After adding 2 points to everyone’s score. PHY2053 Exam 2 Average = 11.6 High = 20 (2 students) Low = 3 After adding 2 points to everyone’s score. R. Field 11/12/2013 University of Florida PHY 2053

Estimated Course Grades 18 students have 100 points! Assumes that you get the same grade on the Final Exam that you averaged on Exam 1 plus Exam 2. Include the first 8 quizzes and assumes that you get the same average on all your remaining quizzes that you have for the first 8 quizzes. Includes the first 9 WebAssign HW assignments and assumes that you get the same average on all your remaining homework assignments that you have for the first 9 assignments. Includes your HITT scores through 10/31/13 and assumes you maintain the same average on the remaining HITT questions. Includes your first 4 Sakai HW assignments and assumes you maintain the same average on the remaining assignments. R. Field 11/12/2013 University of Florida PHY 2053

Traveling Waves: Energy Transport A “wave” is a traveling disturbance that transports energy but not matter. v Intensity: Intensity I = power per unit area Intensity is proportional to the square of the amplitude A! (measured in Watts/m2) Variation with Distance: If sound is emitted isotropically (i.e. equal intensity in all directions) from a point source with power Psource and if the mechanical energy of the wave is conserved then (intensity from isotropic point source) Speed of Propagation: The speed of any mechanical wave depends on both the inertial property of the medium (stores kinetic energy) and the elastic property (stores potential energy). Transverse wave on a string: FT = string tension m = M/L = linear mass density (wave speed) R. Field 11/12/2013 University of Florida PHY 2053

Constructing Traveling Waves Constructing Traveling Waves: To construct a wave with shape y = f(x) at time t = 0 traveling to the right with speed v replace x by x-vt. Traveling Harmonic Waves: Harmonic waves have the form y = A sin(kx + f) at time t = 0, where k is the "wave number“, k = 2p/l, l is the "wave length". and A is the "amplitude". To construct a harmonic wave traveling to the right with speed v, replace x by x-vt as follows: where w = kv. Speed of propagation! Harmonic wave traveling to the right Harmonic wave traveling to the left The phase angle f determines y at x = t = 0, y(x=t=0) = Asinf. If y(x=t=0) = 0 then f = 0. R. Field 11/12/2013 University of Florida PHY 2053

Waves: Mathematical Description wave traveling to the right F Vector A with length A undergoing uniform circular motion with phase F = kx – wt. The projection onto the y-axis gives y = Asin(kx – wt). If t = 0 then One circular revolution corresponds to F = 2p = kl, and hence k = 2p/l (“wave number”). R. Field 11/12/2013 University of Florida PHY 2053

Waves: Mathematical Description wave traveling to the right F Vector A with length A undergoing uniform circular motion with phase F = kx – wt. The projection onto the y-axis gives y = Asin(kx – wt). If x = 0 then One circular revolution corresponds to F = 2p = wT and hence T = 2p/w (“period”). R. Field 11/12/2013 University of Florida PHY 2053

Waves: Mathematical Description In General wave traveling to the right F Overall phase F = kx – wt + f. wave traveling to the left F Period (in s) Frequency (in Hz) Wave Number (in rad/m) Wave Speed (in m/s) Angular Frequency (in rad/s) R. Field 11/12/2013 University of Florida PHY 2053

Waves: Mathematical Description wave traveling to the right vnode x point on string nth node Waves Propagation: A node is a point on the wave where y(x,t) vanishes: (wave speed) Transverse Speed & Acceleration: For “transverse” waves the points on the string move up and down while the wave moves to the right. transverse speed of a point on the string transverse acceleration of a point on the string SHM R. Field 11/12/2013 University of Florida PHY 2053

Waves: Example Problems A transverse wave on a taught string has amplitude A, wavelength l and speed v. A point on the string only moves in the transverse direction. If its maximum transverse speed is umax, what is the ratio umax/v? Answer: 2pA/l The function y(x,t) = Acos(kx - wt) describes a wave on a taut string with the x-axis parallel to the string. The wavelength is l = 3.14 cm and the amplitude is A = 0.1 cm. If the maximum transverse speed of any point on the string is 10 m/s, what is the speed of propagation of the travelling wave in the x-direction? Answer: 50 m/s R. Field 11/12/2013 University of Florida PHY 2053

Waves: Example Problems A sinusoidal wave moving along a string is shown twice in the figure. Crest A travels in the positive direction along the x-axis and moves a distance d = 12 cm in 3 ms. If the tick marks along the x-axis are 10 cm apart, what is the frequency of the traveling wave? Answer: 100 Hz R. Field 11/12/2013 University of Florida PHY 2053