t - 7TX

Vi d u 2 PhiTdng trinh song t a i m o t d i e m c 6 toa d p x t r e n phU'dng t r u y e n soim

v a o i u c t diTdc c h o b d i : u = 5cos(20t - 0,05x) ( c m ) t r o n g d o t t i n h b a n g giay,

Vf d u 1 S o n g t r u y e n t r e n d a y d a i v 6 h a n v d i bifdc song X K h o a n g each giiJa hai

d i e m t r e n d a y dao d p n g c u n g pha each n h a u

A d = 2kA B d = ( 2 k + l ) ? C d = k - D d = k?^

2 ( v d i k = 1 , 2 , 3 , ) e

G i a i

H a i d i e m t r e n d a y e a c h n h a u k h o a n g d dao d p n g c u n g pha k h i :

Phuohg phap giai bai t^p trSc nghigm Co^bpc 12 - Trai HKng

Acp = 2n.— = 2kn

Chon dap an D

Vi du 2 Song truyen tren day dai v6 han c6 bu'dc song X Mai diem tren day dac

dong ngu'dc pha each nhau

Hai diem tren phUdng truyen song dao dong:

• Cung pha each nhau d = k>

NgUdc pha each nhau d = k +

-2 X

Vi du 3 Tren sdi day dan hoi ra't dai c6 song truyen qua Biet tan so song la

f = 20Hz va van toe truyen song la v = 50m/s Hai diem gan nhau nha't tren

day dao dong vuong pha lech pha gdc each nhau

y,' du 4 Hai diem M , N each nhau 28cm tren day c6 song truyen qua luon luon

lech pha vdi nhau mot goe Acp =(2k + l ) ^ vdi k = 0; ±1; ±2;

To'e do truyen song tren day la 4m/s va tan so cua song eo gia tri trong Ichoang ttr 22Hz de'n 26Hz Tan so cua song la

T thi giai he Uj = Acos(coti +cp)

U2 = Acos co(ti + At) + cp

Vi du 1 Tren phu'dng Ox c6 song truyen qua vdi chu ki ciia song la T Vao lue

nao do diem P tren phu'dng Ox c6 li do Ui = 3cm thi sau liic do thdi gian T

diem Pco lido ^ , • ,

= A C O S 2n 27rxp^

= Ui = 3 (cm) Chon dap an C

V i d u 2 T r e n day dai v6 han c6 song truyen qua Chu k i cua song la T V a o lu^,

nao do d i e m P tren day c6 l i do u, = 2cm thi triTdc luc do thdi gian — diem p

V i d u 3 PhUcfng trinh song tai mot diem c6 toa do x tren phu^dng truyen song

vao luc t cho b d i : u = 3cos(7tt - 0,27TX) (cm) trong do t tinh bang giay

L i dp tai mot d i e m nhat dinh tren phifdng truyen song vao luc nao do la

Ui = A/3 cm va l i do nay dang tang thi sau do - s li do tai diem do la:

A Song cd la dao dpng Ian truyen trong mot m o i tru'dng

B Song nu'dc truyen theo cac phu'dng khac nhau tren mat nu'dc v d i cung mot toe dp V

C Song ngang la song trong do cac phan tuf cua m o i tru'dng dao dpng theo phu'dng nam ngang

D Song dpc truyen di/dc trong chat k h i , chat long va chat ran

12.2 Chpn cau dung: Song dpc

A truyen dUdc tren mat nu'dc

B chi truyen du'dc trong chaft ran ' '

C truyen dufdc tren mat nifdc va trong chat ra'n ;

D truyen du'dc trong chaft k h i , long va ran 12.3 Chpn cau sai: Song ngang khong truyen di/dc trong

A cha't ran B chaft long C chat k h i D chan khong 12.4 Co 3 phat bieu nhu'sau ve bu'dc song:

I Bu'dc song la quang di/dng ma song truyen di di/dc trong mot giay

I I Birdc song la quang du'dng ma song truyen d i dufdc trong mot chu k i dao dpng

I I I Bu'dc song la khoang each gii?a hai d i e m tren phiTdng truyen song ma dao dpng tJii hai d i e m do dong pha

Phat bieu dung la:

A Ca I , I I va I I I B Chi cd I va I I

C Chi cd I I va I I I D C h i cd I I '2.5 D o i v d i mot m o i tru'dng nhat dinh thi to'c dp truyen song

A chi phu thupc vao bien dp cua song , • i

B khong d o i

C chi phu thupc vao tan so cua sdng

D phu thupc vao bien dp va tan so cua sdng

203

Phi/Ong phap gi^i bai t j p trSc nghi§m Cc hpc 12 - T d n Trpng Hung

1 2 6 Song truyen tur O tren true Ox, toe do truyen song la v, bu'dc song X Ne\

bieu thiJe dao dong tai O la: Uo = Acoscot thl phu'dng trinh song truyen theo

12.8 Cho mot song cd la song ngang Vao luc t song

C O hinh dang nhu* hinh ve, trong do phan tiir A dao

dong vcti van toe v theo hu'dng chi tren hinh ve

Song dang truyen ve:

A phia ben phai ' \ B phia ben trai

C hu'c^ng cua v D ngu'dc hU'dng cua v

12.9 Mot ngirdi ngoi d bien nhan thay c6 20 ngon song di qua trU'dc mat minh

trong 76 giay Chu ki cua song la: :;nn J M , ? , i? ' V v ; r ; i / i ;

A T = 4s B T = 3,8s C T = 1 5 s

38

D T = —s

76 12.10 Mot ngUdi ngoi d bien thay khoang each giiJa ba ngon song lien tiep la

15m va ngu'di do de'm du'pc 10 ngon song di qua trUde mat mlnh trong th5i

gian 27s Toe do truyen song bien la:

A V = 2,5m/s B V = 2,78m/s C v = 0,4m/s D v = 0,28m/s

12.11 Mot ngu'di go mot nhat bua tren du'dng sat va each day 1530m c6 mot

ngufdi khac ap tai len du'dng sat thi nghe du'dc hai tie'ng biia each nhau 4,2s

Biet toe do truyen am trong khong khi la 340m/s va nho hdn toe do truyen am

trong sat Toe do truyen am trong sat la:

A V = 3600m/s B v = 2700m/s C v = 8400m/s D v = 51 OOm/s

12.12 PhUc^ng trinh song truyen theo true Ox cho bdi: u = 5eos(207it - 0,47tx)

(cm) trong do t tinh bhng giay Chu kl cua song la:

A T = 0,2s B T = 0,4s C T = 0,ls D T = 0,3s

12.13 Phu'cfng trinh song tren true Ox la: u = 3cos 5 7 C t - - X

2 (em) trong do

X tinh bang met Bi/de song la:

A.X^lm B >i = 4m C X = 2em D = 4em

204

j2.14 Phircfng trinh cua mot song ngang truyen tren sdi day dan hoi ra't dai la:

(cm) trong do t tinh bang giay, x tinh bang em Toe do

I u = 4cos 5 0 7 r t - — X

1 0

truyen song tren day la: ' ' - •

A V = 5m/s I T B v = 5cm/s C v = lOm/s D v = lOem/s j2 15 Phu'dng trinh dao dong tai mot diem O tren phifdng Ox la U(, = 2coslOOTtt ' (cm) trong do t tinh bang giay, sau do dao dong truyen den M tren Ox each O

50cm vdi to do 4m/s Phu'cJng trinh dao dong cua M la:

A U M = 2cos(1007tt-7i)(cm) B U M = 2eosl007it (em)

C. U M = 2 cos l O O n t

-2 (cm)

D khac vdi A, B, C

12.16 Tren sdi day dan hoi ra't dai c6 song hinh sin truyen di Phu'dng tnnh dao

dong tai diem M tren day la: u ^ = 5cos 2 5 7 : t - ^

4 (cm) trong do t tinh bang

giay, sau do dao dong truyen den N each M 1 met vdi toe do 5m/s Phu'dng trinh dao dong tai N la:

12.17 Tren day dan hoi kha dai eo song truyen qua Song truyen theo ehieu tif

• M -> N nhu' hinh ve vdi toe do Im/s Biet phiTdng trinh dao dong cua diem N

la: Ufq = 4eos 5 0 7 i t - - (cm), trong do t tinh bang giay M each N 65cm,

I phu'dng trinh dao dong cua M la:

12.18 Day dan hoi Ox kha dai cSng thang nam ngang Cho dau O dao dong dieu

hoa theo phu'dng thang diirng vdi chu ki 0,2s va bien do 3em Toe do truyen dao

I dong tren day la 2m/s Lay t = 0 la lue dau O dao dong qua vj tri can bhng theo

ehieu du'dng Phu'dng trinh dao dong tai diem M tren day each O 1 m la:

A. U M =3 C O S

71

107:t +

-2 (em)

Hhd'dng ph^p giit bit tjp trie nghigm Do hgc 12 - Tran Trgng Hung

12.19 PhiTcfng trinh dao dong cua mot d i e m M tren phiTdng Ox khi c6 song truyej,

qua cho bdi: U M = 2cos(47it - 0,057tx) (cm), trong do t tinh bang giay va x V\n\y

bang cm L i do dao dong cua d i e m M c6 toa do x = 2cm vao luc t = 0,5s la;

A u = 2cm B u = - 2 c m C u = l c m D u = - l c m

12.20 D a u O cua day dan h o i raft dai dao dong theo phiTdng vuong goc vdi d a y

, C O phu'dng trinh: U Q = A C O S — t D i e m M tren day each dau O —bu'dc sono

12.21 D i e m O tren mat nu'dc dao dong vcti phu'dng trinh: Uo = Acos47it, trong d o t

tinh bang giay To'c dp truyen song tren mat nu'dc la 2m/s Khoang each giL7a

hai d i e m gan nhau nhat tren du'dng thang qua O each nhau

A d = l m B d = 2m C d = 0,5m D d = l , 5 m

12.22 M o t day dan h o i kha dai cang ngang D d u O cua day dao dong v d i tan so

36Hz thi tren day c6 song ngang truyen di v d i van toe trong khoang tu" 4m/s

5m/s Quan sat tha'y hai d i e m tren day each nhau 40cm dao dong cung pha

Toe do truyen song la:

A v = 4,8m/s B V = 7,2m/s C v = 4,1 m/s D v = 5,6m/s

12.23 M o t day dan hoi ra't dai c6 song ngang truyen qua vdi van toe v = lOm/s,

t ^ n so song trong khoang tiJf 40Hz - > 60Hz Hai d i e m tren day each nhau

6,25cm se dao dong lech pha v d i nhau goc Acp = k +

-2

- v d i k = 1 , 2 , 3 ,

4 tan so song la:

A f = 2 0 H z B f = I O O H z C f = 50Hz D f = 3 2 H z

12.24 M o t song ngang tren day dan hoi rat dai c6 phU'dng trinh dao dpng tai

d i e m ed tpa dp x vao luc t la: u = Acos(47it - a.x), trong do t tinh bang giay, ^

la hang so diTdng Bie't toe dp truyen song tren day la 16m/s Gia trj cua hang

so a l a :

A a = 0 , 2 5 n ( m ) ^/:,:r.^i.::^:'ry B a = 0,257t (1/m)

C a = 0,57t (m) • V , D a = 0,57t (1/m) v

12.25 M o t song ngang ed phiTdng trinh song la: u = 0,3cos(314t - 5x) (cm), trong

do t tinh bhng giay V a n toe dao dpng cifc dai eua mot phan tuT vat chat khi c6

song truyen qua la:

A v„,ax = 0,3 em/s B v,„ax = 0,6 cm/s

t h i n g dilng v d i phufdng trinh: U Q = 3 e o s 2 t - ^

2 (cm), trong do t tinh bang

giay T r e n day ed song truyen di vdi biTde sdng ~K = 4cm Dang cua day vao

12.28 PhiTdng trinh sdng tren phiTdng Ox la: u = 3cos(57it + 0,4x) (cm), trong do t

tinh bang giay T a i mot d i e m nhat djnh tren day vao liic nao do no cd l i dp 2cm thi sau 1 s d i e m dd cd l i d6:

A u = l c m B u = 2cm C u = - 2 e m D u = - I c m

207

chieu truyen song

12.29 Hinh ve ben bieu dien hlnh dang scfi day

dan hoi ngay thcJi diem t khi c6 song truyen

qua theo chieu tij" trai qua phai trong do diem

P d vj tri can bang va Q d vj tri cao nhat

Hu'dng chuyen dong cua P va Q ngay thcJi

diem t la: - •

f.-A Pdi len, Q d i xuo'ng B P di len, Q diJng yen

C P di xuong, Q di xuong D P di xuong, Q diJng yen

HI/6NG D A N G I A I

12.1 Dap an C

C Sai vl: song ngang la song trong do cac phan tuf cua moi tru'dng dao dony

theo phu'dng vuong goc vdi phu"clng truyen song

12.2 Dap an D Song doc truyen du'pc ca trong chat ran, long va khi

12.3 Dap an A Song ngang truyen du'dc trong cha't ran (va tren mat niTdc)

12.4 Dap an D Chii y rang phat bieu III dung la:

Bu"dc song la khoang each giiJa hai diem G A N NHAU N H A T tren phu'dng

truyen song ma dao dong tai hai diem do dong pha

12.5 Dap an l i Doi vdi mot moi tru'dng nhat djnh thi toe do truyen song khong ddi

-Vao luc t diem A di len theo hu'dng v nen cac diem cung pha C, E, cung i-''

?; len va liic t + — cac diem nay len cao nhat NgUde lai liic t cac diem B, 1^'

4

T dao dong ngu'dc pha vdi A nen di xuong va luc t + — chi'mg xuong thfip

4 ' T ,

nhat Vay luc t + — song la du'dng cong khong lien tuc nhu' tren hinh ve Q^''^

4 ket qua do ta thay song truyen ve ben trai

• Khoang each giifa ba ngon song lien tiep la < h—^ ^ ^ ^

2:^ (Hinh ve) nen: X = — = l,5 (m) \ \

• 10 ngon st5ng lien tiep di qua trifdc mat muih ti'rc C\\Q do vat chat da thifc

27 hien 9 dao d()ng lien tiep nen chu ki song: T = — 3 (s)

\ 5 Toe do truyen song: ^ = — = = 2,5 (m/s)

Phu'dng trlnh song eo dang long quat: u = Acos cot 27rx

So vdi phu'dng trlnh da cho: u = 5cos(20jit - 0,47ix)

Ta dirdc: co = 207i (rad/s)

Phuong ph^p giai bai tjp trie nghigm Co hpc 12 - TrSn Trpng Hung

PhUdng phap giSi bai tgip trie Co !i i(, 12 - TrSn Trpng Hang

Van toe dao dong cua mot phan tuf vat chat khi c6 song di qua la:

