# Ch_16_problems - 530 CHAPTER 16 Superposition and Standing...

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Unformatted text preview: 530 CHAPTER 16 Superposition and Standing Waves SUMMARY The goal of Chapter 16 has been to use the idea of superposition to understand the phenomena of interference and standing waves. GENERAL PRINCIPLES Principle of Superposition The displacement of a medium when more than one wave is present is the sum of the displacements due to each individual wave. ~ _-----'I\~-- ~ IMPORTANT CONCEPTS Standing Waves Two identicallravel ing waves moving in opposite directions create a smnding wave. Antinodes x¥Xx Nodes ---Node spacing is ~A. The boundary conditions deter- mi ne which standing-wave fre- quencies and wavelengths are allowed. The allowed standing waves are modes of the system. APPLICATIONS Beats (loud-soft-loud-soft modulations of intensity) are produced when two waves of slightly different frequencie...;; are superimposed. Loud Soft Loud Soh Loud Soft Loud Interference In general, the superposition of two or more waves into a single wave is called interference. Constructive interference occurs when crests are aligned wilh crests and troughs wilh troughs. We say the waves are in phase. It occurs when the path-length difference !!1d is a whole number of wavelengths. " '.f\ f\ f\ Destructive interference occurs when crests are aligned with troughs. We say the waves are out of phase. It occurs when the path- length difference !YJ.d is a whole number of wavelengths plus half a wavelength. " ~ ~ " .p, " I : ""J=lA o· ' x A standing wave on a string has a node at each end. Possible modes: m=l A standing sound wave in a tube can have different bOllndary oondi tions: open-open, closed-closed, or open-closed. <=> C5b Open-open f,"~IIIGJ 111 = 1,2,3, ... <:2 111=3 ()(XJ Closed -closed f,,,~m(;J 11/ = 1,2,3,. tJ..p in tube C><=2J L 2L Am= - III Open-closed f,"~III(:J <::::::: In = 1,2,3, .. m = 1,3, 5,. . L Standing waves are multiples of a fundamental frequency, the frequency of lhe lowest mode. The higher modes are the higher harmonics. For sound, the fundamental frequency determines the perceived pitch; the hi gher harmonics determine the tone qualily. _____ Fundamental frequency Higher harmonics . ( 111 = 1 \ Our vocal cords create a range of har- monics. The mix of higher harmonics is changed by our vocal tract to create dif- ferenl vowel sounds. +-c'-::--:"c-:-'-:-c"-::c-'---c'.::--L-:c':-:-f(H,) 262 524 786 1048 1572 2096 r-- ~T1oI For homework assigned on MasteringPhysics. go to IMP . h ' www.mastermgpyslcs.com Problem difficulty is labeled as I (straightforward) to m il (challenging). QUESTIONS Conceptual Questions I. Light can pass easily through water and through air. but light will reflect from the surface of a lake. What does th is tell you abollt the speed of light in a ir and in water? ...
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