Giáo trình vật lý đại cương phần 1 (dành cho sinh viên đh chính quy ngành y dược)

Cac tfnh cha't, dac didm cua song dien tti Thang song dien tti QUANG HOC Co sd cua quang hinh hoc - Dung cu quang hoc Cac dinh luat ca ban cua quang hinh hoc Dung cu quang hoc Giao thoa

B0 g i A o d u c v A d A o t a o

DAI HOC THAI NGUYEN BUI VAN THlfiN - NGUYEN QUANG DONG

GIAO TRINH VfiT IV DM CUONG (Danh cho sinh vien dai hoc chinh quy nganh Y - Dirac)

DAI HOC THAI NC-UYEN

TRUNG TAM HOC LIEU

NHA XUAT BAN DAI HOC QUOC GIA HA N 0I

s A c h d u o c x u a t b a n b c ji sir t a i t r o c u a d u A n g i A o d u c d a i h o c 2

MUC LUC

4 Dinh luat bao toan dong lucrng trong co he km 38

8 Dinh luat bao toan co nang trong trudng luc the 44

2 Tinh hoc cha't luu

3

3 Dong luc hoc ch£t luu If tuong 48

1 Thuyet dong hoc chat khf va khf ly tudng 58

2 Phuong trinh trang thai cua khf ly tucmg 60

1 Nguyen ly thu: nhat cua nhiet dong luc hoc 62

2 Nguyen ly thu: hai cua nhiet dong luc hoc 6 8

3 Entropi va nguyen ly thur hai cua nhiet dong luc hoc 71

1 Cau tao va chuydn dong phan tir cua cha't long 81

2 Nhung dai luong dac trung cua ddng dien 108

1 Thf nghiem v& tuong tac tir cua ddng dien 1 1 2

113114120 120

121123125125

126128129131131135146146147154156160160162165172172

173

Dinh luat Ampe ve tucmg tac ttr cua dong dien

Vecto cam ling tti, vecta cudng dd tti trudng

Cam urng dien tir

Thi nghiem ve hien tucmg cam ting dien tti

Cac dinh luat cor ban ve cam ting di6n tti

Mot sd trudng hap dac biet cua cam ting dien tti

Dao dong dien tir - Song dien tir

Cac luan didm cua Macxoen

Su tao thanh song dien tti Cac tfnh cha't, dac didm

cua song dien tti

Thang song dien tti

QUANG HOC

Co sd cua quang hinh hoc - Dung cu quang hoc

Cac dinh luat ca ban cua quang hinh hoc

Dung cu quang hoc

Giao thoa anh sang

Nguyen If Huyghen - Frenen

Ly thuyet chung ve hien tuong giao thoa anh sang

Giao thoa cua hai chum tia sang

Ung dung hien tuong giao thoa

Nhi6u xa anh sang

Ly thuyet chung ve nhilu xa anh sang

N hiiu xa cua song cau qua Id tron

Nhidu xa gay bdi cac song phang

Phan cuc anh sang

a

Anh sang tu nhien va anh sang phan cuc

Su phan cuc anh sang do truyen qua ban Tuamalin day

Dinh luat Malus

3 Phan cuc vi phan xa Dinh luat Brewster 175

3 Thuyet luong tu anh sang cua Einstein va giai thich cac

3 So lupc ve tinh cha't cua chum tia laser 192

3 Tuong tac cua tia phong xa vcti vat chat 204

Chuong 2: (Jng dung mot so ki thuat vat ly vao chan doan

6

Lcfi noi dau

Ngay nay nhifng thanh tUu cua vat ly difdc ling dung rong rai trong nhieu Imh vuc, d5c biet trong Y hoc, nhifng ung dung cua Vat ly hoc nhu: sif dung cac

ki thu^t vat ly trong chin doan va di£u tri, dien tim, dien tam dd, dien nao d6, dieu tri bang nhiet, bang tif trudng, ling dung cua a m va sieu am , chup X quang, sdi quang hoc trong md ndi soi, ting dung cua phong xa, chup hinh c£t ldp vi tinh, chup cdng hudng tir hat nhan, mat va cac dung cu quang hoc, ling dung cua anh sang trong dieu tri, nhifng ting dung cua laser da lam cho nganh Y - Difpc

co mdt su phat trien vudt bac, giup cac th ly thuoc chan doan va di£u tri chinh xac

va cd hieu qua cao

Giang day mdn Vat ly dai ctfdng nham trang bi cho sinh vien nganh Y - Dude nhifng kien thuc vat ly cd ban nhat lien quan phuc vu nganh nghe, va trang bi cho sinh vien phudng phap tu duy khoa hdc, ket hdp vdi thuc tien, cung cap cac khai niem, nguyen ly, quy luat cd ban nhat cua vat ly, de? tif dd ho

cd the hoc cac mdn hoc khac nhu : Hoa vd cd, Hoa - Ly, Ly sinh y hoc, Vat ly tri lieu - phuc hdi chuc nang, Chan doan hinh anh, y hoc hat nhan, va cac mdn hoc khac cd lien quan

Giao trinh nay dude bien soan theo chuong trinh dao tao mdi xay dung cua Trudng Dai hoc Y - Dude - Dai hoc Thai Nguyen Noi dung cua tai lie u cung cap nhifng kie'n thuc cd ban ve: Cd hoc, nhiet hoc, dien hoc, quang hoc, phdng xa, hat nhan nguyen tu phuc vu nganh Y - Dude

Do doi tudng dao tao chu yeu la sinh vien mien nui, nen kha n£ng tiep thu

k ieh thuc vat ly cd nhieu han che' Vi vay, vifc bien soan m dt giao trinh V a t ly dai cifdng vifa dam bao tinh cd ban va he thong kie'n thuc, phu hdp vdi chudng trinh chung cua Bd, vifa phu hdp vdi doi tudng dao tao la mdt viec lam can thiet

Giao trinh d u d e b ien soan lin d a u , do kha nang va kinh nghiem con han che', chSc chin khdng tranh khoi thie'u sot Chung tdi rat mong nhan d u d e su gop y cua cac ban dong nghiep va cac em sinh vien de’ giao trinh ngay cang d u d e hoan chinh hdn

Xin chan thanh cam dn!