Dang cua day la do thi cua u theo x: do la du'dng sin lap lai sau X = 4cm

• Chu y rang liic t = 0 dau O bat dau dao dong nen de'n liic t = 1,5s song truyen di xa nhal la: x,„„ = v.t = —.t vdi T = ^ = ^ _ \ n ^ , ,

r (0 271

x„ „ x = - l , 5 = 6 ( c m ) = 1,5?>

Tom lai dang cua day la hinh A , ^ 5 , , ^ , ,:| ,r,„,

12.28 Daj^ an C ,•>; '•Oi-x. •a.^&":teS>:cfeMVii}|j>'fi(i!iv iVw I'fAil^-anii'

v j : max nen d i e m P dang chuyen dong

V l song truyen qua ben phai nen sau — song truyen di difdc — i?ng vdi

4 • 4

du'dng khong lien iiet: P den P' V a y P dang di xuong ( { ' , 1 < '•»>

^ - Bai 13 G I A O THOA S O N G *' * ' -' ' ^ * T O M T A T L I T H U Y E T

1 H i e n tU'dnjj jjiao thoa ciia hai son<; mat iiirckJ '

- T h i n g h i c m : cho can rung c6 hai m u i nhon Si, S:

cham mat nu'dc dao dpiig

- K e t qua: tren mat nu'dc xuat hien cac gdn song on dinh CO hinh la cac du'dng hypebol vdi tieu diem la «^

- H i e n tu'dng hai song gap nhau tao nen cac gdn song

on dinh goi la hien tu'dng giao thoa cua hai song

Cac gdn song c6 hlnh hypebol goi la cac van giao thoa

7 ^

2 1 3

Phuong phap giai bai tgp trSc nghigm Co hqc 12 - I r a n l:oi).j Hung

2 Cue d a i va ci/c t i e u j , ,

- G o i phifdng trinh dao dpng cua hai nguon S|, S2 la: u^^ = u^^ = Acos(a)t)

thi piiiTdng t n n h dao dong tdng hdp tai d i e m M trong vung giao thoa la:

= 2 A c o s 7 i - ^ 7 — -

{

cos C 0 t - 7 t i; ;,>•,,;• ^-i

- Dao dong tong hdp tai M la dao dgng dieu hoa cung phifdng, ciing chu kl

vdi hai nguon va c6 bien dp: A^^ = 2 A

- V i t r i cac cifc dai giao thoa ifng v d i :

Quy tich cac d i e m nay la nhiJng di/dng hypebol c6 hai t i e u d i e m la Si, S

- chung du'dc g p i la van giao thoa ciTc dai. > > s i i i ' j i * ' '

- V j t r i cac ci/c t i e u giao thoa ilng v d i : , i

Quy tich cac d i e m nay la nhifng du'dng hypebol c6 hai t i e u d i e m la Si, S2

va g p i la van giao thoa circ t i e u

3 D i e u k i e n giao t h o a Song k e t hdp

De CO van giao thoa on dinh Iren mat nu'dc thi hai nguon song S i , S2 phai:

a Dao dpng cung phiTdng, cung chu k i

b Co hieu so'pha khong d d i theo thdi gian

' - Hai nguon nhu" tren gpi la hai nguon ket hdp Hai song do hai nguon k e l

; hdp phat ra la hai nguon ket hdp

^ - H i e n tu'dng giao thoa la hien tu'dng dac triTng cua s6ng

Vjiy iNnn iviiv u v v n r diiy V151

yj' d u 1: T a i hai d i e m S i , S2 tren mat nifdc c6 hai nguon ket hdp gio'ng nhau M

la mot d i e m trong viing giao thoa each Si, S2 Ian lu'dt d i , d2

BiTdc song tren mat nu'dc la X Cho rang bien dp song khong d d i va bang bien

dp dao dpng cua nguon

p p lech pha Acp = (pi - (p2 cua hai dao dpng tai M do hai song truyen tiT Si, S2

Vi d u 2: Can rung trong thi nghiem giao thoa song tren mat nu'dc dao dpng vdi

chu k i T = 0,5s M la mot d i e m tren mat n\idc each hai m u i nhpn Si, S2 Ian lu'cJt di = 20cm va da = 15cm B i e t tdc dp truyen song tren mat niidc la

V = 0,8m/s Dao dpng tai M do Si truyen idi

A Sdm pha hdn dao dpng tai M do S2 truyen tdi goc

-B T r e pha hdn dao dpng tai M do S2 truyen tdi goc

C Sdm pha hdn dao dpng tai M do S2 truyen td'i goc ^ ^|«'

D T r e pha hdn dao dpng tai M do S2 truyen tdi goc ^ ''"-'^ <: - '

G i a i

i D p lech pha cua hai dao dpng tai M

215

X vdi X = v.T = 80.0,5 = 40 (cm)

Nen: Acp = (p,-(p-, = ZTT = — < 0 ^

' - 40 4 : :

, —> cpi < (p:: Dao dpng tai M d o S| truyen tdi t r e p h a h O n dao dpng tai M do

M l a mot d i e m tren mat nirdc trong vung giao thoa each S|, Si k4n lu'Pt d, va

d i Bifck song tren mat nu'dc \a X Cho rang bien dp song truyen tren mat

nu'dc l a khong doi v a bang bien dp cua nguon D p lech p h a Acp = cpi - 92 cua

hai dao dpng tai M d o hai song truyen tij" S,, S2 tdi l a : S ' l n i J i V

ii.^^ = A2 cos(107it + 7t) rv 'ilirtnt

M Ih mot diem tren mat nifdc trong vung giao thoa each Si, S2 Ian liTPt di = 14cni

d2 = 20cm Biet toe dp truyen song tren mat niTdc la v = 0,5 m/s Dp lech pha

Acp = cpi - cp2 cua hai dao dpng tai M do hai song truyen tiT Si, S2 de'n la:

i du 1: T a i hai diem Si, S2 tren mat nu'dc c6 hai nguon dao dc)ng giong het

nhau v d i phu-png trinh: u^^ = u^, =5cos(57it) (mm) M la m o t d i e m tren mat nirdc trong vung giao thoa each Si, S2 Ian lu-pt di = 16cm, d2 = 19cm Biet toe

dp truyen scSng Uvn mat nu'dc la v = 0,45m Cho rang song truyen di vdi bien

dp khong d d i B i e n dp dao dpng tong hdp tai M la:

_ nung

V i d u 2: Tai S|, S2 tren mat niidc c6 hai nguon ket hdp cCing bien do A M

mot diem trong viing giao thoa cua hai song Hai dao dong tai M do hai song

truyen tdi lech pha nhau gdc A(p Cho rhng bien do song khong doi B i e n do

I A M = 2 A cos Acp Chon dap an A

V i d u 3 : T a i hai diem O i , O2 tren mat niTdc c6 hai nguon ke't hdp vdi phu'dng

trinh: UQ^ =yl2cosSnt (cm); U Q , = \/2cos(8jit-7r) (cm)

Song tren mat nu'dc truyen di vdi van tdc 2m/s Coi bien do song khong doi

M la mot d i e m tren mat niTdc trong vung c6 giao thoa each 0|, O2 Ian lu'dt

di = 36cm, d2 = 23,5cm Bien do dao dong tdng hdp tai M la:

y/jdy 4: Tai hai diem 81,82 tren mat nU'dc c6 hai nguon dao dong ket hdp ngU'dc

pha, CLing bien dp V3 cm nU'dc song cua song truyen tren mat nU'dc la 0,3n Coi bien dp song truyen di khong doi Bien dp dao dpng tdng hdp tai diem M trdn mat nU'dc each S|, S2 Ian lu'dt di = 50cm, d2 = 40cm la:

