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Review for Exam 1 Alex Beutel . September 29, 2008 . Physics 143 Constants: h = 6.6 × 10−34 Js m c = 3.0 × 108 s m3 G = 6.67 × 10−11 kgs2 m v = 340 s 1 light-year = 9.46 × 1015 meters Useful trig identity for beats or interference: cos(α) + cos(β) = 2 cos(α + β) cos(α − β) Formulas v= FT = µ B µ (1) (2) Harmonics Wave Equation (3) (4) (5) Power through a wire ν is frequency (6) (7) (8) General gamma (9) (10) (11) (12) (13) SIMPLIFIED 2 Speed of sound in air v = λf n L=λ 2 ∂2y 1 ∂2y =2 2 ∂x2 v ∂t A cos(kx − ωt) 1 P = µω 2 A2 v 2 ω = 2πν 2π λ= k 1 γ(v) = 2 1 − v2 c x x= γ t t= γ x = γ(v)(x − vt) v t =γ t− 2 x c t = γ(v)(t − vx) mA c = mB c + mC c + mD c + TB + TC + TD τ = γτ 2 2 2 (14) (15) (16) Decay energy conservation Decay rate 1 Energy and Momentum Conservation h hf E = = λ c c p = γ(u)mu p= E = γ(u)mc E= mc 2 u2 c2 2 Momentum of a photon Why γ(u) not u ???? v = γ(v) E − (pc) = γ(v) mc2 − vmu c = γ(v) p − v E c2 For a massless particle (17) (18) (19) (20) 1− p= mu 1− p =p E= f =f u= (21) u2 c2 v c v c 1− 1+ (22) (23) p2 c2 + m2 c4 1− 1+ v c v c Relativistic doppler shift Velocity Addition (24) (25) u−v 1 − uv c2 When a collision produces different particles there is a fairly set methodology of equations to follow. In the rest frame, all particles are still. This is important in conjunction with s being an invariant quality meaning it is the same in all frames. s2 = (E1 + E2 )2 − c2 (p1 + p2 )2 In the rest frame, v for each particle is zero therefore all that is left of s2 is: s2 = m1 c2 + m2 c2 Another useful equation for substitution in solving is: E= Stats σx = 1 N −1 (xi − x)2 ¯ (29) (30) p2 c2 + m2 c4 (28) (27) (26) σx σx = √ ¯ N Binomial Distributions x = Np ¯ N p(1 − p) N! PN,p (x) = px (1 − p)N −x (N − x)!x! σx = In equation 33, we get the probability of observing x heads in N flips of a coin. (31) (32) (33) 2 Bell’s Inequality Bell’s Theorem is that Bell’s Inequality exists. If the particles carry the information with them then this must be true: P0,φ + Pφ, π ≥ P0, π 2 2 This is dependent on knowing previously that the spins are opposite. However, when we actually do the experiment (with certain values for φ such as broken. π 4 ), this inequality is Question #9 Energy of system is greater than just m1 + m2 . Also includes energy in the spring being compressed and energy of the band being wrapped around it. Even once the band is cut, before the balls move the spring is still compressed and the energy is: M c2 > m1 c2 + m2 c2 M c2 = γ(v1 )m1 c2 + γ(v2 )m2 c2 Sound Waves If the observer is moving then velocity changes and wavelength is constant. If only the source is moving, velocity is constant and both frequency and wavelength change to adapt to this (based on wavelength). 3 

Document Info

Posted By:

Alex Beutel

Date:

Sunday, September 28, 2008

School:

Duke University

Class:

Physics 143L

Tags:

• Formula Sheet
• Review Sheet
• Relativity
• Physics

About this Document

This is a review sheet for the first exam in Dr. Socolar's Physics 143 class on Optics and Modern Physics.