Thai Nguyen,, ngay 27 thang 2 n2m 2008

CAC t A c g i a

7

P h a n thCr n h a t

Bai md dau CAC KHAI NIEM DAI CUONG

1 Chuyen dong co hoc

La su thay ddi vi tri cua vat hay mot bo phan cua vat trong khong gian theo thdi gian

Chat diem co tfnh tuong doi

Vf du: Electron chuyen dong tren quy dao quanh hat nhan; Trai Dat quay xung quanh Mat Tr6i dupe coi la chat diem

3 He quy chieu

Vat dupe chon lam moc, cung voi he toa do va mot chiec dong ho gin lien voi no, de xac dinh vi tri cua vat khac, goi la he quy chieu

4 Phuong trinh chuyen dong cua chat diem

Trong he toa do De-cac, vi tri cua chat diem M

tai mot thai diem nao do dupe xac dinh boi 3 toa do

x, y, z hoac boi ban kinh vecto r , deu la nhung ham

cua thai gian

x = x(t); y = y(t); z = z(t) r = r(t)

Cac phuong trinh tren goi la cac phuong trinh

chuyen dong cua chat diem

/V

Q

y, z)

5 Quy dao chuyen dong

Quy dao chuyen dong la duong ma chat diem vach ra trong khong gian khi chuyen dong

11

Muon xac dinh duoc dang quy dao, ta phai tim phuong trinh quy dao.

Phuong trinh quy dao la phuong trinh bidu di6n md'i quan he giua cac toa do

Vi du: y = ax2 + bx +c (Quy dao parabol)

6 Tinh chat tirong doi cua chuyen dong

Chuyen dong co tmh tuong doi, tuy theo he quy chieu ta chon, mot vat co the coi la dting yen hay chuyen dong

Vi du: Mot ngudi dang dutig yen tren tau hoa, nhung lai chuyen dong so vdi cay ben dudng

7 Don vi do ludng

M6i mot thuoc tmh cua mot doi tuong vat ly dupe dac trung boi mot hay nhieu dai lupng vat ly Mot trong nhung van de co ban cua vat ly hoc la do ludng cac dai lupng vat ly Ngudi ta phai chon mot dai lupng lam m lu goi la don vi.Tti nam 1971 ngudi ta da chon he don vi do ludng quoc te SI (System International - He quoc te)

Bang 1.1 Bay dai lirgng vat ly co ban trong he SI

Ten dai ludng Ky hieu Ten ddn vi Ky hieu ddn vj

Muon bieu diin nhung sd rat nho hay rat ldn, ngudi ta dung luy thua 10

Thu: nguyen cua mdt dai lupng vat ly la c6ng thtic neu len su phu thudc cua dai lupng do vao cac dai lupng co ban.

Vf du: V^n toe = Chieu dai / Thdi gian

Ta ky hieu thti nguyen van toe la: [Van toe] = L/T = L T1

Don vi cua van toe la: m/s

8 Thur nguyen

thtic tren la hop ly

9 Cac dai lupng vat ly

M6i thuoc tfnh cua mot doi tupng vat ly (Mot vat the, mot hien tuong, mot qua trinh ) dupe dac trung boi mot hay nhieu dai lupng vat ly

Vi clu: Khoi lupng, thdi gian, the tfch, luc, nang lupng

Cac dai lupng vat ly co the la vo hudng hay dai lupng vecto (huu hudng)

9.1 Xac dinh mot dai luong vd hu&ng

Nghla la xac dinh gia tri cua no, co nhung dai lupng vo hudng khong amnhu: The tich, khoi lupng , co nhung dai lupng vo huong ma gia tri co the amhay duong, vf du nhu: dien tfch, hieu dien the

9.2 Xac dinh mot dai luang vecto

Nghla la xac djnh diem dat, phuong, chieu, va do 1dm cua vecto dac trungcho dai lupng do Vf du: luc F, cudng do dien trudng E

Vf du: Cong thtic chu ky cua con ldc: T = 2n

Thti nguyen cua hai ve la: T =

Chuong 1

*

DO NG HOC CHAT DIEM

Dong hoc la mot ph£n cua co hoc nghien ctiu cac quy luat van dong co, khong chu y den nguyen nhan da gay ra anh hudng, tac dong len van dong co

1 V e c to d jc h c h u y e n

Gia thiet co mot chat diem van dong co Sau thdi gian t

vach ra quy dao cong AB Ngudi ta goi do dai cua doan duong

AB la doan duong dich chuyen, ky hieu la S S la mot ham cua

thoi gian:

S = S(t)Neu xet doan duong dich chuyen AB tti A den B hay tti B

ve A thi do dai, tmh chat, do cong khong khac gi nhau Hinh 1.1

Neu la'y A lam goc, B lam ngon, ve vecto AB, ngudi ta

goi vecto AB la vecto dich chuyen, ky hieu la L Vecto dich chuyen L khac doan dudng dich chuyen S ve do dai, do la vecto chi huong chuyen dong Do vay, khong the dung doan dudng dich chuyen S de thay cho vecto dich chuyen L va nguoc lai

Nhung neu xet trong then gian vo cung nho dt, chat diem di duoc doan dudng

vo cung nho dS, vecto dich chuyen tuong ting dL Ta thay ve do ldn dS = dL (day cung chap len cung vi phan)

