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Week 5 Notes

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by: Shanee Dinay

Week 5 Notes PHYS 5B

Shanee Dinay
GPA 3.94

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Day 12 and Day 13 of class. Starting to talk about waves
Intro to Physics II
Class Notes
Intro to Physics, Physics, physics 2, waves
25 ?




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"You can bet I'll be grabbing Shanee studyguide for finals. Couldn't have made it this week without your help!"
Marjory Gorczany Sr.

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This 3 page Class Notes was uploaded by Shanee Dinay on Saturday February 6, 2016. The Class Notes belongs to PHYS 5B at University of California - Santa Cruz taught by A.Steinacker in Fall 2015. Since its upload, it has received 66 views. For similar materials see Intro to Physics II in Physics 2 at University of California - Santa Cruz.


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Date Created: 02/06/16
Day 12 ­ 2/1/2016  Topics for Midterm  ­ fluids of all kinds, not differential equations  ­ harmonic oscillator, up to damping  ­ simple harmonic motion  ­ some problems with damping and resonance after exam  ­   Read 15.1, 15.2, 15.4    Waves  y(x, t) = Asin(kx ­ wt)  displacement amplitude of displacement  t = 0  y(x, t) = Asin(kx)  x = 0  y(x=0, t) = Asin(­wt) = ­Asin(wt)  y(x, t=0) = y(x + λ, t=0)  Asin(kx) = Asin[k(x+λ)]  kλ = 2π  2π The wave number k =  γ   Asin(wt) = Asin[w(t+T)]  wT = 2π → w =  2π = rad angular frequency  T s frequency f →  f =    T1 Ex. v​w​= 0.5 cm/s A = 1cm T = 8s λ = 4cm  k =  π rad ω  =  2π =  π rad  2 cm T 4 cm y(x, t) = 1 cm sin ( π rax − π rat)  2 cm 4 s verify, does 4(x = 0, t = 0) = ? graphs says no!  Initial Phase  Phase φ  =  kx  −  ωt y(x,t) = Asin(φ  + φ )o π π π sin(kx ­ ωt+  )2= sin(φ)cos( ) + c2s(φ)sin( )  2 Ex. y(x, t) = Asin(kx ­ wt) = Asin(x ­ t)k = 1, w = 1    t = 0 y(x, 0) = Asinx  t = π y(x,  ) = Asin(x ­  ) = Asinxcos( ) ­ Acosxsin( )  π 2 2 2 2 2 y(x,  ) = ­Acosx  2 y = Asin(kx ­ wt) ← is a right traveling wave  y = Asin(kx + wt) ← is a left traveling wave  Speed of the Wave    dy dx dt = 0 = Acos(kw ­ wt)[k dt ­ w]  dx dx v(t) if dt ­ w = 0 dt = vw  w w vw​=  kright traveling vw​ = ­k left traveling  Superposition of Waves    Day 13 ­ 2/3/2016  Physics 5b    Women in Physics Mentoring Sign­Ups    y(x,t) = Asin(kx ­ wt + φ o  2π 2π k =  γ w =  T  = 2πf  Example. String  2g T s T​s​ 5N linear density: u  =  m v​w​=  u  √ f = 100 Hz A = 2mm  y(x, t) = Asin(kx ­ wt + φo)  w = 2π f = 200π rad/s  5N vw​=  2 • 10 kg/m0 m/s  √ 2πf k =  γπ vw​=  k=  2π/γ= f • γ  w 200 rad/s k =  w  =  50 m/s = 4π rad/m  t = 0, x = 0  y(x=0,t=0) = A  A = Asin(kx + wt + φ )o φ  =     2 y(x, t) = 2mm sin(4π rmdx ­ 200π rsdt + 2)  y1​= Asin(kx ­ wt) y2​= Asin(kx + wt)  t = π wt =  •  =   π 8 T 8 4 y​(x,  ) = Asin(kx ­  )  y​ (x,  ) = Asin(kx +  )  1​ 8 4 2​ 8 4 once wave shifts A gets smaller  Standing Waves  1. closed closed system  y1​+ y2​= Asin(kx ­ wt) + Asin(kx + wt) = ​ynet​2Acos(wt)sin(kx)  nodes at both ends  y(o, t) = y(L, t) = 0  2π y(x = L, t) = 2Acos(wt)sin(kL) = 0 kL ­ Cπ λNL = nπ  2L vw λ n   n fn  =  n2L  λ1 n = 1, λ  = 2L, L =  2L γ  2. open open system  y​(x, t) = 2Acos(wt)cos(kx)  net​ y(x = 0) = 2Acos(wt) antinode  x = L we also want y(x = L, t) = antinode cos(kL) = ±, kL = nπ  2L λ n n   3. closed open system  y(x, t) = 2Acos(wt)sin(kx)  closed node at 0, and open at L  need antinode at x = L for all t sin(kL) = ±1 kL = (2n + 1)   π 2 2πL  =  (2n + 1)π λn= 4L  for n = 1, 3, 5, …   λn 2 n count quarter wave lengths   


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