(S.h.m & waves).(reflection & refrection).(interferenc) prove s & important rules

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All Physics Proves & Summary Of Rules Edited By Eng : Mustafa Kashif

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Transcript of (S.h.m & waves).(reflection & refrection).(interferenc) prove s & important rules

Page 1: (S.h.m & waves).(reflection & refrection).(interferenc)  prove s & important rules

All Physics Proves & Summary Of Rules

Edited By Eng : Mustafa Kashif

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S.H.M & WaveS

1-prove that, the Total energy of particle is moving in a simple harmonic motion is a Constant….

The differential equation of any particle moving in S.H.M is

Y=A sin (wt+α) y’=A w cos(wt+α)y’’=Aw2 sin(wt+α)y’’=-w2y

K.E=0.5 m y’2=0.5 m w2 A2 cos2(wt+α)1

P.E= =

P.E= =0.5 m w2 y2 P.E= 0.5 m w2 A2 sin2 (wt+ α)

ToTal Energy=Etot= K.E+P.E

E=0.5 m w2 A2[cos2(wt+ α)+sin2(wt+ α)] = 0.5 m w2 A2 Constant

/ / 2y = -w y

y

0- fdy ''my dy

y

0-

y 2

0+ mw ydy

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S.H.M & Waves

Block of mass m attached to a spring the block free to move on horizontal, frictionless surface .if the spring constant is K …Prove that the Block Moves in S.H.M and Determined Angle speed ..

Spring Force F= KX .The eqn of motion MX’’=-KX X’’= -K/M *X The deffrential eq of S.H.M is X’’=-W2X The Block Moves in S.H.M with angular speed W W2=K/MW=(K/M)0.5 T=2Л/W =2Л(K/M)0.5 To Prove that the particle moves in S.H.M ..Prove the realtion between the

angular speed and the distanceAcceleration = -W2(Displacement)

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S.H.M & WaveS

Summary of chapter 1 rules:-

1-General eq of simple Harmonic motion X=A cos(wt+α)

Y=A Sin(wt+α)

W=ө/t =2Л/T

Total energy = K.E+P.E =0.5m W2A2

V=y’ , a =Y’’=-W2 Y

------------------------------------------------------------------------

When Summing 2 or more S.H.M needS some Rules

N N

2 2t i i i i

i=1 i=1

A = [ A Cosθ ] +[ A Sinθ ]

N

i ii=1

t N

i ii=1

A sinθtan(θ ) =

A cosθ

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S.H.M & WaveS

When Summing (n) of S.H.M we use some of rules:-

t 1

αα = (N -1) +α

2

t t tY = A sin(wt +α )

t

nαsin( )

2A =α

sin( )2

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S.H.M & WaveS

To Prove that the wave is Traveling wave Prove that Y is

F(x+vt) or F(x-vt).

-General Eqn of Harmonic wave : Y(x,t) = A Sin(wt-kx+α)

W=2ЛF ,,,, (K) wave num =2Л/ג

(Intensity)

Energy EI = =

Area* time S*t

2 2tautspring

1Power = μw A v

2

2 21Power = μρSw A v

2

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S.H.M & WaveS

Standing waves 1-Position of nodes amplitude=0

x=0.5 m ג

2- position of AntinodeS

x=0.25 (2m+1)ג- To Solve Standing waveS question:-- 1-put the 2 eqn in the form of Y=Asin( ) - 2- sum the 2 eqn with Rule- A[sin(a)+Sin(b)]=A[2cos0.5(a-b)Sin0.5(a+b)]- 3-the term tha don’t have t is the amlitude for standing

wave and be the fn of X only

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4-let the amlitude =0 & amplitude =2A

For Getting Antinodes and nodes placeS

5- draw the standing wave form

6-Put Y axsis Perpendicular on X axsis and in sutable place depen on the places of nodes and antinodes .