Khi chat diem chuyen dong thang, cd quy dao la mot doan thang thi cac vecto djch chuyen vi phan dL trung phuong vdi doan dudng dich chuyen dS

Khi chat diem chuyen dong cong, cd quy dao la mot dudng cong thi cac vecto dich chuyen dL cd phuong tiep tuyen vdi doan dudng dich chuyen dS

2 V a n td 'c■

2.1 Djnh nghla

Van toe la dai luong vat ly dac trung cho su bi6n d6i cua quang ducmg dich chuyen theo thoi gian No chi cucmg do chuyen dong

Ky hieu: v, don vi: m/s (trong he SI)

2.1.1 Van toe trung binh

La ty so g iu a d o an d u d n g dich ch u y en AS m a ch at di^m di d u o c sau k h o an g thdi gian At vdi k h o an g thdi gian At dd:

2.1.2 Van toe titc thdi

La van toe cua chat diem d mot thdi diem xac dinh

v„ = lim — = —

A,-*° At dt

Van toe tuc thdi cd do ldn bang dao ham bac nhat cua quang dudng theo thdi gian

6 mdi thdi diem xac dinh, chat diem cd mot gia tri van toe ttic thdi xac dinh Vay van toe tuc thdi cung la mot ham sd cua thdi gian chuyen dong:

vt = v,(t)

2.2 Vecto van toe

Khi chuyen dong, chat diem cd van toe luc nhanh, luc cham, khi di theo hudng nay, khi di theo hudng khac Do vay, de bieu thi van toe chuyen dong cua mot cha't diem, chung ta phai dung mot vecto de md ta ca ve do ldn va phuong chieu

Ky hieu: vecto van toe v

2.2.1 Vecto van toe trung binh

Sau mot khoang thdi^gian At, chat diem di duoc doan dudng AS, cd vecto dich chuyen tuong ung la AL Vecto van toe trung binh:

= ALv= At

2.2.2 Vecto van toe t&c th&i

Vecto van toe trung binh khong dac trung cho chuyen dong cua chat diem 6 tiirng thdi didm, ta dung khai niem vecto van toe turc thdi (goi tat la vecto van toe)

- Neu chat diem chuyen dong tren mat phang thi toa do cua no cd hai thanh phan (x va y)

v - v x + v y

- Neu chat diem chuydn dong trong khdng gian, van toe cd ba thanh phan

v = v x+ v y+ v z

2.3 Y nghla

+ Vecto van toe v cho biet chuyen dong la cong hay thang, bien doi hay deu

- Neu v cd phuong khdng doi theo thdi gian thi chuyen dong khong doi phuong, quy dao la mot doan thang

- Neu v cd phuong va do ldn khdng doi theo thdi gian thi chuyen dong la thang deu

- Neu v cd phuong va do ldn luon thay doi theo thdi gian thi chuyen ddng la cong, bien doi, quy dao la mot dudng cong

+ Biet do ldn v suy ra quang dudng dich chuyen

v = — => v.dt = dS=> S = [v.dt

G ia toe trung binh cua chuyen dong trong k h oang thdi g ian At la ty sd giua

do bien th ien van toe Av vdi khoang thdi g ian At xay ra do b ien th ien van toe dd.

3.3.2 Gia toe tuc thdi

L a dai lu o n g dac trung cho su bien doi cu a v ecto van toe d tai m o t th d i diem xac dinh (goi la g ia toe).

K hoang thdi g ian At cang nhd thi gia toe tru n g binh can g dac tru n g chm h xac cho su b ien th ien cu a van toe.

a = lim a = l i m — = —

At->0 At->0 At dt Vay: Gia toe la dai luong vecto bang dao ham bae nhat cua vecto van toe theo thdi gian.

3.3 Cac thanh phan cua gia toe

Gia toe la mot dai luong vecto nen ta cd

the phan chia gia toe ra lam 2 thanh phan: gia

toe tiep tuyen a , va gia toe phap tuyen a n

Mdi thanh phan cua gia toe dac trung

cho sir bien doi cua vecto van toe ve moi

phuong dien: do ldn va phuong chieu

Xet mot chat diem chuyen dong cong,

gia su sau thdi gian At rat nhd, sao cho quy

dao MM | cd th6 coi nhu mot cung tren dudng

tron tam O, ban kinh R:

DAI HOC THAI NGUYEN

- Tai di£m M: chat diem co van toe v bi£u di6n bang vecto MA

- Sau thdi gian At, chat didm 6 vi tri M, co vecto van toe v,= v + Avbi£u di6nboi vecto M,A,

=> gia toe a= lim— = lim— L+ lim—

-At-»0 At At->0 At At-*0 At

a=a,+at nVay gia toe a duoc phan tfch thanh hai thanh phan Ta hay tim y nghla cua tCrng thanh phan

3.3.1 Gia toe tiep tuyen

a , = l i m = lim

A t —>0 At At —>0 At

- Phuong cua a, : la phuong cua A v „ khi At —> 0 Nghla la phuong tiep

tuyen vdi quy dao cong tai M Do dd at duoc coi la gia toe tiep tuyen

- Chieu cua a, : la chieu cua A v , , cung chieu V neu v, > v va nguoc lai(nghla la cung chieu chuyen dong, neu chuyen dong nhanh dan, a, nguoc chieu chuydn dong neu chuyen dong cham dan v, < v)

= lim - 1— = lim — = — = — At-»o At A,^° At dt dt'

-Vay gia toe tiep tuyen cd do ldn bang dao ham bae nha't do ldn cua van toetheo thdi gian

Do ldn cua van toe bien doi cang nhieu, a, cang ldn Vi vay, ta noi: gia toe

tiep tuyen dac tning cho sic bien doi cua vecto van toe ve mat do Ion.

