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. 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
3. Today • Wave forms The harmonic waveform • Amplitude and intensity • Wave equations (briefly) • Superposition Lecture 1, p 5
4. 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
5. 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
6. 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
7. 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
8. 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
9. 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
10. 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
11. 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