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Chapter 7 The superposition of waves November 10

Addition of waves of the same frequency Introduct

ion Principle of superposition the total

disturbance at any point of the medium is the

algebraic sum of the constituent individual waves.

7.1 The addition of waves of the same

frequency I) Algebraic method

E0

y

a

x

Phase difference

If the two disturbances are from the same source

but travel different routes

Terms coherent light (e1-e2 constant),

incoherent light constructive interference (d

0, 2p, ...), destructive interference (d p,

3p, ...). A special (simple) case

Superposition of many waves

The interference of coherent waves only

redistributes the energy in space, it cannot

change the total amount of energy.

II) Complex method

III) Phasor method

7.1.4 Standing waves

Two harmonic waves of the same frequency

propagating in opposite directions

Partial standing and partial traveling waves

Question What is the speed of a partial standing

wave?

Read Ch7 1 Homework Ch7 (1-14)

2,6,9,13,14 Due November 21

November 12 Beats and group velocity 7.2 The

addition of waves of different frequency Addition

of two waves of close frequency

Define average w, average k, modulation w,

modulation k as

Carrier

Envelope

Beat frequency

When two waves with close frequency but different

amplitude overlap, they produce beats with less

contrast.

Group velocity

Phase velocity of carrier wave

Group velocity the velocity at which the

modulation envelope advances.

when Dw is small,

In terms of ,

In general, for a laser pulse

Read Ch7 2 Homework Ch7 (15-31)

17(Optional),19,21,23,25,27,30(Optional) Due

November 21

November 14 Anharmonic periodic waves 7.3

Anharmonic periodic waves Goal Resolving a real

wave into component sine waves finding the

frequency, amplitude, and phase. Fouriers

theorem Any function having a spatial period l

can be synthesized by a sum of harmonic functions

whose wavelengths are integral submultiples of l.

Representing f(x) in the frequency domain

frequency spectrum and phase

Fourier analysis finding A0, Am and

Bm Orthogonality of sinusoidal functions

Symmetry conditions 1) f(-x) f(x), even ,

Fourier series contain only cosine terms. 2)

f(-x) - f(x), odd, Fourier series contain only

sine terms.

Example

Read Ch7 3 Homework Ch7 (32-36) 35,36 Due

November 21

November 17 Nonperiodic waves 7.4 Nonperiodic

waves Transition from periodic to nonperiodic

functions

As l ? ?, Fourier series is replaced by Fourier

integrals

Introducing negative frequency useful for

describing symmetric systems.

Pulses and wave packets Example 1 square pulse

Example 2 cosine wave train

- Frequency bandwidth Dk or Dw
- Product of the widths of the wave packet in

k-space and in x-space - For cosine wave train,
- For square wave,
- Generally, for any pulse .

7.4.3 Coherent length Spectral line A colored

band of the spectral component of

light. Linewidths 1) Nature linewidth (10-9-10-8

s), 2) Doppler linewidth, 3) Collisions

(interruption of wavetrains). Coherent time Dtc

1/Dn Coherent length Dlc c Dtc Example White

light Dl 300 nm, Dn 31014 Hz, Dtc 3 fs,

Dlc 900 nm 1.6 l. He-Ne laser Dl 10-6 nm,

Dlc ? 400 m.

Read Ch7 4 Homework Ch7 (37-)

38,42,44,46 Due December 3

Pulses and wave packets Example 3 Gaussian pulse

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