D a n g 3 FHUONQ TRINH DAO DONG TONG HOP CUA

HAI SONG K E T HOP

Ne'u phu'dng trinh dao dpng cua hai nguon ket hdp la: Ui = U2 = Acoscot thi phu'dng trinh dao dpng tdng hdp do hai song tao ra tai mot diem M :

d - d ,

U M = 2 A c o s j i - ^ ^-cos cot - 7 1

Vf d u : Tren mat nU'dc c6 hai nguon ket hdp gio'ng het nhau vdi phu'dng trinh dao

dpng: U| = U2 = 2cosl07it (cm) Tdc dp truyen song tren mat niTdc la 5m/s Cho rhng bien dp song khong thay ddi PhiTdng trinh dao dpng tdng hdp tai M tren mat ni/dc each hai nguon khoang di = 40cm va d2 = 15cm la:

Neu hai nguon ket hdp Si, S 2 dao dpng cung pha: u^^ = u^^ = Acos((i)t) thi:

a V i tri cac ciTc dai giao thoa: d i - d | = k.A, (k = 0; ± ! ; )

b V i t n cac cifc tieu giao thoa: d 2 d| = k +

-2 ^ ( k = 0 ; ± l ; ) 5*

M

V i du 1: T r e n mat nU'dc c6 hai nguon ket hdp ciing pha ciing chu k i T = 0,4s, t o c

dp truyen song tren mat nu'dc la v = 0,8m/s G p i M , N , P, Q la bon d i e m t r c i i

mat nu'ctc nam trong vimg giao thoa c6 hieu khoang each tiT m o i d i e m den hai

nguon (tiJc d : - d|) cho bdi bang sau:

Vay tai Q c6 ciTc tieu giao thoa Chpn dap an D *

V i du 2: T r e n mat niTotc c6 hai nguon ket hdp ngiTdc pha: U | = Acoswt

\ _ ;< ^ ^2 = Acos((ot + 71)

Bu-dc song truyen tren mat nu-dc la X

V j tri cac ciCc dai giao thoa du'dc xac djnh bang b i e u thii'c:

A

V i d u 3: Hai nguon ket hdp ngUdc pha: U i = Acoscot

U2 = Acos(Q)t - n) "' ' "

Bu'dc song tren mat nUdc la A - • »

V i t r i cac ciTc t i e u giao thoa difdc xac djnh bang b i e u thifc:

M la mot d i e m tren mat niTdc c6 ciTc tieu giao thoa khi h i e u khoang each:

A d 2 - d | = 6 , 7 5 ( c m ) B d 2 - d, = - 4 , 5 e m

C d 2 - d , = - 3 , 5 c m D d - d, = l,8em

221

a Hai nguon dao dong cting pha:

• V i tri ciTc dai giao thoa: d2 - d, = kX

• V i tri ciTc tieu giao thoa: d2 - d, =

b Hai nguon dao dong ngu'dc pha:

• Vj tri ciTc dai giao thoa: d2 - di =

• Vj tri ciTc tieu giao thoa: d2 - di =

Xet tru'dng hdp hai nguon ke't hdp 81,82 cung pha

a Neu M la mot diem nam tren van giao thoa ciTc dai thi:

So van giao thoa ciTc dai la so gia tri K cho bdi: — ^ < k < - ^ S | 8 T 8 1 8 9

b Neu M la mot diem nam tren van giao thoa ciTc tieu thi:

So van giao thoa cifc dai la so gia tri k cho bdi: S1S7 1 SiSa 1

Vi du 1: Tren mat nu'otc c6 hai nguon ke't hdp cung pha:ui = U2 = Acos(207it)

Hai nguon each nhau khoang / = 10cm Toe do truyen song tren mat nu'dc la

V = 30cm/s 86' van giao thoa cifc dai quan sat du'dc nam giufa hai nguon la:

A N = 5 B N = 6 C N = 7 D N = 8

:•• , Giai Goi M la giao diem ciia van giao thoa ciTc dai vdi doan th.^ng noi hai nguon

Vay CO 7 van giao thoa cifc dai Chon dap an C

If du 2: Trong thi nghiem giao thoa tren mat nu'dc, hai mui nhon Si, 82 cua cau

I rung cdch nhau 20cm Cau rung dao dong vdi tan so lOHz Toe dp truyen song tren mat nifdc la v = 0,5cm/s So diem ciTc tieu giao thoa tren doan thing no'i hai nguon Si, 82 la:

V i du 3: T a i hai d i e m Si, S2 tren mat nifdc each nhau / = 15cm c6 hai nguon dao

ddng ngiTdc pha: U i = Acos(lOnt)

112 = Acos(107it - 7l)

Toe do truyen song tren mat niTdc la v = 0,4m/s So" d i e m dao dong vcti bicii

do Idn nhat giffa hai nguon dao dong la:

Ne'u hai nguon ke't hdp Si, S2 dao dong cung pha thi vi tri hai diem ciTc dai

giao thoa l i e n tie'p M i , M2 tren doan noi hai nguon Si, S2 du'dc xac dinh bdi:

224

Cty TIMHH MTV DVVH Khang Viet

j<^hoang each M | - M2 la: i = S , M , ~ S , M , =

-j^et qua nay cung dung cho hai d i e m cifc tieu giao thoa lien tiep hoac hai figiion ke't hdp Si, S2 dao dong ngu'dc pha

Vi d i ' 1- f hire hien thi nghiem giao thoa tren mat nu'dc vdi hai nguon ket hdp ciuig

pha C O chu kl 0,3s Biet toe do truyen song tren mat nifdc la 40cm/s Khoang

each hai d i e m cifc tieu giao thoa lien tiep tren du'dng noi hai nguon la

nguon each nhau

V i d i i 2: T r e n mat nu'dc dang c6 cac van giao thoa ta de'm du'dc c6 tat ca 7 du'dng chiJa cac d i e m dao dong vdi bien do ci/c dai Khoang each giffa hai dinh cua hai du'dng nam ngoai cung la 3cm B i e t hai nguon ciing dao dong vdi tan so 20Hz Toe do truyen song la: '

PhtiOng phip g\i\ tap trSc nghigm Co hgc 12 - TrSn Trpng Hiing

C A U HOI VA BAI TAP TRAC NGHIEM

13.1 Hai ke't hdp la hai nguon dao dong

A. CLing bien do, cijng chu ki, cung phu"c(ng

B cijng phu'Ong, cCing tan so', hieu so' pha khong doi theo thdi gian

C cung bien do, ciing tan so', hieu so pha khong doi theo thdi gian

D Cling bien do, ciing phu'dng, hieu so' pha khong doi theo thdi gian

13.2 Hai nguon dong bo la hai nguon ke't hdp •

A cijng bien do B cung tan so' C ciingpha D ciing phu'cJng

13.3 Neu hai nguon ke't hdp ciing pha, thi nhiJng diem tai do dao dong c6 bien

dp ciTc dai la nhffng diem ma hieu du'dng di cua hai song tif nguon truyen tdi

cua hai song truyen tdi diem M cho bdi:

13.5 Hai nguon ket hdp dao dong ngu'dc pha, nhilng diem tai do dao dong c6

bien dp CLTC dai la nhiJng diem ma hieu du'dng di cua hai song tif nguon

truyen tdi la: , '