At->o At A,_>0 At

- Phuong cua an : la phuong cua Avn khi At —» 0 Vecto -Avn hop voi phuong tiep tuyen MC mot goc:

7i - Aa

71 - 0 71

trong do: Aa = goc MOM,

Khi A t -> 0 ; diem M, tien tori trung M; Aa -> 0 do do 0 = ^

Nghla la an co phuong trung v6i phap tuyen cua quy dao cong tai diem M

Vi the an duoc coi la gia toe phap tuyen

- Chieu cua an : la chieu cua Av„, luon hu6ng ve phfa tam cua quy dao, nghla

la hudng ve tam O cua ducmg tron, do do an con duoc goi la gia toe huong tam

Al-^0 R AtAS

do do

( lim v, = v; lim = v)

A t - * 0 * ‘ a,- > o n At '

a„ =R

TOr cong thuc tren ta suy ra: gia toe phap

tuyen dac trung cho su thay doi phuong cua

vecto van toe.

Thuc vay: voi mot gia tri v xac dinh, ban

kinh R cua quy dao cang nho, an cang Ion quy

dao cang cong, nghla la phuong cua v thay d6i cang nhieu va nguoc lai

Hinh 1.5

3.3.3 Ket luan

Vecta gia toe co the phan tfch thanh hai thanh ph&n:

- Gia toe tiep tuyen a, dac trung cho su bien d6i cua vecto van toe v6 do ldn

- Gia toe phap tuyen an dac trung cho su bie'n d6i cua vecto van toe ve phuong

4.1 Chuyen dong thdng bien doi deu

Chuyen dong thang cd v khdng doi phuong, do dd an = 0 Chuyen dong bien ddi nen a * 0

Chuyen dong thang bien doi deu cd [an =0

a, =consta=at+an = a, = const

& t = 0 thi chat diem di duoc quang duong S0; nghla la c = S0

S = a y + v0t + S0

v2 - v02 = 2aS

t2

* Neu vat rai tu do tir do cao h xuong dat, ta co: h = g —

g: gia toe trong truong

v = g.t v2 = 2gh

4.2 Chuyen dong tron

4.2.1 Dinh nghla

Chuyen dong tron la chuyen dong ma su bien d6i ve phuong cua vecto van toe 6 tai moi diem tren quy dao, tai moi thdi diem la bang nhau Quy dao la mot duong tron

an = constDoi voi chat diem chuyen dong tron, ngoai cac dai luong van toe dai, gia toe dai, ngudi ta con dung cac dai luong dac trung khac la van toe goc, gia toe goc de

mo ta chuyen dong

4.2.2 Van toe goc ( co)

Sau thdi gian At chat diem di tir M den M, Ban kmh quy dao quet duoc mot goc A0 Van toe goc trung binh:

Vay: van toe goc tuc then (goi tat la van

toe goc) cd do ldn bang dao ham bae nha't cua goc quay doi vdi thdi gian.

Quy udc ve vecto van toe goc co nhu sau:

+ Cd goc tai tam O

+ Cd dd ldn bang —

dt+ Cd phuong vuong goc vdi quy dao tron

+ Co chieu duoc xac dinh theo quy tac van nut chai: neu quay cai van nut chai theo chieu chuyen dong cua chat diem thi chieu tien hay lui cua than van nut chai la chieu cua vecto van toe goc.

+ Don vi do: rad/s

Hinh 1.8

4.2.3 Gia toe goc

La dai luong vat ly dac trung cho su bien doi cua vecto van toe goc theo thoigian

- Gia toe goc trung binh:

j3 = A co/A t

Gia toe goc tire thdi:

P = lim (3= lim Aco dco

At - »0 At —>0 d t

Gia toe goc P la mot vecto bang dao ham bae nhat cua vecto van toe goc doi vdi thdi gian

+ Cd phuong: la phuong cua co, nghla la

phuong vuong goc vdi mat phang quy dao tron

+ Chi6u: Cd chieu cung chieu vdi van

toe goc co, neu chuyen dong la nhanh dan va

nguoc chieu co neu chuyen dong la cham dan

(co2 < co,)

dco d20 + Do Ion: P = =

dt dt

4.2.4 S u lien he giita van toe dai v , gia toe tiep tuyen a, vdi van toe goc ©

va gia toe goc p

Sau thdi gian dt, chat diem di duoc doan

* *

duoc mot goc d 0

v = [co a R ]

R : v ecto ban k m h q u y dao.

- Do ldn cua gia toe phap tuyen:

5.1 Dao dong la gi?

Chuyen dong dao dong la su chuyen dong lap di lap lai vi tri can bang sau nhung khoang thdi gian nhat dinh, dudi tac dung cua luc dan hoi hay luc chuandan h6i

+ Vi du:

- Dao dong cua Id xo:

C) trang thai can bang: Fhl = 0 Dung ngoai luc keo lo xo lech khoi VTCB mot doan x roi tha ra, vat nang chuyen dong ve vi tri can bang O do tac dung cua mot luc dan hoi Fdh Luc dan hoi bang nhung nguoc chieu vdi ngoai luc

Fdh = -K.xDau (-) do luc dan hoi luon nguoc chieu vdi vecto dich chuyen x

K: he sd dan hoi cua lo xo Phu thuoc ban chat cua lo xo

Den vi tri can bang Fdh = 0 Nhung do quan tfnh, vat tiep tuc chuyen dong sang trai mot doan dung bang x (neu bo qua ma sat cua khdng khf)

Luc do lai xu£t hien luc dan hoi do lo xo phai keo, lo xo trai d£y, vat qua lai

vi tri can bang roi sang phai

Qua trinh cu: lap lai nhu vay nhieu Mn sau tiirng khoang thdi gian bang nhau Ngudi ta goi chuyen dong dd la chuyen dong dao dong

