phys124s11-l08

phys124s11-l08 - 1 RG, Physi cs & Ast r onomy Physics...

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Unformatted text preview: 1 RG, Physi cs & Ast r onomy Physics 124 Spring 2009 Physics 124 Spring 2011 L8 25 Mar 2011 Physics 124, Spring 2011 • Welcome back from Spring Break! • 2 nd exam Monday night, April 4, 9:40 PM – same setup as CH1 – One cheat sheet allowed (both sides). – ARC 103: sections 04, 05, 07, 08, 09, 12, 16, 19 – HILL 114: sections 01, 02, 03, 15, 18 – SEC 111: sections 06, 10, 11, 13, 14 – Email Profs. Gershenson ([email protected]) “immediately” if you need makeup. Those taking makeup will be given coordinates by email. • Covers this week's lecture + previous three weeks of lecture: – Chapters 13, 15, 16 (SHM, traveling waves, sound, standing waves and interference) – There are no typos on the exam! Note on 1 st exam grading 2 RG, Physi cs & Ast r onomy Physics 124 Spring 2009 Physics 124 Spring 2011 L8 25 Mar 2011 Physics 124, Spring 2010 • This week: interference and standing waves • Basic point: when you have two waves, their amplitudes add – → destructive interference & nodes – → constructive interference & anti-nodes – → standing waves – → harmonics – → musical instruments – → beat effects – ... 3 RG, Physi cs & Ast r onomy Physics 124 Spring 2009 Physics 124 Spring 2011 L8 25 Mar 2011 Today: Superposition/Interference – ch 15.6-8, 16.4-7 Superposition: Wave amplitudes add Example: two waves, y 1 = Acos kx − t and y 2 = Acos kx − t Recall cos (α+β) = cos (α) cos (β)− sin (α) sin (β) What is the sum? Use = kx − t / 2 and = / 2 to get: y 1 = Acos cos Asin sin y 2 = Acos cos − Asin sin y 1 y 2 = 2Acos cos = 2Acos kx − t / 2 cos / 2 New amplitude: 2Acos / 2 New phase: / 2 So: y 1 = Acos − and y 2 = Acos 4 RG, Physi cs & Ast r onomy Physics 124 Spring 2009 Physics 124 Spring 2011 L8 25 Mar 2011 Superposition/Interference = n , n an even integer Special cases 2Acos / 2 ± 2A = n , n an odd integer y 1 y 2 = 2Acos / 2 cos kx − t / 2 New amplitude: 2Acos / 2 New phase: / 2 2Acos / 2 destructive interference constructive interference cos / 2 = cos , cos , cos 2 , cos 3 , ... cos / 2 = cos / 2 , cos 3 / 2 , cos 5 / 2 , ... Other 's lead to results between these limiting cases full wave length offsets half wave length offsets 5 RG, Physi cs & Ast r onomy Physics 124 Spring 2009 Physics 124 Spring 2011 L8 25 Mar 2011 Superposition/Interference = n , n an even integer Special cases 2Acos / 2 ± 2A = n , n an odd integer y 1 y 2 = 2Acos / 2 cos kx − t / 2 New amplitude: 2Acos / 2 New phase: / 2 2Acos / 2...
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This note was uploaded on 03/24/2011 for the course PHYSICS 123 taught by Professor Madey during the Fall '08 term at Rutgers.

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phys124s11-l08 - 1 RG, Physi cs & Ast r onomy Physics...

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