A d 2 - d , = k - B d 2 - d i =k?u

C d 2 d , = k +

-2 D d - d , = k + - X

13.6 Tai hai diem S|, S2 tren mat nu'dc c6 hai nguon ke't hdp cijng pha, cung tan

so" f - 20Hz To'c d p truyen song tren mat nu'dc la v = 30cm/s D p lech ph''

ciia hai song tai diem M tren mat nu'dc each hai nguon Ian lu'dt d| = 12cm

dn = 13cm la:

A Acp = — R a d B A(p = Y ^ a d C A(p = ^ R a d D Acp = —Rad

Cty TNHH MTV DVVH Khang Vi§t

13.7 Tren mat nu'dc c6 hai nguon ke't hpp dao dong ngu'dc pha:

U | = Acos207it U 2 = Acos(207xt + 71) To'c dp truyen song tren mat nu'dc la 0,5m/s M mot diem tren mat nifdc each

hai nguon Ian lu'dt d| = 15cm va d2 - 18cm Dp lech pha ciia hai song tai M la:

A Acp = ^ R a d B Acp = y R a d C Acp = y R a d D Acp = y R a d

13.8 Trong thi nghiem giao thoa tren mat nu'dc, bien dp song truyen di khong doi va bang icm tai diem M tren mat nirdc hai song truyen tiT hai nguon den

lech pha nhau y - r a d Bien dp song tong hdp tai M la: " ' ' ' '

A A M = 2cm B A M = 0,5cm C AM=l,5cin D A M = l c m

13.9 Hai nguon ke't hdp tren mat nu'dc cd phiTdng trinh Ui = U 2 = 2cos(207rt)(cm)

To'c dp truyen song la 0,4in/s M la mot diem tren mat nifdc each hai nguon Ian lu'dt 15cm va 12 cm Bien dp song tong hdp tai M la

13.10 Tren mat nu'dc cd hai nguon ke't hdp ngu'dc pha cting bien dp y/l cm

Birdc song la 0,3m M la mot diem tren mat nu'dc each hai nguon Ian lu'dt

7cm va 12cm Bien dp dao dong tong hdp tai M la

A A M = lyfZcm B A M = 2cm C A M = V2 cm D A M = 1 cm

13.11 Hai nguon ke't hdp tren mat nu'dc cd phu'dng trlnh U | = U 2 = \fi cos(87tt)(cm) To'c dp truyen song tren mat nu'dc la 48cm/s M la mot diem tren mat nu'dc each hai nguon Ian lu'dt 20cm va 18cm Phu'dng trlnh dao dong tong hdp tai M la

f A U M = 3cos(87it - — )(cm) B U M - 2cos(8Ttt - — )(cm)

6 2

C U M = 3cos(87it - — )(cm) D U M = 2cos(87tt - — )(cm)

4 6 13.12 Hai nguon ke't hdp S,, S2 tren mat nifdc dao dong gio'ng nhau:

Phuong phap giai bai t$p trSc nghijm Co hgc 12 - Trjn Trpng Hung

13.14 Ha i nguon ke't hdp Si, S2 tren mat nu'dc dao dong vdi phu'dng trinh:

To'c do truyen song tren mat nirctc la 0,4 m/s M la mot diem tren mat nirdc

each hai nguon Ian lu'dt 6cm va 7cm Phu'dng trinh dao dong tong hdp tai M la

A. U M = 4cos(207it - - ) (cm) , B U M = 2^2 c o s ( 2 0 7 i t - — ) (cm)

C U M = 4cos(20TCt + — ) (cm) D U M = 2V2 cos(207rt + -—) (cm)

4 4 13.16 Mai nguon ket hdp S|, S2 tren mat niidc giong het nhau Bu'dc song truyen

tren mat nu'dc la 4cm M la mot d i e m nam tren mat nufdc each S|, S2 Ian krdt

16cm va 10cm K e tu" du'dng trung triTc cua S1S2, diem M nam tren van giao

thoa : •' .\:

A ciTc dai thti" nha't , B cifc dai thu" hai

C ci/c t i e u thu-nhat , , , , , 4 , , ^,1,, , D ci/c tieu thi?hai

13.17 H ai nguon ket hdp 0 | , O2 tren mat nUdc c6 phu'dng trinh dao dong:

U | = U2 = Acos(57tt)

V a n toe truyen song la 15cm/s M la mot d i e m tren mat nUdc each O i , O2 Ian

lu'dt 0 | M = 16cm va O j M = 25cm Ke tiT du'dng trung triTc cua O1O2 diem M

nam tren van giao thoa

A ciTc tieu thu'nhat ' ' ' B cifc tieu thii'hai

C ci/c dai thu' nha't D ciTc dai thiJ hai

13.18 T r e n mat nu'dc c6 hai nguon ket hdp A va B each nhau 20cm vdi phu'dng

trinh dao dong: U A = U B = c o s c o t (cm)

Bifck- song A = 8cm B i e n dp song khong d o i G p i I la mot d i e m tren du'dng

trung triTc cua A B dao dong cDng pha vdi cac nguon A, B va gan trung diem

O cua A B nha't (hinh ve)

d i e m dao dong cifc dai nam tren doan S1S2 la

A 5 B 9 C 12 D 7 13.21 T r e n mat nu'dc cd hai nguon ke't hdp cung pha Si, S2 each nhau l0,75cm

phat ra hai song cung bien dp, cung tan so' gdc 20rad/s To'c dp truyen song la

3,18cm/s Lay — ~ 0,318 So' d i e m dao dong cifc tieu tren ,|, L2 la

71

A 18 B 20 C 22 D 16 13.22 T r e n mat nifdc c6 cac van giao thoa cua hai nguon ke't h d p i'i, "2 cung pha

Bu'dc song la 8cm Khoang each tiT dirdng trung triTc cua : ii2 den van giao thoa ci/c tieu dau tien (ke tij' du'dng trung trifc) doc theo S1S2 la

13.6 D a p an B =^ '

D o lech pha: z\cp - 2 7 i ^ ^ , v d i X = - = — = 1,5 (cm)

, 1 3 - 1 2 471 , , nen A(p = 27t = — (rad)

D o l e c h p h a c u a h a i s o n g tai M : Acp = (p, - 92 = 2n~—^-TT , vdi

D o lech pha cua hai dao dong tai M : Acp = 2 7 t ^ ^ ^ ' + n = 2n

B i e n do dao dong tong hctp tai M :

Vay: M nhn tren van giao thoa ciTc.tieu thuf

hai (ve phia gan S, hdn S,) nhir hinh ve

Vi I la trung diem cua S1S2 nen: di = d2 = —

Vay U i = 2Acos0.co.s (Ot - 71 — /

X = v.T = 0,23.0,2 = 0,046(m) = 4,6(cm)

i" 5

20 , 20 nen < k < -4,6 4,6

^ , 3 < k < 4,3

k = - 4 , 0, 4: CO 9 diem

|.21 Dap an D : : T = 2 ^ = i ^ = ^ ( s )

13.22 D a p an D

DiTdng tiling trirc cua S1S2 la van giao thoa ciTc dai

Khoang each tiT van giao thoa ciTc dai t d i ciTc tieu ke' tie'p la:

