{"id":1507,"date":"2018-02-06T18:06:19","date_gmt":"2018-02-06T18:06:19","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-osuniversityphysics\/?post_type=chapter&p=1507"},"modified":"2018-02-06T18:06:20","modified_gmt":"2018-02-06T18:06:20","slug":"16-chapter-review","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-osuniversityphysics\/chapter\/16-chapter-review\/","title":{"raw":"16 Chapter Review","rendered":"16 Chapter Review"},"content":{"raw":"
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Key Terms<\/span><\/h3>\r\n
\r\n \t
antinode<\/strong><\/dt>\r\n \t
location of maximum amplitude in standing waves<\/dd>\r\n<\/dl>\r\n
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constructive interference<\/strong><\/dt>\r\n \t
when two waves arrive at the same point exactly in phase; that is, the crests of the two waves are precisely aligned, as are the troughs<\/dd>\r\n<\/dl>\r\n
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destructive interference<\/strong><\/dt>\r\n \t
when two identical waves arrive at the same point exactly out of phase; that is, precisely aligned crest to trough<\/dd>\r\n<\/dl>\r\n
\r\n \t
fixed boundary condition<\/strong><\/dt>\r\n \t
when the medium at a boundary is fixed in place so it cannot move<\/dd>\r\n<\/dl>\r\n
\r\n \t
free boundary condition<\/strong><\/dt>\r\n \t
exists when the medium at the boundary is free to move<\/dd>\r\n<\/dl>\r\n
\r\n \t
fundamental frequency<\/strong><\/dt>\r\n \t
lowest frequency that will produce a standing wave<\/dd>\r\n<\/dl>\r\n
\r\n \t
intensity (I<\/em>)<\/strong><\/dt>\r\n \t
power per unit area<\/dd>\r\n<\/dl>\r\n
\r\n \t
interference<\/strong><\/dt>\r\n \t
overlap of two or more waves at the same point and time<\/dd>\r\n<\/dl>\r\n
\r\n \t
linear wave equation<\/strong><\/dt>\r\n \t
equation describing waves that result from a linear restoring force of the medium; any function that is a solution to the wave equation describes a wave moving in the positive\u00a0x<\/em>-direction or the negative\u00a0x<\/em>-direction with a constant wave speed\u00a0v<\/em><\/dd>\r\n<\/dl>\r\n
\r\n \t
longitudinal wave<\/strong><\/dt>\r\n \t
wave in which the disturbance is parallel to the direction of propagation<\/dd>\r\n<\/dl>\r\n
\r\n \t
mechanical wave<\/strong><\/dt>\r\n \t
wave that is governed by Newton\u2019s laws and requires a medium<\/dd>\r\n<\/dl>\r\n
\r\n \t
node<\/strong><\/dt>\r\n \t
point where the string does not move; more generally, nodes are where the wave disturbance is zero in a standing wave<\/dd>\r\n<\/dl>\r\n
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normal mode<\/strong><\/dt>\r\n \t
possible standing wave pattern for a standing wave on a string<\/dd>\r\n<\/dl>\r\n
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overtone<\/strong><\/dt>\r\n \t
frequency that produces standing waves and is higher than the fundamental frequency<\/dd>\r\n<\/dl>\r\n
\r\n \t
pulse<\/strong><\/dt>\r\n \t
single disturbance that moves through a medium, transferring energy but not mass<\/dd>\r\n<\/dl>\r\n
\r\n \t
standing wave<\/strong><\/dt>\r\n \t
wave that can bounce back and forth through a particular region, effectively becoming stationary<\/dd>\r\n<\/dl>\r\n
\r\n \t
superposition<\/strong><\/dt>\r\n \t
