Week 5 Notes
Week 5 Notes PHYS 5B
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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. vw= 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 Ts 5N linear density: u = m vw= 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) = ynet2Acos(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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