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)/26. 7. 10. You have a stopped pipe of adjustable length next to a taut 62.0 cm, 7.25 g wire under a tension of 4110 N. You want to adjust the length ofthe pipe, so that, when it produces sound at its fundamental frequency (first harmonic), this sound causes the wire to vibrate in its second overtone with very large amplitude. How long should the pipe be? Two organ pipes, open at one end and closed at the other, are each 1.14 m long. One is now lengthened by 3.00 cm. Find the beat frequency that they produce when playing together in their first overtone. Two people are talking at a distance of 3.0 m from where you are and you measure the sound intensity as 1.1 x 10'7 W/mz. Another student is 4.0 m away from the talkers. What sound intensity does the other student measure? Assume that the sound spreads out uniformly and undergoes no significant reflections or absorptions. A carousel that is 5.00 m in radius has a pair of 600 Hz sirens mounted on posts at opposite ends on the edge. The carousel rotates with an angular velocity of 0.800 rad/s. A stationary listener is located at a distance from the carousel. The speed of sound is 350 m/s. (Hint: The relations between linear and angular velocity is v 2 Rev) a. What is the longest wavelength reaching the listener from the sirens? b. What is the largest beat frequency the listener hears from the sirens? Light of wavelength 525 nm passes through two slits separated by 0.500 mm and produces an interference pattern on a screen 7.80 m away. The intensity at the central maximum is 10. What is the distance on the screen from the centre of this central maximum to the point where the intensity due to double-slit interference has fallen to 1/2 [0