Physics A2 - Lecture 1 - Huynh Quang Linh

Nội dung text: Physics A2 - Lecture 1 - Huynh Quang Linh

1. Welcome to Physics A2 Faculty: Lecturer: HUYNH QUANG LINH TA: TRAN DUY LINH All course information is on the web site. Format: Active Learning (Learn from Participation) Homework: Do it on the web !! Lecture: Presentations, demos, exercises, etc. Discussion: Forum, seminars. Textbook: [1] H.D. Young & R.A. Freedman: University Physics with Modern Physics, 12th Edition, Addison Wesley, 2007 [2] N.T.B.Bay et al.: General Physics A2, HCMUT Publisher, 2009 (vietnamese). Lecture 1, p 1
2. WWW and Grading Policy Almost all course information is on the web site Here you will find: announcements course description syllabus lecture slides discussion forum homework assignments sample exams gradebook The official grading policy Homework and seminars: 30% Midterm test: 20% Writing Exam : 40% Attendance: 10% Lecture 1, p 2
3. What is Physics A2 all about? (1) Many physical phenomena of great practical interest to engineers, chemists, biologists, physicists, etc. Wave phenomena  Classical waves (brief review)  Sound, electromagnetic waves, waves on a string, etc. Interference!  Traveling waves, standing waves  Interference and the principle of superposition  Constructive and destructive interference  Amplitudes and intensities  Colors of a soap bubble, . . . (butterfly wings!)  Interferometers  Precise measurements, e.g., Michelson Interferometer  Diffraction:  Optical Spectroscopy - diffraction gratings  Optical Resolution - diffraction-limited resolution of lenses, Lecture 1, p 3
4. What is Physics A2 all about? (2) Quantum Physics Particles act like waves! Particles (electrons, protons, nuclei, atoms, . . . ) interfere like classical waves, i.e., wave-like behavior Particles have only certain “allowed energies” like waves on a piano The Schrodinger equation for quantum waves describes it all. Quantum tunneling Particles can “tunnel” through walls! Scanning tunneling QM explains the nature of chemical bonds, microscope (STM) molecular structure, solids, metals, image of atoms and semiconductors, lasers, superconductors, . . . electron waves Waves act like particles! When you observe a wave (e.g., light), you find “quanta” (particle-like behavior). Instead of a continuous intensity, the result is a probability of finding quanta! Probability and uncertainty are part of nature! Lecture 1, p 4
5. Today Wave forms The harmonic waveform Amplitude and intensity Wave equations (briefly) Superposition Lecture 1, p 5
6. Wave Forms We can have all sorts of waveforms: v Pulses caused by brief disturbances of the medium Wavepackets: like harmonic waves, but v with finite extent. We usually focus on harmonic waves that extend forever. They are useful because they have simple math, and accurately describe a lot of wave behavior. Also called “sine waves” Lecture 1, p 6
7. The Harmonic Waveform (in 1-D) 2 y x, t A cos x vt  Acos kx 2 ft  A cos kx  t  y is the displacement from equilibrium. A function of vAspeed amplitude (defined to be positive) two variables: 2 x and t.  wavelengthk   wavenumber  f frequency  2 f  angular frequency A snapshot of y(x) at a fixed time, t: Wavelength  v Amplitude A defined to be x positive A This is review from Physics 211/212. For more detail see Lectures 26 and 27 on the 211 website. Lecture 1, p 7
8. Wave Properties Period: The time T for a point on the wave to undergo one complete oscillation. For a fixed position x : Period T Amplitude A A t Speed: The wave moves one wavelength, , in one period, T. So, its speed is:  v f T Frequency: f = 1/T = cycles/second. Movie (tspeed) Angular frequency:  = 2 f = radians/second Be careful: Remember the factor of 2 Lecture 1, p 8
