Quiz 2

Physics 7C Fa 2008Lecture 3: Waves

Quiz 2

Understanding Interference

Reviewing the Basics

Constructive Interference: total phase equivalent

Destructive Interference: total phase separated by half cycle

Note: these waves have identical periods and wavelengths, but that is not always the case!

Interference for differing frequencies: Beats.

1 2 3 4 5

What type of interference occurs at each point?

Interference for differing frequencies: Beats

1 2 3 4 5

Interference for differing frequencies: Beats

1 2 3 4 5

The carrier frequency

The beat frequency

Interference for differing frequencies: Beats

What’s happening at the gold arrows? What’s happening at the black arrows?

Checking 1D interference

Two speakers are wired into different function generators with slightly different frequencies. They have identical wiring, and are placed face-to-face. What type of interference results? A) Constructive B) Destructive C) Partial D) Depends on what time you choose E) Insufficient information to decide

Checking 1D interference

Two speakers are wired into different function generators with slightly different frequencies. They have identical wiring, and are placed face-to-face. What type of interference results? A) Constructive B) Destructive C) Partial D) Depends on what time you choose E) Insufficient information to decide

Introducing 2D Interference:The Ripple Tank

Try to spot… Places that are very deep Places that are very shallow Places that are “normal” depth Places two crest combine Places two troughs combine Places a crest meets a trough

d

Two slits create two overlapping wave fronts

CrestTrough

2D Interference

Conceptually, nothing new! Temporal contribution if frequencies differ

Typically same medium & same source Pathlength difference contribution

How far has each wave traveled? Phase constant contribution

By how much do phases differ? (Typically same phase difference, though not always!)

Summary: Just like 1D interference, but typically you only need to think about pathlength difference!

d

Two slits create two overlapping wave fronts

CrestTrough

d

Two slits create two overlapping wave fronts

CrestTrough

What type of interference occurs at the marked spot?

a) Constructiveb) Destructivec) Partiald) Time-dependent

d

Two slits create two overlapping wave fronts

CrestTrough

Why?

a) x=0b) x=/2c) xd) None of the above

x2

Two slits create two overlapping wave fronts

CrestTrough

Why?

a) x=0b) x=/2c) xd) None of the above

x1

x1=x2 so x=0!

d

Two slits create two overlapping wave fronts

CrestTrough

What type of interference occurs at the marked spot?

a) Constructiveb) Destructivec) Partiald) Time-dependent

d

Two slits create two overlapping wave fronts

CrestTrough

Why?

a) x=0b) x=/2c) xd) None of the above

d

Two slits create two overlapping wave fronts

CrestTrough

What type of interference occurs at the marked spot?

a) Constructiveb) Destructivec) Partiald) Time-dependent

d

Two slits create two overlapping wave fronts

CrestTrough

Why?

a) x=0b) x=/2c) xd) None of the above

d

Two slits create two overlapping wave fronts

CrestTrough

Why?

a) x=0b) x=/2c) xd) None of the above

x2x1

x1>x2 now…x1=2x2=1.5

Another interesting phenomenon

What are you seeing? Look carefully A) Constructive Interference Only B) Destructive Interference Only C) Beats D) Pathlength-dependent Interference: both

constructive & destructive depending on position E) Partial Interference

What is x?

a

b

d

c

e

What is x?

a

b

d

c

e

Laser Interference

In DL you will use a shortcut to calculate pathlength difference: d sin = x

Review: 2D Interference Why calculate d sin ?

• d sin estimates the pathlength difference (x). That is, how much further does the wave travel from slit 1 compared to from slit 2.

• When the wave splits through the slits, frequency and don’t change, so only pathlength matters!

• Constructive interference occurs if one wave travels a whole number of wavelengths further than the other

• if x=n=0 or 2, 4, 6, etc.• Destructive interference occurs if one wave travels a half

number of wavelengths further than the other • if x=(n/2)(for n odd)= or 3, 5, 7, etc.

• …so d sin = m determines type: constructive, destructive, or partial

Standing Waves

Fundamental

Standing Waves

2nd Harmonic

3rd Harmonic

N = “node”A = “antinode”

Standing Waves

2nd Harmonic

3rd Harmonic

• What type of interference occurs at a node?

a) Constructive

b) Destructive

c) Time-dependent

d) Depends which node

Standing Waves

2nd Harmonic

3rd Harmonic

• What type of interference occurs at an antinode?

a) Constructive

b) Destructive

c) Time-dependentd) Depends which

antinode

Standing Waves

2nd Harmonic

3rd Harmonic

• What type of interference occurs at an antinode?

a) Constructive

b) Destructive

c) Time-dependentd) Depends which

antinode

Superposition of 2 traveling harmonic waves

The period and wavelength are exactly the same. One wave travels to the right, one to the left.

Checking 1D interference

Two speakers are connected to the same function generator with reversed wiring. One speaker is placed a half wavelength in front. What type of interference results? A) Constructive B) Destructive C) Partial D) Depends on what time you choose E) Insufficient information to decide

Checking 1D interference

Two speakers are wired to the same function generator. The phase constants differ by /2. One speaker is placed a quarter wavelength in front. What type of interference results? A) Constructive B) Destructive C) Partial D) Depends on what time you choose E) Insufficient information to decide