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