9. Wave Properties Example Displacement vs. time at x = 0.4 m 0.8 0.4 y(t) 0 -0.4 Displacement mm in Displacement -0.8 0 .02 .04 .06 .08 .1 .12 .14 .16 Time, t, in seconds What is the amplitude, A, of this wave? What is the period, T, of this wave? If this wave moves with a velocity v = 18 m/s, what is the wavelength, , of the wave? Lecture 1, p 9
10. Solution Displacement vs. time at x = 0.4 m 0.8 T 0.4 A y(t) 0 -0.4 Displacement mm in Displacement -0.8 0 .02 .04 .06 .08 .1 .12 .14 .16 Time, t, in seconds What is the amplitude, A, of this wave? A = 0.6 mm What is the period, T, of this wave? T = 0.1 s v = f = /T If this wave moves with a velocity v = 18 m/s, what is the wavelength, , of the wave?  = vT = 1.8 m Note that  is not displayed in a graphLecture of y1,( pt ).10
11. Act 1 v A harmonic wave moving in the y positive x direction can be described by the equation y(x,t) = A cos(kx - t). x Which of the following equations describes a harmonic wave moving in the negative x direction? a) y(x,t) = A sin(kx t) b) y(x,t) = A cos(kx + t) c) y(x,t) = A cos( kx + t) Lecture 1, p 11
12. Solution v A harmonic wave moving in the y positive x direction can be described by the equation y(x,t) = A cos(kx - t). x Which of the following equations describes a harmonic wave moving in the negative x direction? v y a) y(x,t) = A sin(kx t) b) y(x,t) = A cos(kx + t) x c) y(x,t) = A cos( kx + t) In order to keep the argument constant, if t increases, x must decrease. Lecture 1, p 12
13. The Wave Equation For any function, f: The appendix has a f(x – vt) describes a wave moving in the positive x direction. discussion of f(x + vt) describes a wave moving in the negative x direction. traveling wave math. You will do some What is the origin of these functional forms? problems in discussion. They are solutions to a wave equation: 22ff1 x2 v 2 t 2 The harmonic wave, f = cos(kx ± t), satisfies the wave equation. (You can verify this.) Examples of wave equations: d22 p1 d p Sound waves: p is pressure dx2 v 2 dt 2 22 Electromagnetic waves: d Exx1 d E Also E B and B See P212, lecture 22, slide 17 dz2 c 2 dt 2 y x y Lecture 1, p 13
14. Amplitude and Intensity Intensity: How bright is the light? How loud is the sound? Intensity tells us the energy carried by the wave. Intensity is proportional to the square of the amplitude. Amplitude, A Intensity, I Sound wave: peak differential pressure, po power transmitted/area (loudness) EM wave: peak electric field, Eo power transmitted/area (brightness) For harmonic waves, the intensity is always proportional to the time-average of the power. The wave oscillates, but the intensity does not. 2 E For a harmonic wave, the time average, Example, EM wave: IE 11 2 oc 2 0 denoted by the <>, gives a factor of 1/2. oc We will usually calculate ratios of intensities. The constants cancel. In this course, we will ignore them and simply write: I = A2 or A =  I Lecture 1, p 14
15. Wave Summary y  The formula y x , t A cos kx t describes a harmonic plane wave A of amplitude A moving in the +x direction. x For a wave on a string, each point on the wave oscillates in the y direction with simple harmonic motion of angular frequency . 2  The wavelength is  ; the speed is vf  k k The intensity is proportional to the square of the amplitude: I  A2 Sound waves or EM waves that are created from a point source are spherical waves, i.e., they move radially from the source in all directions.  These waves can be represented by circular arcs:  These arcs are surfaces of constant phase (e.g., crests)  Note: In general for spherical waves the intensity will fall off as 1/r2, i.e., the amplitude falls off as 1/r. However, for simplicity, we will neglect this fact in Phys. 214. Lecture 1, p 15