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S.H.M & WaveS

Doppler effectThe movement in same direction:

The movement in opposite direction

rr s

s

v + vf = f

v + v

rr s

s

v + vf = f

v v

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Reflection & Refraction

Prove(1) Define the Critical angle өc is and Polarized angle өp and drive the relation between them

The critical angle өc is the incident angle over which there is total internal reflection (no transmission to the second medium )

If n1>n2

n =n2/n1<1

As өi increase , өt increase

If өt =90 өi = өc

n1sin өc =n2 sin 90

Sin өc = n2/n1=n

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Reflection & Refraction

Prove(2)-Derive the equation for the amplitude reflection and transmitted coefficient in TM mode (rtanseverse magnetic mode parallel electric mode).

From maxwell’s eqn

Applying continuity of B-compnents

Bi+Br=Bt

Applying Conuity of E-components

EiCos(өi)-ErCos (өi)=EtCos (өt) 2

Using E/B=v=c/n

B=n*E/c substitute in (1)

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Reflection & Refraction

1

2 t1 i 2 r

2i r t

n En E n E+ =

c c cn

E +E = En

2

1

nlet = n

n

i r tE +E = nE

Substitute from 3 in 2

3

i i r i i r t

i i t r i t

i trp

i i t

1E cosθ -E cosθ = (E +E )cosθ

nE [nCosθ - cosθ ] = E [ncosθ + cosθ ]

ncosθ - cosθEr = =

E ncosθ + cosθ

Divide the eqn 3 by Ei

tr

i i

pp

EE1+ = n

E E

1+r= t

n

tp

i

Et =

E

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Reflection & Refraction

Prove (3)Derive the equations for the amplitude reflection and transmitted coefficent in T E mode (normal elctric field Mode)

-applying continuity of E- components

Ei+Er=Et 1

Applying continuity of B-components

-BiCosөi+Brcosөi=-Btcosөt 2

By using E/B=v=c/n

B=nE/c substitute in 2

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Reflection & Refraction

2 t1 i 1 ri i t

2i i r i t t

1

i i r i t t

n E-n E n Ecosθ + cosθ = - cosθ

c c cn

-E cosθ +E cosθ = - E cosθn

-E cosθ +E cosθ = -nE cosθ 3

tr

i i

tn n

i

EE1+ =

E E

E1+r = t =

E

Substitute from 1 in 3

Dividing eqn 1 By Ei

i i r i i r t

i i r i i r t

i i t r i t

i trn TE

i i t

-E cosθ +E cosθ = -n[E +E ]cosθ

X(-1)

E cosθ -E cosθ = n[E +E ]cosθ

E [cosθ -ncosθ ] = E [cosθ +ncosθ ]

[cosθ -ncosθ ]E= r r =

E [cosθ +ncosθ ]

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Reflection & Refraction

Prove(4) Draw the relation between amplitude reflection coefficient and incident angle for both external and internal reflection.

For external reflection

At өi=0 normal incdence

Өt=0 from snell’s law

+ve value

i tn

i t

[cosθ -ncosθ ]r =

[cosθ +ncosθ ] n

1-nr =

1+n

i trp

i i t

ncosθ - cosθEr = =

E ncosθ + cosθ

p

n -1r =

n +1

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Reflection & Refraction

At өi=90

rp =-1

rn =-1

At ө= өp

rp=0

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Reflection & Refraction

For Internal reflection

N=n2/n1<1

At ө =0 өt=0

At өt=90

өi= өc

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Reflection & Refraction

Important RuleSn1=c/v1n2=c/v2n=n2/n1Өi= өrSnell law- n1sinөi=n2sinөt_____________________External reflectionn=n2/n1=nH/nL>1The Beam tranmitted near from the verticalөt> өin2>n1

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Reflection & Refraction

Internal reflection

Өt> өi

n1>n2

n<1

When өt=90 өi is called ө(c) crtical angle

The beam transmitted far from vertical

Є= Є(r)* Єo

Intensity=0.5 Єo n c Eo2

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Reflection & Refraction

In Normal mode (TEM) in Parallel Mode(TMM)

i trn TE

i i t

[cosθ -ncosθ ]E= r r =

E [cosθ +ncosθ ]

tr

i i

tn n

i

EE1+ =

E E

E1+r = t =

E

i trp

i i t

ncosθ - cosθEr = =

E ncosθ + cosθ

pp

1+ r= t

n

tp

i

Et =

E

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Interference

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