Interference (I) Combination of two or more waves to form a - - PowerPoint PPT Presentation

Interference (I)

Conditions for interference:

• Coherence: the sources must maintain a constant

phase with respect to each other

• Monochromaticity: the sources consist of waves of a

singe wavelength Combination of two or more waves to form a composite wave. Use Superposition Principle u(P,t)=u1(P,t)+u2(P,t) Waves can add constructively or destructively

• Interference. Phase shift.

What can introduce a phase shift?

• Waves from different, out of phase sources
• Sources in phase, but travel different

distances

• Double slit,
• Diffraction
• Thin films
• Waves traveling in opposite direction

Standing waves (I)

λn=2L/n; fn=c/ λn=n f0; with f0=c/(2L) Fundamental f0, n-th harmonic fn=n f0

Standing waves(II)

Wave groups (I)

• A harmonic wave does not carry information (only a

number f or λ)

• Two harmonic waves carry two numbers and so on

Wave groups (II)

∫

∆ + ∆ −

+ − =

2 / 2 /

d )) ( ) ( cos( ) ( ) , (

k k k k

k k t k kx k a t x u ϕ ω

) cos( ) ( ) , ( t x k t v x A t x u

g

ω − − =

⇒

• For larger information we need an enormous

amount of harmonic waves in a small interval in wave number, wavelength or frequency: [k0-∆k/2, k0 -∆k/2]

• r [f0-∆f/2, f0 -∆f/2]
• A(x-vgt) carries all the information

Wave groups (III)

• Phase velocity v=v(k)
• Dispersion ω=ω(k)
• Group velocity vg≠v0
• Band width ∆f<<f0

Wave modulated in amplitude A(x-vgt) Modulating wave cos(k0x-ω0t) carrier signal

d d

k g

k ω v       =