a(t) = -W2A cos(wt + ) Am = =, where m = 1,3, 5, ... p = -tan-1/ xow B = (10 db) log10 (), 10 = 10-12 W/m2 Etot = }KAZ = kx2 + Imv2 fB = Ja - fb 2 W = 2 ( simple pendulum ) fL = (7. ) mga W = (physical pendulum) Is 2- = DIUs (+ behind, - front) 1 = Icm + Md2 sin(a) = - Fdamp = -bv Us x(t) = Ae-(zm) cos(w't + $) (damped) M = - W = b2 Vm Amz (damped) n A = Fm = (forced and damped) 12 - 1 = ml, where m = 0, +1, +2, ... V( k-mwa) +62 wa 12 - 1 = (m + 2) 1, where m = 0, + 1 , + 2 , .. Waves 21(12 - 71) v = af a y(x, t) = A sin(kx + wt + $) 12 - 1 = d sin(0m) w = 2nf = 4, k = 271 Small angle, bright fringes: 0m = ma, 7, where m = 0, +1, +2, ... Vstring = Small angle, dark fringes: Om =- (m+z )1 d , where m = n = - 0, +1, +2, ... ystand (x, t) = 2A sin(kx) cos(wt) ym = L tan(0m) am = m, where m = 1, 2, 3, ... Small angle: ym ~ Lom E fn = 21 7 , where n = 1, 2, 3, ... 1 = 10 Cos - fn = nf1 INN 12 Pave = =VUFW2 42 Low -to-high n, phase shift of It YURT Vsound = 0 100 AL m Ah = 2Ax Pmax = kBA 1 = VBpw242_Pmax 2t = \\(m+3)a depending on n values 2 Bp Open-open/closed-closed: 1 = _ n am = 24 m' where m = 1, 2, 3, ... a sin (0m) = ma Open-closed: 1 = 10 sin [wasin(0) /x])2 na sin(0)/2Midterm 2 Practice Problems 1. 5. To speakers that are 15.0 m apart produce in-phase sound waves of frequency 250.0 Hz in a room where the speed of sound is 340.0 m/s. A woman starts out at the midpoint between the two speakers. The room's walls and ceiling are covered with absorbers to eliminate reflections, and she listens with only one ear for best precision. a. What does she hear: constructive or destructive interference? Why? b. She now walks slowly toward one ofthe speakers. How far from the centre must she walk before she first hears the sound reach minimum intensity? Maximum intensity? Coherent light of frequency 6.32 x 1014 Hz passes through two thin slits and falls on a screen 85.0 cm away. You observe that the third bright fringe occurs at +/- 3.11 cm on either side of the central bright fringe. a. How far apart are the two slits? b. At what distance from the central bright fringe will the third dark fringe occur? A researcher measures the thickness of a layer of benzene (n = 1.50) floating on water by shining monochromatic light on the film and varying the wavelength of the light. She finds that light of wavelength 575 nm is reflected most strongly from the film. What does she calculate for the minimum thickness of the film? Adjacent antinodes of a standing wave on a string are 15.0 cm apart. A particle at an antinode oscillates in simple harmonic motion with amplitude 0.850 cm and period 0.0750 s. The string lies along the +x-axis and is fixed at x = 0. a. How far apart are the adjacent nodes? b. What are the wavelength, amplitude, and speed of the two traveling waves that form the pattern? c. Find the maximum and minimum transverse speeds of a point at an antinode. d. What is the shortest distance along the string between a node and an antinode? A uniform cylindrical steel wire, 55.0 cm long and 1.14 mm in diameter, is fixed at both ends. To what tension must it be adjusted so that, when vibrating in its first overtone, it produces the note D-sharp of frequency 311 Hz? (p5 = 7.8 x 103 kg/m3)