Lect_31_post

# Lect_31_post - PHYS 221 Exam 2 S2016 140 Avg 120 100 80 60...

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A B C D F Extra credit 0 20 40 60 80 100 120 140 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 PHYS 221 Exam 2 S2016 Avg

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Lecture 31 Energy. Intensity. Interference. Beats.
ACT: A sixth sense? A large ammunition factory and a town are separated by a rocky hill, at a horizontal distance of about 5 km. An accident produces a huge explosion in the middle of the night. What do the town folks experience? A. First the room shakes, and then they hear an explosion. B. First they hear an explosion, and then the room shakes. C. They hear an explosion and the room shakes at the same time.

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5 km Time for sound wave to reach the town: granite granite 6000 m/s Y v ρ Λ Ξ Μ Ο = = Μ Ο Ν Π Through hill (granite): 5000 m 0.8 s 6000 m/s x t v = = = This happened in California during WWII. Most people woke up (distressed…) to the light quake and then heard the explosion. Many attributed this to a sixth sense that had warned them of the imminent disaster. The sixth sense was just the laws of wave propagation… Through air: t = x v = 5000 m 343 m/s = 14.6 s 14 seconds later!
Wave energy Work is clearly being done: F . dr > 0 as hand moves up and down. This energy must be moving away from your hand (to the right) since the kinetic energy (motion) of the end of the string grabbed by the hand stays the same. P

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Transfer of energy The string to the left of x does work on the string to the right of x , just as your hand did: x Energy is transferred or propagated.
Power Energy of a mass in SHM (attached to a spring k ) 2 2 2 1 2 E kA A ω = 2 k m ω Λ Ξ = Μ Ο Ν Π This energy propagates at speed v . the average energy per unit time that flows in the direction of propagation should be proportional to v 2 2 P v A ω For harmonic waves on a taut string (see appendix): P = 1 2 μ F ω 2 A 2 = 1

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