16. Superposition A key point for this course! d y+ z dy dz Use the fact that + The derivative is a dx dx dx “linear operator”. Consider two wave equation solutions, h1 and h2: 2h11  2 h  2 h  2 h 1 1 and 2 2 x2 v 2  t 2  x 2 v 2  t 2 22 h++ h 1 h h Add them: 1 2 1 2 x2 v 2 t 2 h1 + h2 is also a solution !! In general, if h1 and h2 are solutions then so is ah1 + bh2. This is superposition. It is a very useful analysis tool. Lecture 1, p 16
17. Wave Forms and Superposition We can have all sorts of waveforms, but thanks to superposition, if we find a nice simple set of solutions, easy to analyze, we can write the more complicated solutions as superpositions of the simple ones. v v It is a mathematical fact that any reasonable waveform can be represented as a superposition of harmonic waves. This is Fourier analysis, which many of you will learn for other applications. We focus on harmonic waves, because we are already familiar with the math (trigonometry) needed to manipulate them. Lecture 1, p 17
18. Superposition Example Q: What happens when two waves collide? A: Because of superposition, the two waves pass through each other unchanged! The wave at the end is just the sum of whatever would have become of the two parts separately. Superposition is an exact property for: • Electromagnetic waves in vacuum. • Matter waves in quantum mechanics. • This has been established by experiment. Many (but not all) other waves obey the principle of superposition to a high degree, e.g., sound, guitar string, etc. Lecture 1, p 18
19. Act 2 Pulses 1 and 2 pass through each other. Pulse 2 has four times the peak intensity of pulse 1, i.e., I2 = 4 I1. NOTE: These are not harmonic waves, so the time average isn’t useful. By “peak intensity”, we mean the square of the peak amplitude. 1. What is the maximum possible total combined intensity, Imax? a) 4 I1 b) 5 I1 c) 9 I1 2. What is the minimum possible intensity, Imin? a) 0 This happens when one of the pulses is upside down. b) I1 c) 3 I1 Lecture 1, p 19
20. Solution Pulses 1 and 2 pass through each other. Pulse 2 has four times the peak intensity of pulse 1, i.e., I2 = 4 I1. NOTE: These are not harmonic waves, so the time average isn’t useful. By “peak intensity”, we mean the square of the peak amplitude. 1. What is the maximum possible total combined intensity, Imax? a) 4 I1 Add the amplitudes, then square the result: b) 5 I 1 AIIIA2 2 4 1 2 1 2 1 2 2 2 c) 9 I1 2 IAAAAAAItot tot 1 + 2 1 +2 1 9 1 9 1 2. What is the minimum possible intensity, Imin? a) 0 This happens when one of the pulses is upside down. b) I1 c) 3 I1 Lecture 1, p 20
21. Solution Pulses 1 and 2 pass through each other. Pulse 2 has four times the peak intensity of pulse 1, i.e., I2 = 4 I1. NOTE: These are not harmonic waves, so the time average isn’t useful. By “peak intensity”, we mean the square of the peak amplitude. 1. What is the maximum possible total combined intensity, Imax? a) 4 I1 Add the amplitudes, then square the result: b) 5 I 1 AIIIA2 2 4 1 2 1 2 1 2 2 2 c) 9 I1 2 IAAAAAAItot tot 1 + 2 1 +2 1 9 1 9 1 2. What is the minimum possible intensity, Imin? a) 0 Now, we need to subtract: 2 2 2 2 b) I1 IAAAAAAItot tot 1 2 1 2 1 1 1 c) 3 I1 Lecture 1, p 21
22. Appendix: Traveling Wave Math y 2 2 Why is f(x ± vt) a “travelling wave”? y(x) Ae x / 2 Suppose we have some function y = f(x): x y 22 y(x) Ae (x d) / 2  y= f(x - d) is just the same shape shifted a distance d to the right: x Suppose d = vt. Then: x = d y • f(x - vt) will describe the same shape v (x vt)22 /2  moving to the right with speed v. y(x) Ae • f(x + vt) will describe the same shape x x = vt moving to the left with speed v. Lecture 1, p 22