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First semester sophomore physics: The advantages of waves & oscillations with semi-coordinated lab Walter F. Smith Physics Dept. Haverford College Haverford PA Conference on Laboratory Instruction Beyond the First Year of College Philadelphia, July 25, 2012

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A tension in education: depth vs. breadth Sophomore physics: varies quite widely One common approach: Modern Physics Relativity Quantum mechanics Nuclear physics Particle physics Statistical mechanics

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Approach to sophomore physics at Haverford College: Rigorous quantum mechanics in lecture and lab Lecture:

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Advantages: Quantum mechanics is very exciting to students! Central to many hot areas of research (e.g. q. computing, q. info) Philosophically challenging (e.g. entanglement, locality, …) Required for many of our most impressive results (transistors, solar power) and most important challenges Gives students a real insight into the physics major before they declare Disadvantages: Only 1-2 weeks on relativity in first 2y (during 1 st -year e&m) There are many exciting areas of physics that don’t involve q.m.

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Our experience at Haverford: Originally, students began study of quantum right after two semesters of intro Most students struggled, achieved poor understanding New system: Semester 1: Waves and Oscillations Semester 2: Quantum Mechanics Works very well! Increased number of majors (~12 per year, with student body of 1200) Excellent, supportive atmosphere among majors

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Advantages of Waves & Oscillations in the sophomore year: Important in most areas of physics Electricity & magnetism Anything involving quantum Acoustics Plasmas Nanoscience Provides exactly the mathematical ideas and techniques needed for quantum (and many other areas), in a less intimidating classical context Differential equations Complex exponentials Matrix math Hilbert space and orthogonal function analysis (e.g. Fourier analysis) Eigenvalue equations Bra-ket notation

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Advantages of sophomore Waves & Oscillations (ctd.): Most of material is new to students (e.g. coupled oscillators), but connected to things they’ve studied before & understand Gives students a feeling of the challenge they will see in upper-level courses

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Text: Connections to current research: Whale calls: Total internal reflection fluorescence microscopy: Prof. Christopher Clark, Cornell Univ. A. Gunnarson et al., Nano Letters 8, (2008).

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Connections to “everyday” life: Magnetic Resonance Imaging Quartz crystal from a watch Dr. Erhard Schreck

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Web support with custom-developed applets & links to web resources Custom-developed coupled pendulum and Hilbert space applet Link to Physical Review Focus summary of Physical Review Letters paper on bat sonar Prof. Rolf Müller, Shandong Univ.

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Bra-ket notation for coupled oscillators

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Refreshing writing style Humor when appropriate Check it out Thursday in Poster Session I

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Semi-coordinated lab: Goals of our first-semester sophomore lab: Transition to more independent lab work: Second semester sophomore lab Advanced lab (junior / senior) Research Provide common background of experimental expertise: Simple electronics (input & output impedance, scope operation, op amps) Better understanding of optics Coherent presentation of results Three oral reports Two full-length written reports Reinforcing data analysis: Uncertainty analysis, curve fitting Another tension in education: creativity/exploration vs. learning the ropes

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Another tension: Challenging your students to stretch themselves vs. Discouraging them Oral reports: Presentations based on data graphs, tables, etc. (not PowerPoint) Given to an instructor Presentations in pairs Typically about 30 minutes

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Overview of the lab: Another tension: Reinforcing understanding vs. introducing new material At a variety of intervals Connected to old material (reading, class, problem sets, lab, exams, other courses, research) Using different parts of the brain New context Half-credit, usually taken in the same semester as the lecture component

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First five weeks are single-week labs, done in unison by pairs, coordinated with lecture. Week 1: Input and output impedance for DC circuits Essential concepts for all electronics Week 2: High- & low-pass filters Connects to complex notation for AC circuits in lecture Week 3: Resonant circuits Connects to ideas in lecture Week 4: Diodes Crystal radio; synthesizing concepts Week 5: Op amps What is an amplifier? What is gain? Feedback The connection between a schematic & physical circuit Debugging

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Last 9 weeks are a series of two week labs (plus a week off!). Done in rotation by pairs of students. Not coordinated with lecture. Why only semi-coordinated? Equipment costs Allowing students to encounter some things in lab first Variability in timing between the lecture & lab is OK Less sense of competition for fastest completion Students who’ve done the lab previously help the current students, building camaraderie.

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Dispersion relation of water waves The beginnings of how to be really clean Challenging non-linear curve fitting Dispersion relations can be non linear

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Torsional oscillator (TeachSpin) & coupled oscillators Connects to key concepts from lecture Further practice with scopes, function generators Computer acquisition of voltages Reinforces concepts of Faraday’s Law, and creating B with current wiki.brown.edu/confluence/display/ PhysicsLabs/Experiment+120

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Diffraction as a Fourier transform and spatial filtering Connection to lecture Deeper understanding of optics Practice thinking in reciprocal space Simple optical design exercise: beam expander Optical setups using research-grade components Aspects of laser safety

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Ultrasound imaging Applications of wave ideas to a new context 3B Scientific

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Shortcomings include: Main equipment used for two of the two-week labs will never be used again. (water waves, ultrasound) In our current version of Advanced Lab, students don’t revisit op amps. Students rarely use them in research. Because the two-week labs are only semi-coordinated, the connection to lecture is different for different students

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Conclusions: Sophomore: waves & oscillations first semester quantum mechanics second semester semi-coordinated labs High level of student interest Students know what they’re getting into when they major. First semester labs continue building a good foundation of experimental skills and intuition. Helpful to have a connection between lab& lecture, but exact coordination is not necessary, or even always preferred.

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