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PH300 Waves The Great Wave off Kanagawa Katsushika Hokusai 2013 What is a wave? ● Pulse or Oscillation that Propagates through Media ● What is transferred? ● What sorts of Media? Harmonic Waves 8/23/2013 8/23/2013 Exercise Consider a mechanical wave y(x,t)= 0.2cos(π/8(x-32t)) where x is measured in meters and t is measured in seconds Determine: a. b. c. d. e. f. g. Amplitude Wave Number Wavelength Speed Frequency Period Angular Frequency A=0.2 m k=π/8 m-1 λ=16 m v=32 m/s ν=2 Hz T=0.5 s ω=4π s-1 Exercise Consider a mechanical wave y(x,t)= 0.2cos(π/8(x-32t)) where x is measured in meters and t is measured in seconds Determine: a. b. c. d. e. f. g. Amplitude Wave Number Wavelength Speed Frequency Period Angular Frequency A=0.2 m k=π/8 m-1 λ=16 m v=32 m/s ν=2 Hz T=0.5 s ω=4π s-1 Harmonic Waves • Alternate Representation Assuming y(x,t)=Acos k(x+vt) can obtain y(x,t)=Acos(kx+ωt) Or the equivalent y(x,t)=Acos 2π(x/λ+t/T) 8/23/2013 Velocity and Acceleration 8/23/2013 Problem In the open sea, a tsunami usually has an amplitude less than 40 cm and a wavelength longer than 80 km. Assume that the speed of the tsunami is 740 km/h. What are the approximate maximum vertical velocity and acceleration that such a tsunami will give to a ship floating on the water? Will the crew of the ship notice the passing tsunami? 8/23/2013 Velocity in y vy~ π/500 m/s Acceleration= vy/A = (pi/500) (1/0.4) m/s2 = 0.0001 m/s2 g=10 m/s2 8/23/2013 Depth of Ocean Monitor Open Ocean, 600 km SE of Tokyo Δy 1.1 m http://www.youtube.com/watch?v=w3AdFjklR50 8/23/2013 Superposition and Interference Tutorial 16 example 8/23/2013 8/23/2013 8/23/2013 8/23/2013 8/23/2013 8/23/2013 8/23/2013