1 Sijf phan xa ciia song

a Vat can cd dinh: K h i phan xa tren vat can co dinh, song phan xa liion

luon ngiTde pha v d i song tdi d d i e m phan xa

b Vat can tu do: K h i phan xa tren vat can tiT do, song phan xa luon luon

cung pha v d i song toti d d i e m phan xa

2 Song diYng

- Song truyen tren sdi day trong trifdng hdp xuat hien cac niit va cac bung

g p i la JwV7^ , : tij

N u t la cac d i e m luon luon du'ng yen

B u n g la cac d i e m luon luon dao dong v d i b i e n do Idn nha't ,,

- H a i nut hoac hai bung lien tuc each nhau

X • ^ • '

N u t va bung l i e n tuc each nhau —

4

- D i e u k i e n de co song diTng tren mot sdi day cd hai dau cd dinh la chieu

dai cua sdi day phai bang mot so nguyen Ian nufa biTdc song:

2

- D i e u k i e n de co song diTng tren sdi day co mot dau cd dinh, mot dau tu do

la chieu dai cua sdi day phai bang mot so' le Ian — :

- S o n g p h a n xa tai B : u',5 = A e o s ( ( o t ± J i ) Song tdi

- Song phan xa tai M v d i M B = d: u'^ = A e o s

2, N e u B la vat can tiT do thi , , ^

- Song phan xa tai B : u'^ Aeoscot

- Song phan xa tai M v d i M B = d: u'^^^ = A e o s

Vi du 1: Day m e m A B co dau B co djnh T a i dau A ta tao ra mot dao dong thi tren

day CO song truyen tdi B vdi toe do 20m/s Phifdng ti'inh song tdi tai B la:

u,j = 2 c o s ( l 0 0 7 t t ) ( c m )

• Cho rang b i e n do song truyen tren day khong d o i PhU'dng trinh song phan xa

a i M each dau B 0,5m la u;^ = 2 c o s

I PhU'dng trinh song phan xa tai B : ujj = 2 c o s ( l 0 0 7 t t - 7 i ) ( c m )

PhU'dng trinh song phan xa tai M :

|,du 2: D a y A B dUdc tha de dau B ttf do T r e n day co song t r u y e n tif dau A

t;ide'n B Bi/dc song t r u y e n tren day la 2m/s PhU'dng trinh song t d i tai dau B la:

(em) PhU'dng trinh song phan xa tai d i e m M tren day

20Tit + 5

2

' UB = 5cos each dau B 0,5m la:

235

D a n g 2 PHUOING T R I I M I SONG TOING HOP

cuA SONG T 6 I VA SONG PHAN XA

Bie't b i e u thu'c song t d i t a i B la Un = Acos((ot) M la m o t d i e m t r e n d a y each

dau co" d j n h B k h o a n g d B i e u thiJc song t o n g h d p c u a s o n g t d i va song phan

-T = - ^ = 0 , 2 ( s )

?, = v T = l 00.0,2 = 2 0 ( c m )

( 2n.— + — cos l O T T t - -

tdi t a i B l a : U B = Acoscot M la m o t d i e m each B k h o a n g d

B i e u thu'c s o n g t o n g h d p t a i M cua song t d i va song p h a n x a l a :

Phuong p h ^ p giai bai t g p t r ^ c n g h i g m Co hqc 12 - Tr5n T r q n g Hung

Bieu thitc song tdi tai M : u^^ = Acos cot +

27t-BieuthuTcsongphanxa t a i B : ujj = U R =Acoscot ' ' '

( 2nd^

Bieu thiJc song piian xa tai M : = Acos cot

-Bieu thufc song tong hdp tai M : u ^ u ^ + U M = A

- N e u B l a vat can tir do thi: u = 2Acos-—-.coscot

D a n g 3 : PflJT V A B y N G

- Nut la cac diem luon luon diJug yen

- Bung la cac diem dao dong vdi bien do Idn nha't

Hai nut lien tuc hoac hai bung lien thuc each nhau

-X

- Nut va bung lien tuc each nhau — ' '

/i du 1: Tren day c6 song difng Biet to'c do truyen song la lOOm/s, tan so' song

la 50Hz Khoang each ba nut lien tuc la: „••

A Im B 2m C 3m D 4m

G i a i

v 100

r x = =-f 50 = 2(m) Khoang each ba nut lien tuc la: 2.— = 2(m)

D a n g 4 TIM S O NITT - S O ByiNG TREN DOAN D A Y C O SONG DUNG

1 Hai dau la hai nut: = n ^ (n = 1, 2, 3, ) So niit la n + 1

|i du 1 Day AB dai Im c6 song dCfng xay ra vdi A va B la hai nut Toe do

truyen song tren day ]h 50m/s, tan so'song la lOOHz Ke ea hai niit d A va B

thi tren day ed

A 4 n u t - 5 bung B 5 n u t - 4 b u n g C 4 nut - 3 bung D 3 n i i t - 4 bung

0,5 ^ so bung = n = 4

239

V i du 2: T r e n day c6 song diTng xay ra Bie't to'c do truyen song tren day la

lOOm/s, chu k i cua song la 0,01s Ke ca hai bung d hai d i e m M va N thl lir tvl

de'n N CO tat ca 5 bung Khoang each ti^ M den N la:

Vi du 3: D a y A B dai 0,9 m treo thang diJng vcti dau B de tu" do Cho dau A d a o

dong l i e n tuc v d i tan so 50Hz thi tren day c6 song diTng Toe do truyen song

tren day la 20m/s T r e n day c6:

=> So m i i t = So bimg = ^^y-!-= = 5 Chon dap an A

Vi du 4: T r e n day c6 song diJng B i e t bu'dc song la 0,5m O va M la hai diei

tren day v d i O M = 62,5cm T a i O c6 nilt thu" nhat thi tai M c6:

A nut thl? 2 B niitthLir 3 C bung thi? 2 D bungthur3

G i a i

T a c 6 : ^ ^ = 5 = > O M = 5 ^ (m = 5)

X/4 5 0 / 4 4

m + 1 5 + 1 ,

V i O la niit nen M la bung: So bung = — — = -—— = 3

Vay tai m c6 bung thu" 3

Chon dap an B

240

1 du 5: M o t o'ng di/ng difng trong c6 chiJa nUdc. D o cao Idp nu'c'Jc

CO the dieu chinh T a i mieng o'ng c6 dat mot am thoa nam ngang

nhU" hinh ve A m thoa dao dong v d i tan so' 500Hz To'c do truyen song trong khong k h i la 340m/s : i : i

D i e u chinh inifc nUdc sao cho cot khong k h i c6 chieu cao thich hdp till trong ong c6 song difng v d i bung tai mieng ong va nut tai mat nirdc K h i chieu cao cot khong khi trong o'ng thay d o i trong

khoang tLi'45cm den 60cm, ke ca bung song d mieng ong, trong o'ng

• So sanh phu'dng tiinh tong quat vdi phifdng trlnh da cho se tlm dqdc X va T

• To'c do truyen song: v = ^

Vi du 1 : Bieu thiJc song difng tren day cho bdi: u = 2acos

trong do d tinh bang cm Bu'dc song la:

Phiiang phap gi^i bai tjip trac nghi$m Co hgc 12 - Iran Irgng'HiTng

V i d u 2: T r e n day dan hoi c6 song difng xay ra v d i phiTdng trinh;

u = 2Acos(47td).coslOOTtt trong do d tinh bang met, t bang giay To'c do triiyen

song tren day la:

= 1 0 0 7 i - > T = 0 , 0 2 ( m )

T6C do: V = - = — = 25 (m/s) Chpn dap an D ,

T 0,02 i U J i , v

V i d u 3: Song difng xay ra tren day A B c6 dau B co dinh, l i do dao dong d diem

