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

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Adding phasors Two phasors, initially φ out of phase, and after rotating through θ = ωt

θ

φ

time=0, θ= 0

PLUS

θ

Later time, phase change = θ

φ

θ

Resultant - unit initial amplitudes

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Addition of N = 50

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vectors with relative phase Ď&#x2020; = 1

50

50

40

40

30

30

20

20

10

50

40

30

Addition of N = 50

50

40

30

20

10

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0

10

20

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vectors with 10 relative phase Ď&#x2020; = 2

20

50

50

deg Addition of N = 50

vectors with relative phase Ď&#x2020; = 10

50 20

50

40 30

40

30 40

30

20 50

20

10

10

10

deg

0

10

20

30

40

50

50

40

30

20

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40

30

20

10

0

10

20

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10 20 30 40 50

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20

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vectors with relative phase Ď&#x2020; = 10

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500 400 300 200 100

500

400

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0

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Two equal-amplitude sinusoids combine to give a resultant which is a product of a carrier and an envelope. The frequencies of these are the half-sum and half-difference of the original frequencies.

The beat frequency, the frequency at which the amplitude varies, is the difference between the original frequencies.

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2

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5

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The beat frequency, the frequency at which the amplitude varies, is the difference between the original frequencies.

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