Physics NYC Equation Sheet Simple Harmonic Motion x F kx = − () cos( ) ω φ = + xt A t 2 2 f T π ω π = = 2 L T g π = 2 m T k π = 2 1 2 v K m = g U mgh = 2 1 2 s U kx = 2 1 2 total E K U kA = + = Quantum Physics hc E hf λ = = 0 φ = − eV hf !"# = ! h p λ = ( ) 1 cos e h mc λ φ Δ = − Δx Δp x ≥ () 2 2 2 1 2 8 n nh E nE mL = = 2 () sin( ) n nx x L L π ψ = 1 2 2 13.6eV n E E n n − = = Waves and Sound ( , ) A cos( ) yxt kx t ω = ± 2 k π λ = v f k ω λ = = F v μ = 2 2 1 av 2 F P A μ ω = SW (,) sin( )sin( ) yxt A kx t ω = f beat = Δf = f a − f b av P I A = 0 10log I I β = f L = v ± v L v v S ! " # # $ % & & f S Relativity 0 γ Δ = Δ t t 0 γ = l l 2 2 1 1 u c γ = − 2 1 / − = − x x x ' v u v vuc 2 1 / + = + x x x v u v vuc V AB = V AD +V DB 1 + V AD V DB c 2 p = γ m v 2 2 E mc K mc γ = = + ( ) ( ) 2 2 2 2 = + E mc pc Interference and Diffraction sin d m θ λ = ( ) 1 2 sin d m θ λ = + sin a m θ λ = 2 sin π φ θ λ = d 2 sin π β θ λ = a 1.22 λ θ = D 2 max cos 2 I I φ = 2 max sin( / 2) /2 I I β β = Constants Speed of sound in air (20°) = 343 m/s Threshold of hearing: 12 2 0 1.0 10 W/m I − = × Audible range: 20 Hz to 20000 Hz Visible spectrum: 400 nm to 700 nm 8 3.00 10 m/s c = × 19 1 eV 1.60 10 J − = × 31 e 2 9.11 10 kg 0.511 MeV/ m c − = × = 27 p n 2 1.67 10 kg 938 MeV/ m m c − = = × = 34 15 6.63 10 Js 4.14 10 eV s h − − = × ⋅ = × ⋅ 2 9.81 m/s g = 1 13.6 eV E = − for hydrogen atom e = 1.6 x 10 -19 C