M each dau B khoang d vao liic t cho bdi: u = 2cos 0,05nd +

D i e m nut each dau C O dinh B khoang: d = k - = 12,5k (cm) (k = 0, 1,2,

I V d i d = 37,5 (cm) thi k = = 3 : do la d i e m nut Chon dap an A

'.'1.' • 12,5

D a n g 6 T I M C A C H A N G S O C H U A B I E T

T R O I N G B I E U T H l T C S 6 N G D O N G

^27cd

Chu y ! B i e u thiJc song difng c6 dang: u = 2Acos

thi bien do cua song cho b d i : a = 2 A

V

f27ld ^ cos + a

X - + a cos f2n t + P

V I d u 1: D o a n day m e m A B treo thang du-ng, dau B de tif do T r e n day cd

s6n;-dijfng xay ra v d i b i e u thiJc song dij-ng la u = U Q C O S c o s c o t , trong do d

X

khoang each ttr dau B den d i e m M tren day Uo la hang so diTdng

242

T a i d i e m M each dau B khoang — co bien do dao dong la 2cm

D o Idn cua U Q la:

:i - > Uo = 4 (cm) Chon dap an C .) s.' '^>ji.i' \.^^rj , =

-1 d u 2: T r e n day m e m A B v d i dau B co djnh c6 song difng xay ra v d i bieu thiJc

n

song di^ng la: u = 2acos bd + cos ' l O T l t - i ^ '

2 trong do a, b la cac hang so'

diTdng, d la khoang each lii d i e m M tren day den dau B B i e t toe do truyen

; song tren day la lOOm/s Hang so b bang:

T a i mot d i e m tren day co song diJ-ng thi d i e m do se dao dong (trCr d i e m niit)

V a n toe dao dong tai mot d i e m M (toa do X M ) la dao h a m cua l i do u theo t tai

2 4 3

V i d u 1: T r e n d a y m e m A B vdi d a u B c o ' d i n h c 6 song dij'ng Phifdng trinh soii^

difng la: u = 2cos 0,057rx +

-•1 cos 8m 2 (cm) trong do x la khoiing each

tCr d i e m M tren day den dau B tinh bang cm va t tinli bang giay V a n toe d;i a o

dpng tai d i e m M each dau B 5cm vao liic t = - ^ s la:

V a n toe dao dong tai M : v = = 8V27:sin

' ' C A U HOI V A BAI TAP T R A C N G H I E M

14.1 Chon cau dung: 1

Song phan xa va song t d i tai vat can

A luon luon ciing pha • B luon luon ngU^dc pha ^

C C O dinh luon luon ngiTdc pha D tiT do luon l u o n ngu-dc pha

14.2 Chon cau sal

Song difng ' ' ' '

A CO song tdi va song phan xa la cac song ke't hdp

B g o m hai song thanh phan (Song t d i va song phan xa) khong t r u y e n di nen

goi la song difng .'•

C C O cac niit va cac bung co dinh trong khong gian i •

D la ket qua cua sif giao thoa cua hai song

14.3 Cac ni'it tren mot sdi day co hai dau co djnh each dau co dinh

A nu'a bu-de song B phan tuT bifdc song

C so' le Ian niVa bqdc song D so nguyen Ian niVa bqdc song

244

Cty TNHH MTV DVVH Khang Viet

l4.4 Cac bung tren mot sdi day co hai dau ce dinh each • M ,• r •,; M

A bung k e t i e p phan tifbUdc song

B niit ke' tie'p nu'a bifdc song

C diiu C O dinh khoang bhng so' le Ian phan tu'bu'dc song

D dau co' dinh khoang bang so' nguyen Ian nu'a budc song

)4.5 D i e u k i e n de ed song dij'ng tren sdi day cd mot dau co' djnh, mot dau tir do

la chieu dai sdi day phai bang mot

A so le k i n phan tu"bifdc song B so'nguyen Ian phan tu'bu'dc song

C so' le Ian niYa birdc song D so nguyen Ian nu'a budc song

14.6 Day m e m A B cang ngang cd dau B giu" co dinh Bieu tMc song tdi tai B la:

birdc song X M la mot d i e m tren day each dau co dinh B khoang d D p lech

pha cua song tdi va song phan xa tai cung d i e m M la:

14.8 T r e n day m e m A B v d i dau B co dinh cd song tdi truyen de'n B v d i bien dp

A , bu'de song X B i e n dp dao dong tong hdp ciia song tdi va song phan xa tai

X

d i e m M tren day each dau co dinh B khoang — la:

A a = AV2 B a = 2A C a = A

2 1.9 D a y M N treo thang diJng v d i dau N de tif do nhu" hmh ve Cho

| d a u M dao dpng vdi bien dp A thi song tdi truyen de'n N v d i bu'de

*sdng X B i e n dp dao dpng tdng hdp ciia song t d i va song phan xa tai

^diem P tren day each dau N khoang

Phuang phap giai bai tap t r i e nghigm Co hgc 12 - Trin Trgng Hiing

14.10 T r e n d a y c6 s o n g dCfng x a y r a B i e t b i e n dp c i j a song t(5i la 2 c m t h i b i e n

d o dao d p n g c u a s o n g d i f n g t a i d i e m b u n g l a :

A a = 2 c m B a = 2 > / 2 c m C a = 4 c m D a = 4 > / 2 c r i i

14.11 M o t d a y A B c6 d a u B co d i n h T r e n d a y c6 song t r u y e n v d i toe d p 4m/s

S o n g t d i t a i d a u B l a : Uu = %/2 cos(207rt) (cm) phu'dng trinh song tong hpp cua

song tcti va song p h a n xa t a i d i e m M tren d a y each d a u B k h o a n g 10cm l a :

s o n g t d i t r u y e n de'n B v d i toe d p t r u y e n song la 5m/s Phu'dng t r l n h song tdi

t a i B l a : Uu = 2cos(107:t) (cm), phu'dng trlnh song t o n g h d p tai M t r e n day each

M.16 B i e u thu'c s o n g d i f n g t r e n d a y co d a u c a n tiT d o l a : u = acos(5Tcd).cos(bt)

I t r o n g d o a, b la cac h a n g so' du'dng, d la k h o a n g each lii m o t d i e m t r e n day

|: de'n d a u d a y t i n h b 5 n g m e t ; t t i n h bang g i a y B i e t toe d p t r u y e n s o n g t r e n d a y

e a c h d a u B k h o a n g x ( d d n v i : m ) l a : u = 2cos(107ix).cos((ot) ( c m ) B i e n d p dao d p n g c u a d a y t a i d i e m each d a u B k h o a n g 7,5cm l a : • >

A a = V3 c m B a = \/2 c m C a = 1,5cm n ^ D a = — c m 14.20 T r e n d a y A B co song di/ng x a y ra B i e u thu'c song d i f n g t a i d i e m M t r e n day

each d a u B k h o a n g x ( t i n h b a n g c m ) cho b d i : u = 4cos nx + —

Phmng phap giai bai tgp U&c nghi^m Co hpc 12 - Iran Trpng Hi/ng

14.22 Day mem A B dai 2m cang ngang vdi hai dau A, B co' dinh Khi tren day

C O song diTng xay ra ta quan sat dirdc 3 bung Biet tan so' song la 216Hz Toe

do truyen song tren day la:

