Major Concepts of Physics PHY102 – Lecture #3 12015Syracuse University

Lecture #3Lecture #3How do the waves mix each How do the waves mix each

other up? Interferenceother up? Interference

January 21January 21stst, 2015, 2015Prof. Liviu MovileanuProf. Liviu Movileanu

wwww.physics.syr.edu/MajorConceptsPhysics2015.html lmovilea@syr.edu

Room 211, Physics Bldg., 443-8078Room 211, Physics Bldg., 443-8078

Major Concepts of Physics Major Concepts of Physics PHY102PHY102

Major Concepts of Physics PHY102 – Lecture #3 22015Syracuse University

1. Review the quantitative description of waves1. Review the quantitative description of wavesReview quantitative parameters describing Review quantitative parameters describing

waveswavesReview periodical expressions describing wavesReview periodical expressions describing wavesSimple Harmonic Motion (SHM)Simple Harmonic Motion (SHM)

2. What is the interference?2. What is the interference?Constructive and Destructive Interference Constructive and Destructive Interference

(Hypothesis)(Hypothesis)Young’s double-slit experiment (Experimental Young’s double-slit experiment (Experimental

evidence)evidence)Interference patterns (Interpretation)Interference patterns (Interpretation)

3. Lecture demonstration (double-slit 3. Lecture demonstration (double-slit interference)interference)4. Repeat Sam’s demonstration…another beaker 4. Repeat Sam’s demonstration…another beaker 5. Announcements5. Announcements

Lecture objectivesLecture objectives

Major Concepts of Physics PHY102 – Lecture #3 32015Syracuse University

Quantitative understanding of Quantitative understanding of waves waves

Major Concepts of Physics PHY102 – Lecture #3 42015Syracuse University

 

Periodicity of waves: time and spacePeriodicity of waves: time and space

Major Concepts of Physics PHY102 – Lecture #3 52015Syracuse University

Simple Harmonic Motion (SHM)Simple Harmonic Motion (SHM)

Idea: Any object that is initially displaced slightly from a stable equilibrium point will oscillate about its equilibrium position. It will, in general, experience a restoring force that depends linearly on the displacement x from equilibrium: Hooke's Law:

Fs = - kxx is the displacement, or the distance of the mass from the equilibrium pointand k is a constant that depends on the system under consideration. The equilibrium point is considered at x=0

The units of k are: [k] =

Total energy=Kinetic energy + potential energy

m

N

22

22 mvkxEEE pktot

Major Concepts of Physics PHY102 – Lecture #3 62015Syracuse University

Simple Harmonic Simple Harmonic MotionMotion

Definitions:

•Amplitude (A): The maximum distance that an object moves from its equilibrium position. A simple harmonic oscillator moves back and forth between the two positions of maximum displacement, at x = A and x = - A .

•Period (T): The time that it takes for an oscillator to execute one complete cycle of its motion. If it starts at t = 0 at x = A , then it gets back to x = A after one full period at t = T .

Major Concepts of Physics PHY102 – Lecture #3 72015Syracuse University

Simple Harmonic Simple Harmonic MotionMotion

Definitions:

•Frequency ( f ): The number of cycles (or oscillations) the object completes per unit time. f = 1/T The unit of frequency is usually taken to be 1 Hz = 1 cycle per second.

•Simple Harmonic Oscillator: Any object that oscillates about a stable equilibrium position and experiences a restoring force approximately described by Hooke's law. Examples of simple harmonic oscillators include: a mass attached to a spring, a molecule inside a solid.

Major Concepts of Physics PHY102 – Lecture #32015Syracuse University

Interference can be observed only with Interference can be observed only with coherent lightcoherent light

 

8

Major Concepts of Physics PHY102 – Lecture #3 92015Syracuse University

Constructive Interference:Constructive Interference:Amplitudes are added upAmplitudes are added up

When the waves are in-phase, we have constructive interference.

Major Concepts of Physics PHY102 – Lecture #3 102015Syracuse University

Destructive InterferenceDestructive Interference

When the waves are 180 degrees out-of-phase,

we have destructive interference.

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Interference: How does it work? Interference: How does it work?

 

Maximum

Minimum

Major Concepts of Physics PHY102 – Lecture #3 122015Syracuse University

The issue was settled in 1801 by the experiment of Thomas Young. Light passes through two holes. Demonstration: The Young Experiment Observe: Some places light adds, at other places it cancels. This would not happen if light is a particle.  If so, the intensity would always add.

Wavelength Wavelength

Major Concepts of Physics PHY102 – Lecture #3 132015Syracuse University

The Thomas Young double-slit The Thomas Young double-slit experiment experiment

The pattern consists of a series of bright and dark parallel bands called fringes

Constructive interference occurs where a bright fringe occurs

Destructive interference results in a dark fringe

Major Concepts of Physics PHY102 – Lecture #3 142015Syracuse University

Interpretation of Interference Interpretation of Interference DataData

• The upper wave has to travel further than the lower wave

• The upper wave travels one wavelength further

• Therefore, the waves arrive in phase

• A bright fringe occurs

Major Concepts of Physics PHY102 – Lecture #3 152015Syracuse University

Interference Patterns, 2Interference Patterns, 2

Interference Patterns, 3

• The upper wave travels one-half of a wavelength farther than the lower wave

• The trough of the bottom wave overlaps the crest of the upper wave (180 phase shift)

• This is destructive interference

• A dark fringe occurs

Major Concepts of Physics PHY102 – Lecture #3 162015Syracuse University

Interference Equations, 5Interference Equations, 5

• The positions of the fringes can be measured vertically from the zeroth order maximum

• y = L tan θ L sin θ• Assumptions

– L>>d– d>>λ– tan θ sin θ

θθ is small and therefore the is small and therefore the approximation approximation tan tan θθ sin sin θθ can be usedcan be used

Major Concepts of Physics PHY102 – Lecture #3 172015Syracuse University

• For bright fringes (use sinθbright=m λ/d)

• For dark fringes (use sinθdark=λ (m + ½)/d)

21,0,bright mmd

Ly

21,0,2

1dark

mm

d

Ly

Major Concepts of Physics PHY102 – Lecture #3 182015Syracuse University

Interference Equations, FinalInterference Equations, Final

Major Concepts of Physics PHY102 – Lecture #2 192015Syracuse University

1. Reading: Chapter 25th, Sections 25.1, 25.4Example 25.1, Example 25.4

2. First Workshop this week!

3 Homework #1 for the next week (on paper): Please pick up the print outs

4. Do you want to be challenged? More MCAT preps?Problems 25.1, 25.4

AnnouncementsAnnouncements