phenomenon that occurs when two or more waves arrive at the same point<\/dd>\r\n<\/dl>\r\n
\r\n \t
transverse wave<\/strong><\/dt>\r\n \t
wave in which the disturbance is perpendicular to the direction of propagation<\/dd>\r\n<\/dl>\r\n
\r\n \t
wave<\/strong><\/dt>\r\n \t
disturbance that moves from its source and carries energy<\/dd>\r\n<\/dl>\r\n
\r\n \t
wave function<\/strong><\/dt>\r\n \t
mathematical model of the position of particles of the medium<\/dd>\r\n<\/dl>\r\n
\r\n \t
wave number<\/strong><\/dt>\r\n \t
2<\/span>\u03c0<\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span><\/span><\/span>2\u03c0\u03bb<\/span><\/span><\/dd>\r\n<\/dl>\r\n
\r\n \t
wave speed<\/strong><\/dt>\r\n \t
magnitude of the wave velocity<\/dd>\r\n<\/dl>\r\n
\r\n \t
wave velocity<\/strong><\/dt>\r\n \t
velocity at which the disturbance moves; also called the propagation velocity<\/dd>\r\n<\/dl>\r\n
\r\n \t
wavelength<\/strong><\/dt>\r\n \t
distance between adjacent identical parts of a wave<\/dd>\r\n<\/dl>\r\n<\/div>\r\n<\/div>\r\n
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Key Equations<\/span><\/h3>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Wave speed<\/td>\r\nv<\/span>=<\/span>\u03bb<\/span>T<\/span><\/span>=<\/span>\u03bb<\/span>f<\/span><\/span><\/span><\/span><\/span><\/span>v=\u03bbT=\u03bbf<\/span><\/span><\/td>\r\n<\/tr>\r\n
Linear mass density<\/td>\r\n\u03bc<\/span>=<\/span>mass of the string<\/span><\/span>length of the string<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03bc=mass of the stringlength of the string<\/span><\/span><\/td>\r\n<\/tr>\r\n
Speed of a wave or pulse on a string under\r\n
<\/div>\r\ntension<\/td>\r\n
\u2223\u2223<\/span>v<\/span>\u2223\u2223<\/span><\/span>=<\/span>F<\/span>T<\/span><\/span><\/span>\u03bc<\/span><\/span><\/span><\/span>\u203e\u203e\u203e\u221a<\/span><\/span><\/span><\/span><\/span><\/span>|v|=FT\u03bc<\/span><\/span><\/td>\r\n<\/tr>\r\n
Speed of a compression wave in a fluid<\/td>\r\nv<\/span>=<\/span>\u0392<\/span>\u03c1<\/span><\/span><\/span><\/span>\u203e\u203e\u221a<\/span><\/span><\/span><\/span><\/span><\/span>v=\u0392\u03c1<\/span><\/span><\/td>\r\n<\/tr>\r\n
Resultant wave from superposition of two\r\n
<\/div>\r\nsinusoidal waves that are identical except for a\r\n
<\/div>\r\nphase shift<\/td>\r\n
y<\/span>R<\/span><\/span>(<\/span>x<\/span>,<\/span>t<\/span><\/span>)<\/span><\/span>=<\/span>[<\/span>2<\/span>A<\/span><\/span>cos<\/span>(<\/span>\u03d5<\/span>2<\/span><\/span><\/span>)<\/span><\/span><\/span>]<\/span><\/span>sin<\/span>(<\/span>k<\/span>x<\/span>\u2212<\/span>\u03c9<\/span>t<\/span>+<\/span>\u03d5<\/span>2<\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>yR(x,t)=[2Acos(\u03d52)]sin(kx\u2212\u03c9t+\u03d52)<\/span><\/span><\/td>\r\n<\/tr>\r\n
Wave number<\/td>\r\nk<\/span>\u2261<\/span>2<\/span>\u03c0<\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span><\/span><\/span>k\u22612\u03c0\u03bb<\/span><\/span><\/td>\r\n<\/tr>\r\n
Wave speed<\/td>\r\nv<\/span>=<\/span>\u03c9<\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/span>v=\u03c9k<\/span><\/span><\/td>\r\n<\/tr>\r\n