- Con lac dan

•* p

Hinh 1.11

Lay mot soi day manh, khdng co gian,

chieu dai / Mot dau day buoc vao vat nang

khoi luong m, dau kia buoc vao ban cd dinh Ta

co mot con lac don

Thoat dau dudi tac dung cua trong luc P

con lac dting yen

Tac dung mot ngoai luc lam cho con lac

lech ra khoi phuong thang durng mot goc lech a Sau dd thdi tac dung ngoai luc

6 vi tri mdi, trong luc P cua vat nang duoc phan chia ra 2 thanh phan:

P = P t + P n

P ,: theo phuong keo dai cua day treo

P n: cd tac dung keo con lac ve vi tri can bang

6 vj tri can bang P n= 0 Nhung do con quan tfnh no lai tiep tuc sang trai (gia thiet nhu ban dau bai toan de ra: day treo manh, goc a nhd, bo qua ma satcua khdng khi) Con lac lech sang trai mot goc dung bang a va luc dd P n lai xuathien keo vat ve vi tri can bang Cur nhu vay chuyen dong cua con lac lap di lap laisau nhung khoang thdi gian nhu nhau

Luc P n la luc gay ra chuyen dong dao dong:

Pn = P.sina

Vi a nhd ■=> sin a « a Ta cd:

Pn = P aTuong tu cong thuc cua dinh luat Hook

Fdh = - K.x

Pn goi la lire chuan dan hoi

5.1.2 Phirong trinh dao dong dieu hoa

Trong 2 vf du tren neu khdng cd ma sat

va goc lech a ve 2 phfa doi vdi

hien trong mot thdi gian dai.

Dao dong nhu vay ta goi la dao dong dieu hoa Trong dao dong nay do lech cuc dai (hay bien do) khong doi theo thdi gian Nguoc lai, neu co ma sat cua moi trudng, do lech cue dai (hay bien do) se giam d£n, sau mot thdi gian se ngurng chuyen dong Ta goi la dao dong tat dan.

* Thiet lap phuong trinh

Ta lay vf du ve dao dong cua lo xo de thiet lap phuong trinh dao dong dieu hoa

Luc dan hdi gay ra gia toe cho chuyen dong dao dong Theo dinh luat Hooke:

Theo dinh luat Niuton II:

F = m.ad2S d2x

a = —- = —- dt2 dt2

v d 2x -> F = m.——

dt2

Tur (1) va (2): -K.x = m.x

m x + K.x = 0 Day la phuong trinh vi phan cap hai cd ve phai bang 0

Vi m > 0 nen ta cd the’ chia cho m:

x + — x = 0 m

(K, m > 0, K: he sd dan hoi cua lo xo)

Dat — = o r, ta cd: x + co2.x = 0

m

Giai ra ta duoc 2 nghiem

x, = a.cos (co.t + a) x2 = a.sin(co.t + a')trong do: a a a ' la nhung h in g so phu thuoc vao di j u d ien ban d i n cua bai toan.

x: ly do dao dong

a: ly do dao dong cuc dai hay bien d6 cua dao dong,

a = xmax ting voi cos (co.t + a) = ±1

( co.t + a ): la mot goc, goi la pha cua dao dong

co: tan so goc (toe do goc cua vecto bien do dao dong)

co = •— ; co = —

m T

t: Thai gian dao dong

T: Chu ky dao dong La thoi gian de dao dong thuc hien mot dao dong toan phan

a : la goc, la pha dau cua dao dong, umg v6i t = 0

Do ngoai lire tac dung, cac phan tu

nay rdi khoi vi tri can bang va bat dau dao

dong Cac dao dong nay do cac lien ket

phan tir, duoc lan truyen sang cac phan tir

xung quanh Nhu vay khi co song truyen

qua trong moi trudng cac vimg dan, nen

lien tiep tuan hoan trong khong gian va

theo thoi gian (hinh 1.12)

Gia sir vi mot ly do gi day, mot phan tir O cua moi truong bi lech khoi vi tri can bang Phan tu A se tac dung len O mot lire keo, phan tir B se tac dung len Omot luc day O se dich chuyen sang trai Luc toi trang thai (c) thi A lai day O va

B lai keo Ket qua phan tir O se thuc hien duoc mot dao dong toan phan Do dac diem cua moi trudng dan hoi, phan tir O cung tac dung vao phan tir A va B dao dong nay se lan truyen trong moi truong tao thanh song co hoc O goi la nguon phat song

6.3 Cac loai song

Khi truyen trong moi trucmg dong nh<ft va dang hudng, dao dong se lan truyen ve moi phfa vdi van toe nhu nhau De don gian ta chon mot phuong nao

do, goi la phuong truyen song

Neu phuong truyen song ma cac ph&n tu cua moi trudng dao dong vuong goc vdi phuong truyen song, goi la song ngang Vf du : song anh sang, song tren mat nude

Ne'u cac ph£n tu cua mdi trudng dao dong song song vdi phuong truyen song thi dd la song doc Vf du: song di chuyen cua lo xo khi co dan, song am

Cac mdi trudng chat ran ton tai dong thdi ca song doc va song ngang Mdi trudng long va khf truyen duoc song doc

Phucmg dao dong Phuong dao dong Phuong truyen

La khoang cach ngan nhat giua cac

phan tir cua mdi trudng dao dong dong pha

hoac la quang dudng song truyen di duoc

trong mot chu ki

VD: Khoang cach tir E (hinh 1.14)