A V = 216m/s B v = 162m/s C v = 348m/s D v = 288m/s

14.23 Tren day dai 75cm vdi hai dau co' dinh c6 song dij'ng Tan so' song tren

day la 430Iiz, toe do truyen song trong khoang tiT 200m/s den 300m/s Toe do

truyen song la - - • , , ,

A V = 348m/s B v = 215m/s C v = i 52m/s D v = 425m/s

14.24 GiCTa hai dau day co dinh va cho day rung khi day rung vdi tan so 20011/

thi tren day co ta't ca 3 nut (ke ca hai niit d hai dau) Khi day rung vdi tan so

400Hz (to'c do truyen song tren day van khong doi) thi tren day co

A 7 niit B 6 nut C 5 niit D 4 niit

14.25 Day mem dai 80cm cang ngang hai dau De co song dCrng tren day thi day

phai rung vdi tan so thich hdp, trong do tan so be nhat la 185Hz Biet rang toe

* do truyen song tren day khong doi To'c do truyen song la:

A v = 296m/s B v = 340m/s C v = 125m/s D v = 462m/s

14.26 Day A B dai I m du'dc treo thang di'fng vdi dau B de tu" do Cho dau A dao

dong lien tuc vdi tan so' lOHz thi tren day co song dij'ng vdi dau A coi nhir

nut To'c do truyen song tren day la 8m/s tren day co:

A 5 bung - 5 niit B 3 b u n g - 3 nut ; v,.!) i r t ' l

C 5 b u n g - 4 ni'it D 3 b u n g - 4 nut

14.27 Day A B = I m co song diTng vdi dau A la niit, B la bung, tren day co ta't cii

3 bung Biet tan so' song la 100Hz To'c do truyen song tren day la:

A v = 133,3m/s B v = 266,7m/s C v = 80m/s D v = 160m/s

14.28 Tren day co song dCfng O A va B tren day co hai bung va giffa chung cd

hai nut Biet to'c do truyen song tren day la 192m/s va tan so' song la l20Hz

Chieu dai A B la:

A 3,2m B 2,4m C 2,0m D 1,6m

H a 6 N G D A N G I A I

14.1 Dap an C '

Song phan xa va song tdi tai vat can co'dinh luon luon nguCdc pha (con tai vat

can tu" do luon luon cijng pha) ; : , ,

14.2 Dap an B

B Sai VI hai song thanh phan ciia song diTng la song tdi va song phan xa van

truyen theo hai chieu ngu^dc nhau

Dieu kien de co song dCfng tren sdi day co mot dau co' dinh, mot dau tu" do la

I chieu dai sdi day: / = m ^ vdi m = 1, 3, 5,

l 4 6 D a p a n B ' ^•rhu^uy'^ - - r » - : ^ ' - i - • - :

Song phan xa tai dau co dinh B ngu'dc pha vdi song tdi tai B nen:

U u = - 2 cos 207rt +

-4 (cm) Song phan xa tai M do song phan xa tai B truyen tdi nen:

Goi song tdi tai B la: U B = Acos((ot) thi '

Song phan xa tai B: Ujj =-Acos(cot)

Song phan xa tai M : = - A c o s cot 27rd = Acos cot n 27Td

X

Do lech pha cua song tdi va song phan xa tai M :

249

Phifong I'liap oiai hai tfii) tiSc ngriicm CO hQC ^•^ - Iran Irgng HiJng

2nd 2nd 4nd

Acp = cpM - ( P M = — — + - — - + n = —— + n

A A A, ,, , J ,,,,, ,i , 14.8 D a p a n A

j^huong phap gi^i bai tjp trie nghi^m Co HQC 12 - TrJn Trpng Hung

So phiTdng trinh da cho vdi phu'dng trinh to'ng quat: 11,r

2 3

71 3T , 7tX + — = + k T l

Co: / = n — = n > — - — : khong doi

14.25 Dap an A

De CO song dCfng tren d;iy c6 hai dau co' dinh:

/ = n — = n — (vdi n = 1, 2, 3, ) ^ — = — : khong doi

-a Song dm lit nhQng song cd truyen trong cue moi trudng khi, long, ran

b Nguon dm Id cdc vat dao dong

Tan so cua am phat ra bang tan so dao dong cua nguon am

c Am nglie dU(/c - Ha dm - Sieu dm

- A m nghe du^dc (am thanh) co tan so tiT 16Hz den 20000Hz

b Ciftyng do dm va mijtc cifdng do dm "

- Cu'dng do am 1 tai mot diem la dai lUdng do bang nang iu'dng ma song truyen qua mot ddn vi dien tich tai diem do va vuong goc vdi phUdng truyen song trong mot ddn vi thdi gian Ddn vj cu'dng do am la: w/m^

- Mtfc cu'dng do am, ki hieu la L, ddn vj dexiben (dB) du'dc tinh bang cong thiJc L(dB) = 10/g — vdi ]() la cu'dng do am chuan

c Am c(f bun vu hoa dm

Khi nhae cu phat ra am co tan so fo goi la am cd ban thi cung dong thdi phat ra cac am co tan so 2f(), 3fo, goi la hoa am thi? hai, thu" ba, Tap hdp cac hoa am tao thanh pho cua nhae am

BAI TAP C d B A N

D a n g 1 TIINH CUdiNG D O AW T A I MOT D I E M

Nhae lai dinh nghTa:

Cifdng do am tai mot diem la dai Iu'dng do bang nang li/dng ma song ixm

truyen qua mot ddn vj dien tich dat vuong goc vdi phu'dng truyen song tai diem do trong mot ddn vj thdi gian: 1 = w

S.t Vdi w la nang Iu'dng (Jun) truyen qua dien tich S (m^) trong thdi gian t

Vi d u 1: Mot song am co dang hlnh cau du'dc phat ra tJjT nguon N co cong sua't P Biet rang nang Iu'dng am du'dc phat ra va truyen di giong nhau theo moi hudng va moi trirdng khong hap thu am Cu'dng do am tai mot diem each nguon am mot khoang d la:

I tinhbdi: S = 47rd'

VI moi tru'dng khong hap thu am nen trong thdi gian t nSng liTdng am w do nguon phat ra cung la nang Iu'dng da truyen qua dien tich S

Vi nang lufdng am truyen di giong nhau theo moi hu'dng nen nang Iu'dng

am truyen qua moi ddn vi dien tich (dat vuong goc vdi phu'dng truyen) trong thdi gian t la:

255

Vi dii 2: Mot nguon am phat song am hnih cau truyen di deu iheo moi hudii^

rang nang krong am diMc bao loan Tai diem each nguon am l,2i

cUcJng do am la 0,5 VV/m" Khi dich di 20cm (ke tiJ" vj tri trtTcfc) thi cu'dng do

am lang len \'a bang

A I = 0,60 W/m' B I = 0,72 W/nr C I 0.84 W/m^ D I = 0,96 W/iir

(Jiiii

Cifdng do am tai vi tri dau: I,

Tai vi tii sau: IT = 47td;

Mile cu'dng do am la: L (dctn vi B) = / g — hoac L (ddn vj dB) = 10/g —

Vdi lo la cu'dng do am chuan = 10''^ W/m^

Vi du 1: Tieng nhac nhe nghe difdc trong phong la 40db ihl cu'dng dp am ciia no

so vdi cu'dng dp am chuan gap

A lOMan B 40 Ian C 4 idn D 10'°lan

I du 2: GiCTa cu'dng dp am I|, I2 vdi cac mi?c cu'dng do am tadng i^ng L,, L2

chiing lien he bang he thiJc: