6 Pages

Lect 01 Feb12

Course: PHYS 107, Fall 2009
School: University of Rochester
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1 Lecture February 12, 2002 Today: Thursday: Lab: 1 The Nature ofSound 1st 1 The Nature of Sound 2nd Lab 1: Problem Solving & Oscilloscope HW1: 0 Materials Pasco Function Generator Oscilloscope Pasco oscillator Speaker Base guitar string & masses & board Bell-jar with pump & bell Rope with tape to mark a point Long slinky Wave machine Simulation of gas? Simulation of...

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1 Lecture February 12, 2002 Today: Thursday: Lab: 1 The Nature ofSound 1st 1 The Nature of Sound 2nd Lab 1: Problem Solving & Oscilloscope HW1: 0 Materials Pasco Function Generator Oscilloscope Pasco oscillator Speaker Base guitar string & masses & board Bell-jar with pump & bell Rope with tape to mark a point Long slinky Wave machine Simulation of gas? Simulation of compression /rarefaction passing through gas? Alans video of a slinky longitudinal pulse? Handouts: Syllabus Lab 1 Office Ho ur Survey Brief Intro. o Instructor: Eric Hill Edu.: B.A. Carleton College, PhD U. of Minn. Condensed Matter Physics Research: STM studies of surface processes of individual molecules. Schedule: 221 and 107 this semester (so Ill be a little less available than I was last). Office Hours: To Be Determined o Physics 107 The bare stats: This is Physics 107. It is an algebra based M1 science course that meets Tuesdays & Thursdays at 9:30 & again Thursday at 11:00 for Lab. Overview: In this course well study the three Ps of sound: Production, Propagation, and Perception. Our coverage will have mostly a music bent, but I will stay within the realm of physics. The level of our coverage will be algebraic qualitative. I want you to come out of this course understanding the process on a level that increases your enjoyment of listening to music and that informs your decisions as a performer or composer. o Students How many music majors Musicians 1 Physics majors Calculus High school physics Administrative: Take Role o Check whos there & that they are signed- up for lab o I have been approached by a number of students interested in adding this class, if youre here today, and youre still interested at the end of the lecture, see me and well figure it out. o Office Hour Survey Instructions: Grayed out times are off limits, mark an N in the time blocks where you have a conflict, mark a Y in the blocks that are good for you, pass it on. o Open door policy, whether its an office hour or not, Im generally available in the white time blocks. Syllabus o Walk-through, step-by-step. Website: Intro page with the bare info. & links to the Policies & Expectation, Schedule, and a list of related websites. Policies and Expectations : Essentially what youve got in your hand. Schedule : the back page of what youve got in your hands + updated with the HW assignments, links to the Lab work-sheets, links to the HW solutions, and links to my lecture notes. List of Related Websites: Some sites for courses offered at other institutions and some sites with specific resources, like info. on the working of the human ear. Contacting Me: call, e- mail, drop by my office. E-mail: When, in the course of working on homework, you come up with a question, or you just want to check your answers, feel free to e- mail me. Drop-by: When I get the Office Hours survey back, Ill select a few hours to set-aside; however, any time block that isnt gray on that schedule, you can drop by. A copy of that schedule is on my door & on my web-site (from the course website, just click on my name). Text: Musical Acoustics by Donald E. Hall. They look like this (hold it up). Ive seen them in the Bookstore; hopefully there are enough for everyone. 2 Reading: Read before coming to lecture, and lecture will be more meaningful & youll be prepared to ask questions. Homework: The homework will be mathematical physics problems. The math will be algebra. My guess is that there are at least a few students in here who have never had a physics course and havent had a math course in quite a while. Ive posted a couple of documents regarding problem solving technique (see links in the Homework section of the Policies and Expectations and at the top of the schedule). For part of the first lab period, well work on a problem in small groups to try to dust off your skills. Feel free to work with your class-mates, but do turn- in your homework individually. Note: while the homework is only worth 8% of your grade, it prepares you for the exams which are worth 56%. Assigned daily, over material just covered Graded Boolean, but with the ability to redo improve homework skills & decrease grading time Read Homework section of Syllabus & see schedule. Laboratory: Most weeks there is a laboratory experience that accompanies the material were going over in lecture & that youre working over in the homework.. Lab is some time during our double block on Thursday. Lab hand-outs o Lab hand-outs are available in lecture a day or two before lab and are already available on the course website. o Prior to coming to class on Thursdays, you should read over the hand-out and address the pre- lab questions. o During the lab, you will fill out the lab handout and at the end of the lab period you will turn it in. Presentaion During the last 4 days of class, each of you will be responsible for giving a presentation on the workings of an instrument, or some other device. Each of you will be responsible for reviewing a number of your classmates presentations. 3 Presentation proposals will be collected ~ the week of the 2nd Exam. Exams There will be two in-class exams and a comprehensive final. The exams will be closed book, closed notes. Necessary equations will be provided. Schedule Look through the topics of the weeks Ch 1. The Nature of Sound o What is sound? o From everyday experience, if I asked you what you used to detect sound, youd say your ears; if I asked you where particular a sound was coming from, you could point it out. But how do your ears perceive it, how does the source produce it, and how does it propagate from the source to you? And what is sound anyway? o These are the questions well address in this course, the topics are the 3 Ps of acoustics Production Propagation Perception Introduction Defining Sound is tricky, it means different things to people in different fields. The best compromise, for the sake of this course is to say that sound is the three step process. A sound is a production, a propagation, and a perception. Well start our study with the middle step, for it turns out to be the simplest of the three. But to give us a sense of baring, and focus our attention on the salient features that define sound, and thus must be propagated, well superficially touch on production and perception first. So lets get started with the beginning: production. o Production o Lets examine a few sound sources and see whats in common. Voice: With your hand on your throat and noticing what you feel, go ahead and introduce yourself to your neighbor. Q: what did you feel? A: Something was moving, back-and-forth, quickly, almost buzzing. String: Demo: pluck the guitar string. Q: what do you see? 4 A: the string moving, back-and- forth, quickly, almost blurring. o Conclusion: Sound is produced when something moves, back-and- forth, quickly something vibrates. o Through the term, well look in more depth at some of the ways different instruments produce sounds and how they color the sound to produce unique timbres. Lets jump to the end: perception. o Listen to these vibrations. o Pitch o Demo: Pasco Function generator driving the Pasco oscillator with a square wave, hold a board over it for it to hit into, also displayed on an oscilloscope. Start very slow and dial up. o Explain equipment: Function Generator, produces an electrical signal that repeats itself at the frequency displayed. 20 in the screen means 20 times a second. Oscilloscope plots an electrical signals magnitude vs. time. Oscillator this moves in synch with the electrical signal of the function generator. o Start as just a periodic tap, as the frequency of tapping increases, slowly blurs together into a continuous tone, the tone rises with the increased frequency of tapping, until finally the tone disappears. o Repeated discrete motion, within a range of frequencies, is perceived as a steady tone. o Pitch = our perception of the sound being treble or base. It reflects how frequently the motion repeats. o Demo: Drive a regular speaker, start well below 20 Hz and end over 20000Hz. o How low a frequency do you hear? o How high a frequency do you hear? o Our ears are designed to perceive as a tone only motion in a certain range of pitches, or frequencies. o Loudness o Demo: Dial up the amplitude of the function generator, they can see on oscilloscope. o As the electrical signals amplitude increases, i.e., it varies over a wider range, the speaker cone moves further with each of its vibrations, making the vibrations more violent. o Loudness = our perception of the sounds strength or weakness. It reflects the violence of the repeated motion. o Motion in the Ear o Much later in the semester well get into how the ear works, but for now, Ill just say that the doorway to the ear, so to spe...

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Meeting 26December 1, 2004Approximation Algorithms(read Section 35 on Approximation Algorithms in C ORMEN , L EISERSON , R IVEST, S TEIN)98 UQT q8eddD( q 55 63 4(1 Vertex Cover. The rst problem we consider is nding the minimum set of vertices in
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Meeting 25November 29, 2004NP-Complete Problems(read Section 34 on NP-Completeness in C ORMEN , L EISERSON , R IVEST, S TEIN)Step 2. Convert each clause into disjunctive normal form. The most mechanical way uses the truth table for each clause, as ill
Duke - CPS - 130
%!PS-Adobe-2.0 %Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %Title: Book.dvi %Pages: 3 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: Times-Roman Helvetica Times-Bold Times-Italic Courier %EndComments %DVIPSWebPage: (www.radi
Duke - CPS - 130
%!PS-Adobe-2.0 %Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %Title: Book.dvi %Pages: 3 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: Times-Roman Helvetica Times-Bold Times-Italic %EndComments %DVIPSWebPage: (www.radicaleye.c
Duke - CPS - 130
Meeting 24November 22, 2004Easy and Hard Problems(read Section 34 on NP-Completeness in C ORMEN , L EISERSON , R IVEST, S TEIN)P92 B5 1 i`@47dX h$#8g7 X `V7A2X 7 B5 1 B 5 1 8 fe@47dX cb7 #Ua`YX B5 1 W2VA7 7 R $#UTSQAs an example consider the shorte
Duke - CPS - 130
Meeting 23November 17, 2004Pattern MatchingThis material is not covered in our textbook but you can read about pattern matching in Chapter I.3 of Algorithms on Strings, Trees, and Sequences by G USFIELD.the sequence starts with a non-empty sequence of
Duke - CPS - 130
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Duke - CPS - 130
Meeting 23November 15, 2004Searching with StringsThis material is not covered in our textbook but you can read about keyword trees and sufx trees in Chapters I and II of Algorithms on Strings, Trees, and Sequences by G USFIELD.o1p1t a2 3 1 1 2t
Duke - CPS - 130
%!PS-Adobe-2.0 %Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %Title: Book.dvi %Pages: 3 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: Times-Roman Times-Bold Courier Times-Italic %EndComments %DVIPSWebPage: (www.radicaleye.com
Duke - CPS - 130
Meeting 21November 10, 2004String Matching(read Section 32 on String Matching in C ORMEN , L EISERSON , R IVEST, S TEIN)HOCUSPOCUSABRA BRACADABRA. ABRA ABR AB A CADABRA ACADABRA RACADABRA BRACADABRAThe straightforward approach to solving this problem
Duke - CPS - 130
Meeting 20November 8, 2004Union-Find(read Section 21 on Data Structures for Disjoint Sets in C ORMEN , L EISERSON , R IVEST, S TEIN)This section presents two data structures for the disjoint set system problem we encountered in the implementation of K
Duke - CPS - 130
%!PS-Adobe-2.0 %Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %Title: Book.dvi %Pages: 3 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: Times-Roman Times-Italic Times-Bold Courier %EndComments %DVIPSWebPage: (www.radicaleye.com
Duke - CPS - 130
%!PS-Adobe-2.0 %Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %Title: Book.dvi %Pages: 4 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: Times-Roman Times-Bold Times-Italic Courier %EndComments %DVIPSWebPage: (www.radicaleye.com
Duke - CPS - 130
Meeting 19November 3, 2004Minimum Spanning Trees(read Sections 23 on Minimum Spanning Trees in C ORMEN , L EISERSON , R IVEST, S TEIN)aepdg hi; while is not a spanning tree do find a safe edge ; endwhile. There are safe edges as long as is a p
Duke - CPS - 130
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Duke - CPS - 130
Meeting 18November 1, 2004Shortest Paths(read Sections 24 and 25 on Shortest Paths in C ORMEN , L EISERSON , R IVEST, S TEIN)One of the most common operations in graphs is nding shortest paths between vertices. This section discusses three algorithms:
Duke - CPS - 130
%!PS-Adobe-2.0 %Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %Title: Book.dvi %Pages: 3 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: Times-Roman Times-Bold Times-Italic Courier %EndComments %DVIPSWebPage: (www.radicaleye.com
Duke - CPS - 130
%!PS-Adobe-2.0 %Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %Title: Book.dvi %Pages: 3 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: Times-Roman Times-Bold Times-Italic Courier %EndComments %DVIPSWebPage: (www.radicaleye.com
Duke - CPS - 130
Meeting 17October 27, 2004Graph Search(read Section 22 on Elementary Graph Algorithms in C ORMEN , L EISERSON , R IVEST, S TEIN)2 1 0 )( ' % " &$#! which is symmetric. Often the number of edges is quite3 40 1 2 3 4VFigure 83: A sample graph with
Duke - CPS - 130
Meeting 16October 25, 2004Splay Trees, IIThis material is not covered in our textbook. You can read about splay trees in Section 7.3 of Data Structures and Their Algorithms by L EWIS , D ENENBERG and about optimum weighted binary search trees in Sectio
Duke - CPS - 130
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Duke - CPS - 130
Meeting 15October 20, 2004Splay Trees, IThis material is not covered in our textbook but you can read about splay trees in Section 7.3 of Data Structures and Their Algorithms by L EWIS , D ENENBERG.Node Z IG Z IG Node return Z IG Z IG . 4 3 2 1 1 2
Duke - CPS - 130
%!PS-Adobe-2.0 %Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %Title: Book.dvi %Pages: 3 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: Times-Roman Times-Bold Times-Italic Courier %EndComments %DVIPSWebPage: (www.radicaleye.com
Duke - CPS - 130
Meeting 14October 18, 2004Fibonacci Heaps, II(read Section 20 on Fibonacci Heaps in C ORMEN , L EISERSON , R IVEST, S TEIN)We still need to discuss the D ECREASE K EY and the D ELETE operations for Fibonacci heaps. Both change the structure of the hea
Duke - CPS - 130
Meeting 13October 13, 2004Fibonacci Heaps, I(read Section 19 on Binomial Heaps and Section 20 on Fibonacci Heaps in C ORMEN , L EISERSON , R IVEST, S TEIN)4 9 10 11 87 95 94 10 11 8 15+15=12 15 13 9Figure 63: Binomial trees of heights 0, 1, 2,
Duke - CPS - 130
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Duke - CPS - 130
%!PS-Adobe-2.0 %Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %Title: Book.dvi %Pages: 3 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: Times-Roman Times-Bold Times-Italic Courier %EndComments %DVIPSWebPage: (www.radicaleye.com
Duke - CPS - 130
Midterm ExamOctober 4, 2004Midterm(75 minutes open book exam)(b) There are 14 different parenthesizations, and they are 23723('&$2&$" ) #) # #" #" # 21343('1&'&$" ) #) # #" #" # 213('635$1%$" ) # #" ) # #" # 2110($&'&$%$" ) # #" #" #" #endwhile; unt
Duke - CPS - 130
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Duke - CPS - 130
Meeting 12October 4, 2004Amortized Analysis(read Section 18 on Amortized Analysis in C ORMEN , L EISERSON , R IVEST, S TEIN)Amortization is an analysis technique that can inuence the design of algorithms in a profound way. Later, we will see a few dat
Duke - CPS - 130
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Duke - CPS - 130
%!PS-Adobe-2.0 %Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %Title: Book.dvi %Pages: 3 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: Times-Roman Times-Bold Times-Italic Courier %EndComments %DVIPSWebPage: (www.radicaleye.com
Duke - CPS - 130
Meeting 11September 29, 2004Solving Recurrence Relations(read Section 4 on Recurrences in C ORMEN , L EISERSON , R IVEST, S TEIN)Recurrence relations are perhaps the most important tool in the analysis of algorithms. We have encountered several method
Duke - CPS - 130
Meeting 10September 27, 2004Greedy Algorithms(read Section 16 on Greedy Algorithms in C ORMEN , L EISERSON , R IVEST, S TEIN)A scheduling problem. Consider a set of activities, . Activity has start time and nish time . Two activities and overlap if .
Duke - CPS - 130
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Duke - CPS - 130
Meeting 9September 22, 2004Dynamic Programming(read Section 15 on Dynamic Programming in C ORMEN , L EISERSON , R IVEST, S TEIN)Figure 41: The rst parenthesization takes elementary multiplications. second takes34t xw0 0s ivh0Although the resulting
Duke - CPS - 130
%!PS-Adobe-2.0 %Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %Title: Book.dvi %Pages: 3 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: Times-Roman Times-Bold Courier %EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSComma
Duke - CPS - 130
Meeting 8September 20, 2004Hash Tables(read Section 11 on Hash Tables in C ORMEN , L EISERSON , R IVEST, S TEIN).0T0.x x.m 1Figure 38: Each table element is a pointer to a linked list.Hashing. In hashing we store at a location , where is a fu
Duke - CPS - 130
Meeting 7September 18, 2004Skip ListsThis material is not covered in our textbook but you can read about skip-lists in Section 6.3 of Ordered Lists in Data Structures and Their Algorithms by L EWIS , D ENENBERG.In searching it is important that the da
Duke - CPS - 130
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Duke - CPS - 130
%!PS-Adobe-2.0 %Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %Title: Book.dvi %Pages: 3 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: Times-Roman Times-Bold Times-Italic Courier %EndComments %DVIPSWebPage: (www.radicaleye.com
Duke - CPS - 130
Meeting 6September 13, 2004Red-Black Trees(read Section 13 on Red-Black Trees in C ORMEN , L EISERSON , R IVEST, S TEIN)Binary search trees are an elegant implementation of the dictionary data type, which requires support for item S EARCH (item), void
Duke - CPS - 130
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Duke - CPS - 130
Meeting 5September 8, 2004Binary Search Trees(read Section 12 on Binary Search Trees in C ORMEN , L EISERSON , R IVEST, S TEIN)ancestors rootBinary trees. We have used binary trees repeatedly and now return to a more formal and systematic introductio
Duke - CPS - 130
Meeting 4September 6, 2004Selection(read Section 9 on Medians and Order Statistics in C ORMEN , L EISERSON , R IVEST, S TEIN)Deterministic Selection. The randomized selection algorithm takes time proportional to in the worst case,13int RS ELECT int