Don vi do: m, cm, ^im, nm

6.4.2 Chu ky dao dong (T)

Thdi gian can thiet de mot diem cua mdi trudng thuc hien mot dao dong toan phan

6.4.3 Van toe truyen song (c)

Hinh 1.14

Quang dudng truyen song truyen duoc trong mot don vi thdi gian Don

Tan so goc bang tan so quay nhan vdi 2 n

Don vj do: rad/s

6.4.6 Phitomg trinh song

Xet trudng hop budc song doc Gia sir 2 phan tu cua mdi trudng 1 va 2 cach nhau mot khoang dy theo phuong truyen song y (hinh 1.15) khi chung d vi tri can bang

Do bi kfch dong cac phan tu 1 va 2 lech khoi vi tri can bang mot khoang x

va x+dx Khoang cach giua hai phan tu bay gid la (dx + dy)

Khi dd van toe dao dong cua phan tu trong mdi trudng la

7 S o n g d m vd sieu dm

7.1 Dinh nghla

Song am va sieu am la nhung dao dong truyen trong cac moi trudng vat cha't dan h6i (ran, long, khf) dudi dang song doc Song am khdng truyen trong chan khdng

7.2 Su khac nhau giufa song am va sieu am

Tieu chu^n dd phan biet song am va sieu am la tan so

Vdi tan sd 109Hz -» 1013 Hz: sieu sieu am 1013Hz la gidi han tren vi budc song d tan so nay vao khoang chieu dai khoang cach giua cac phan tu chat ran.Sieu am cd mang nang luong Nang luong sieu am, chfnh la dong nang dao dong va the nang dan hoi cua cac phan tir mdi trudng

- Cudng do sieu am (I): duoc tfnh la nang luong sieu am truyen qua mot don

vi dien tfch dat thang goc vdi phuong truyen song trong mot don vi thdi gian.Don vi do cua cudng do sieu am la: W/m2

Van toe truyen am phu thuoc vao mat do mdi trudng va tfnh chat dan hoi cua mdi trudng Trong qua trinh truyen am , cudng do am cang di xa nguon cang giam mau vi cac ly do sau:

- Cac phan tir cua mdi trudng dao dong, ma sat vdi mdi trudng do dd cd mot phan nang luong dao dong phai dung de thang ma sat va bien thanh nhiet nang lam nong mdi trudng

- A m trong khi truyen gap mat phan cach 2 mdi trudng cung phan xa, khuc

xa, nhidu xa tuong tu anh sang Chfnh hien tuong phan xa lam giam rat nhieu cudng do song am di tdi

7.3 Nguon phat sieu am

Hinh 1.16

Sieu am phat ra ttr cac nguon thien nhien thudng la

t&n so thap, nang luong nho va phan tan Trong ky thuat (b) Y //////7 7 /.

dung cac may phat dac biet, bien nang luong dien thanh

nang luong sieu am Sieu am phat ra co tan so 6n dinh, co

the thay ddi dupe theo y muon Nang luong ldn, tap trung

va thay doi duoc

Muon thu sieu am, ngudi ta dung bo phan cam bien Bien d6i tin hieu sieu

am thanh tin hieu dien Tin hieu dien qua cac mach khuech dai dac biet va duoc ghi giCr bang man hinh huynh quang hay phim anh

Nguon phat sieu am dua tren hien tuong dien ap nghich: mot ban thach anh duoc cat song song vdi true luc giac va vuong goc vdi true quang tao thanh ban thach anh ap dien Ngudi ta ma hai mat de tao thanh mot tu dien, hoac kep no vao giira 2 ban cua mot tu dien phang Khi tac dung mot hieu dien the U giua hai ban

tu dien, ban thach anh bi tac dung mot luc nen (hay gian tuy dau cua dien tfch) lam bien thien chieu dai cua ban Thay U bang mot nguon dien xoay chieu tan so

V, ban thach anh bi dao dong cudng btic phat ra sieu am 6 day nang luong dien

da bien thanh nang luong co hoc dudi dang sieu am lan truyen vao mdi trudng xung quanh vdi tan sd cd the den 50MHz

Nguon phat sieu am dua tren hien tuong tti giao: Mot thanh sat tti khi bj tti hoa thi do dai cua no se ngan di chtit it Dat mot thanh sat tti vao trong long mot cuon day da noi vdi mot nguon dien xoay chieu t£n so' cao Tti trudng trong long cuon day bien thien vdi tan so bang tan so cua ddng dien xoay chieu Do hien tuong tti giao, thanh sat tti cd chieu dai dao dong vdi tan sd nhu tan so cua nguon dien, trd thanh ngudn phat sieu am khi tan so > 20.000Hz Nguon phat sieu am

loai nay cd the dat tdi tan so 109 Hz

7.4 Su hap thu song am va sieu am

Khi truyen qua mdi trudng, nang lupng sieu am bi giam di do hien tupng hap thu Hien tupng hap thu tuan theo quy luat:

I = I 0.e

trong do x : be day ldp chat

I : cudng do sieu am truyen qua

I0 : cudng do sieu am tdi

a : he so hap thu

-He so a ty le vdi binh phuong t<fo so co, ty le nghjch vdi mat do mdi trudng

va lap phuong van toe Tuc la a phu thuoc vao tfnh cha't cua mdi trudng

Don vi do cua a:nepe/cm

Ngoai ra ta con do he sd ha'p thu bang dexiben (dB/cm)

Vf du: a mau = 0.09dB/cm; a than=2dB/cm; a xuong=8dB/cm

Cac bo phan khac nhau cua co thd cd trd am khac nhau se ha'p thu song sieu

am khac nhau Tren hinh anh ta thay do dam nhat khac nhau

Trong dd trd am cua mdi trudng dinh nghla:

Z = D.vvdi D : khoi lupng rieng ciia mdi trudng

v : van td'c truyen song am

Sieu am bi hap thu nhieu trong khdng khf Khi dieu trj hoac chuan doan ngudi ta de dau sieu am sat da va tren da boi mot ldp parafin hoac ngam dau sieu

am lan bo phan can dieu tri vao nude

7.5 Su truyen am qua mat phan cach giura hai moi trudng

Cung nhu moi qua trinh song, song am khi truyen qua mat phan cach hai mdi trudng cung mot phdn bi phan xa lai, mot phan truyen qua Khi hai mdi trudng cd trd am khac nhau thi su phan xa cang manh

He so phan xa dupe dinh nghla la ty so giura cudng do cua song phan xa va cudng do cua song tdi

R - ’ <

T

vdi If: cudng do cua song phan xa

Ii: cudng do cua song tdi

Su phu thuoc cua he so phan xa vao tfnh cha't cua cap mdi trudng (1) va (2) nhu sau:

Khi truyen song am vao mSu vat ta phai boi mot ldp md co"tra am trung gian giua tra am cua khong khi va vat kiem tra.

7.6 Ung dung cua sieu am trong y hoc

7.6.1 Lfng dung cua sieu am trong dieu tri

Do co tan so rat 1dm (buoc song be) nen khi lan truyen ft bi nhi6u xa, truyentuang doi thing va ta co the lam chum sieu am hoi tu len cac vi trf c&n thiet bang cac dang dac biet cua d£u phat sieu am Khi truyen qua moi trucmg, do moi trudng cd ma sat va hap thu nhiet nen cudng do cua sieu am giam theo quy luat:

I = I0e'axtrong dd, I0 la cudng do luc bat dau vao mdi trudng, I la cudng do luc ra khoi mdi

trudng, neu mdi trudng cd chieu day x, con a la he sd hap thu cua moi trudng, e

la ca so logarit tu nhien bang 2,71828.

Qua thuc nghiem ngudi ta thay a ty le vdi binh phuong tan sd, ty le nghich

vdi mat do mdi trudng nen sieu am bi hap thu nhieu trong khdng khf, dong thdi

do mat phan gidi cua mdi trudng nao dd vdi mdi trudng khdng khf phan xa nhieu song sieu am nen khi dieu tri hoac chan doan dung song sieu am ngudi ta de dau phat sieu am sat da va d tren da phai boi mot ldp dau, hoac ngam ca dau phat sieu

am l&n bo phan can dieu tri vao nude Su hap thu nang luong sieu am cua mdi trudng the hien bang su tang nhiet do Mire tang cua nhiet do phu thuoc vao ty le cua mdi trudng, nhiet do mdi trudng ben ngoai Lai dung dac tfnh nay, ngudi ta dung sieu am lam dan cac mach mau ngoai bien de tang cudng tfnh tham thaucua te bao bieu bi, do dd cd tac dung chong viem

Luc qua mat phan gidi giua hai mdi trudng, sieu am tao nen sue ep vao mat nay Sire ep ty le thuan vdi luong sieu am di tdi Vi vay, khi nhung dau phat sieu

am vao nude, sieu am cd the lam nude ban len cao tdi vai cm Nhd cd sue ep nay cac to chirc nong cua co the bi chan dong, dd la mot cach xoa bop te bao, mot tac dung rat quy trong dieu tri chung viem te bao

Sieu am la song doc, khi truyen no lam bien dang nen dan mdi trudng: cd vi tri mat do mdi trudng ldn vi cac phan tu bi ep lai; cd vi trf mat do mdi trudng nho vi cac phan tir dan cach xa nhau Khi cong suat may ldn, tai noi mat do mdi trudng ldn, ap suat nen cd the tdi hang van atmotphe; con tai noi mat do nhd cac phan tir

bi dan ra vdi “ap suat dan” cd tri sd tuong tu Luc dan cac phan tir nhu vay dii ldn

de thang luc hut giua cac phan tir, mdi trudng khi ay tu durt va tao thanh Id vi mo Neu qua trinh nay xay ra trong nude thi nhung Id nay se bi hoi nude hoac cac khf hoa tan chiem chd Hien tuang tao thanh Id ddng vai trd quan trong, gdn lien cac hien tuang dien, dien hoa duoc ap dung trong nhieu nganh Do hien tucmg tao

thanh 16, cac te bao song dac biet la hong c£u va trich trung co the bi vd Trong y hoc dung hien tuong tao thanh 16 dd chong dong mau, diet trung.

V'l sieu am truyen qua dupe cac mo trong co the, lam cho cac te bao b chan dong, co the ha'p thu cua sieu am mot nhiet lupng dang ke nen ngudi ta dung no

de chua mot so benh, chlng nhung 6 ngoai da ma con ca 6 trong sau

Nhung benh chua bang sieu am hieu qua nhat la cac chting dau cac day th£n kinh, dac biet la day than kinh toa, thap khdp

Luu y khong dung sieu am dieu tri cho nhung ngu6i co thai, dang bi lao, bi sot va tre em

Gan day, ngudi ta da bat dau dung nhung song sieu am co cuong do ldn (1,4x107 W/m2) de pha huy cac to chtic benh trong sau nhu soi than, u tuyen, v.v

Mo ra mot trien vong rat huu fch trong y hoc

7.6.2 Ifng dung sieu dm vao chan doan

Sieu am dupe ting dung vao ch&i doan benh la nh6 cac dac diem sau:

- Co the tao ra chum sieu am song song hoac hoi tu vao mot diem nho, hoac phan ky

- Chum sieu am song song truyen qua moi trudng, bi moi trudng hap thu, cu6ng do giam theo quy luat:

7.6.3 Chan doan bang hinh anh sieu dm

So do nguyen ly cach tao hinh anh sieu am dd chan doan benh nhu sau:

* Hinh anh tao nen nhd chum sieu dm truyen qua tucmg tu nhu tao anh X

quang trong chan doan (hinh 1.17).