A periodic wave<\/td>\r\ny<\/span>(<\/span>x<\/span>,<\/span>t<\/span><\/span>)<\/span><\/span>=<\/span>A<\/span><\/span>sin<\/span>(<\/span>k<\/span>x<\/span>\u2213<\/span>\u03c9<\/span>t<\/span>+<\/span>\u03d5<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>y(x,t)=Asin(kx\u2213\u03c9t+\u03d5)<\/span><\/span><\/td>\r\n<\/tr>\r\n
Phase of a wave<\/td>\r\nk<\/span>x<\/span>\u2213<\/span>\u03c9<\/span>t<\/span>+<\/span>\u03d5<\/span><\/span><\/span><\/span><\/span><\/span>kx\u2213\u03c9t+\u03d5<\/span><\/span><\/td>\r\n<\/tr>\r\n
The linear wave equation<\/td>\r\n\u2202<\/span>2<\/span><\/span>y<\/span>(<\/span>x<\/span>,<\/span>t<\/span><\/span>)<\/span><\/span><\/span>\u2202<\/span>x<\/span>2<\/span><\/span><\/span><\/span>=<\/span>1<\/span>v<\/span>2<\/span>w<\/span><\/span><\/span><\/span><\/span>\u2202<\/span>2<\/span><\/span>y<\/span>(<\/span>x<\/span>,<\/span>t<\/span><\/span>)<\/span><\/span><\/span>\u2202<\/span>t<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22022y(x,t)\u2202x2=1vw2\u22022y(x,t)\u2202t2<\/span><\/span><\/td>\r\n<\/tr>\r\n
Power in a wave for one wavelength<\/td>\r\nP<\/span>ave<\/span><\/span><\/span>=<\/span>E<\/span>\u03bb<\/span><\/span><\/span>T<\/span><\/span>=<\/span>1<\/span>2<\/span><\/span>\u03bc<\/span>A<\/span>2<\/span><\/span>\u03c9<\/span>2<\/span><\/span>\u03bb<\/span>T<\/span><\/span>=<\/span>1<\/span>2<\/span><\/span>\u03bc<\/span>A<\/span>2<\/span><\/span>\u03c9<\/span>2<\/span><\/span>v<\/span><\/span><\/span><\/span><\/span><\/span>Pave=E\u03bbT=12\u03bcA2\u03c92\u03bbT=12\u03bcA2\u03c92v<\/span><\/span><\/td>\r\n<\/tr>\r\n
Intensity<\/td>\r\nI<\/span>=<\/span>P<\/span>A<\/span><\/span><\/span><\/span><\/span><\/span><\/span>I=PA<\/span><\/span><\/td>\r\n<\/tr>\r\n
Intensity for a spherical wave<\/td>\r\nI<\/span>=<\/span>P<\/span>4<\/span>\u03c0<\/span>r<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>I=P4\u03c0r2<\/span><\/span><\/td>\r\n<\/tr>\r\n
Equation of a standing wave<\/td>\r\ny<\/span>(<\/span>x<\/span>,<\/span>t<\/span><\/span>)<\/span><\/span>=<\/span>[<\/span>2<\/span>A<\/span><\/span>sin<\/span>(<\/span>k<\/span>x<\/span><\/span>)<\/span><\/span><\/span>]<\/span><\/span>cos<\/span>(<\/span>\u03c9<\/span>t<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>y(x,t)=[2Asin(kx)]cos(\u03c9t)<\/span><\/span><\/td>\r\n<\/tr>\r\n
Wavelength for symmetric boundary\r\n
<\/div>\r\nconditions<\/td>\r\n
\u03bb<\/span>n<\/span><\/span>=<\/span>2<\/span>n<\/span><\/span>L<\/span>,<\/span><\/span>n<\/span>=<\/span>1<\/span>,<\/span>2<\/span>,<\/span>3<\/span>,<\/span>4<\/span>,<\/span>5<\/span>...<\/span><\/span><\/span><\/span><\/span><\/span>\u03bbn=2nL,n=1,2,3,4,5...<\/span><\/span><\/td>\r\n<\/tr>\r\n
Frequency for symmetric boundary conditions<\/td>\r\nf<\/span>n<\/span><\/span>=<\/span>n<\/span>v<\/span>2<\/span>L<\/span><\/span><\/span>=<\/span>n<\/span>f<\/span>1<\/span><\/span>,<\/span><\/span>n<\/span>=<\/span>1<\/span>,<\/span>2<\/span>,<\/span>3<\/span>,<\/span>4<\/span>,<\/span>5<\/span>...<\/span><\/span><\/span><\/span><\/span><\/span>fn=nv2L=nf1,n=1,2,3,4,5...<\/span><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/section><\/div>\r\n
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Summary<\/h3>\r\n<\/div>\r\n
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16.1<\/span>\u00a0<\/span>Traveling Waves<\/span><\/h4>\r\n