1b24 waves optics and acoustics lecture 1 of 33 (ucl)

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1B24 Waves Optics and Acoustics Lecture 1 of 33 (UCL)

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Page 1: 1B24 Waves Optics and Acoustics Lecture 1 of 33 (UCL)

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Page 2: 1B24 Waves Optics and Acoustics Lecture 1 of 33 (UCL)

Oscillatory Systems

m

T

θ

l

x

m g

m2t

xd

d

2.. m g.. sin θθ( ).. 0

For small θ,

2tθθd

d

2 g

lθθ.. 0

ωω2 g

l

I

θ

c

I2t

θθd

d

2.. c θθ.. 0

ωω2 c

I

m

k

x

m2t

xd

d

2.. k x.. 0

ωω2 k

m

m

x

TT

2 l

m2t

xd

d

2.. 2 T.. x

l.. 0

ωω2 2 T..

l m..

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Page 3: 1B24 Waves Optics and Acoustics Lecture 1 of 33 (UCL)

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Page 4: 1B24 Waves Optics and Acoustics Lecture 1 of 33 (UCL)

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Page 5: 1B24 Waves Optics and Acoustics Lecture 1 of 33 (UCL)

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Page 6: 1B24 Waves Optics and Acoustics Lecture 1 of 33 (UCL)

2x ρρ l..2t

xd

d

2.. 2 ρρ.. g.. x.. 0

where l is the length ofthe fluid column

ωω2

2g

l..

x

ρ

m

m2t

xd

d

2.. A ρρ.. g.. x.. 0

where A is the cross-sectional area of the tube

ωω2 A ρρ.. g..

m

CL q

L2t

qd

d

2.. q

C0

ωω2 1

L C..

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Page 7: 1B24 Waves Optics and Acoustics Lecture 1 of 33 (UCL)

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