Hinh 1.17

1 Dau va may phat sieu am

2 Doi tupng khao sat

3 Dau va may thu sieu am da truyen qua doi tupng

4 Bo bien doi tin hieu sieu am thanh hinh anh

* Hinh anh tao nen nhd chum sieu dm phan xa tif cac mat phan giiri doi

tuong khao sat vcri moi trKcmg xung quanh (hinh 1.18).

1- May phat va dau phat - thu sieu am

2- Doi tupng khao sat

3- Bo bien doi tin hieu sieu am thanh hinh anh va ghi lai

%

8 H ieu ting D o p p le r vd ting dun g

8.1 Hieu ung Doppler la gi?

Khi nguon phat va nguon thu song am dting yen tuong doi voi nhau thi khi nguon phat phat ra tan so f, nguon thu nhan dupe song am cung voi tan so f Nhung khi nguon phat va nguon thu chuyen dong tuong doi voi nhau thi tan so phat va thu se khac nhau Ta thay ro dieu do

Khi dung yen (nguon thu) ta nghe thay tieng o to lai gan voi tan so cao dan len va khi o to di xa thi tan so lai thap dan di (nghe nhu tram xuong)

Vay hieu ung Doppler la hieu ung lech tan so giua nguon phat va nguon thu thu dupe khi chung chuyen dong tuong doi voi nhau

8.2 Giai thich

Goi v: van toe chuyen dong cua nguon phat f0 : tan so cua nguon phat f : tan

so cua nguon thu

Tai thoi diem t = 1 g iay tir luc phat, may phat phat ra dao dong thu f0 Khi do dao dong dau tien cach may phat mot doan la (c-v)

trong do, c la van toe truyen song am.

f = - = —— {

A c - v 0Tijr day ta suy ra do dich tan so:

Af = 0 khi v = 0: nguon phat va nguon thu dting yen (f = f0)

Af > 0 khi v > 0: nguon phat den gan nguon thu T£n so thu ldn hon tan so phat (f > f0 )

Af < 0 khi v < 0: Nguon phat di xa nguon thu Tan so thu be hon tan so phat (f < f0)

8.3 Ung dung

Hieu ung Doppler dung de xac dinh toe do chuyen dong cua cac vat khi xac dinh dupe do dich chuyen tan so A f Nguon phat dung yen, phat ra tan so f0, gap doi tupng chuyen dong phan xa lai vdi tan so f

Luc song am quay ve nguon phat lai dong vai trd may thu Trong may sieu

am Doppler ngudi ta dung d£u dd (phat - thu)

Trong thuc te, ngudi ta dung de do toe do tau hoa, o to dang chay

Trong Y hoc, do su co bop cua co tim, do toe do di chuyen cua hong ciu, luu

lupng mau, chuan doan cac benh ve tuln hoan mau

Chuong 2

Dong lire hoc la phan co hoc nghien cun moi lien he giura chuyen dong co hoc va tuong tac giua cac vat

Vf du: Mot ngudi dang dung yen tren con tau chuyen dong thang deu Khi

dd ngudi cung chuyen dong vdi van toe v = const Bdng nhien tau dung lai, do quan tfnh ngudi van tiep tuc chuyen dong, nen ngudi bi nga ve phfa d trudc Tuong tu ngudi bi nga ve phfa sau khi tau dang dung yen bat dau chuyen dong

Phat bieu: Gia toe ma chat diem thu duac ty le thuan vai luc tac dung len

chat diem va ty le nghich vai khoi luong cua chat diem.

36

F = m a (2)Phuang trinh (2) goi la phuong trinh co ban cua dinh luat Niuton II Tir phuong trinh tren, ta co the xac dinh dupe gia toe cua mot chat diem khi bie t cac lire tac dung Tir do neu biet vi trf, van toe ban dau, no cho phep xac dinh trang thai chuyen dong cua cha't diem.

2.2 Bieu thurc tong quat cua djnh luat Niuton II

Tir phuang trinh ca ban:

F= ^ dtDay la bieu thuc tong quat cua dinh luat Niuton II

Phat bieu: Toe do bien thien ddng luong cua chat diem theo thdi gian bang

luc tong hop tac dung len no

3 D in h lu a t N iu to n thuf ba■ ■

Dinh luat Niuton thu III xet mot he vat tuong tac vdi nhau

Dinh luat phat bieu: Khi chat diem A tac dung len chat diem B mot luc F, thi

nguoc lai chat diem B se tac dung len chat diem A mot luc F, co cung phuong, nguoc chieu voi F, va cd do Ion bang do Ion cua F, (hai luc Fj va F2 true doi nhau)

Mot trong hai lire duoc goi la luc tac dung, luc con lai goi la phan lire.

Chu y: Hai lire F, va F2 co diem dat khac nhau ( F, dat len B va F2 dat len A)

Chung khong triet tieu nhau

Vf du: Ngudi boi dung tay va chan d^y nude ve phfa sau, phan luc cua nude

se day ngudi do ve phfa 6 trudc

Suy rong ra neu co mot he gom nhieu cha't didm, chi tac dung vdi nhau ma khong tac dung vdi ben ngoai thi tong cac luc cua he (noi luc) bang khdng

4 D jn h lu a t b a o to a n d d n g lu o n g tro n g co he k in

Dong lupng la mot dai lupng dac trung cho chuyen dong ve mat dong lire

Co he km la mot he co hoc gom n chat diem tuong tac vdi nhau, nhung khdng tuong tac vdi mdi trudng ngoai

Ta hay xet mot co he km gom 3 chat diem, mdi chat diem se chiu tac dung cua hai chat diem kia

dtTheo dinh luat Niuton III