F = -kx.
x(t) = Acos(ωt + φ), v(t) = -ωAsin(ωt + φ), a(t) = -ω2Acos(ωt + φ) = -ω2x.
ω = sqrt(k/m) = 2πf = 2π/T.
Pendulum: T = 2π(L/g)1/2
Traveling waves: y(x,t) = A sin(kx ± ωt + φ)
Waves on a string: v = (F/μ)1/2
Sound level: β = 10 log10(I/I0)
Beat frequency: |f1 - f2|
Standing sound waves:
tube of length L with two open ends: L = nλ/2, n = 1, 2, 3, ...
tube of length L with one open end and one closed: L = nλ/4, n = odd integer
f = f0(v - vobs)/(v - vs) (velocity components in the direction of v are positive)
Ideal gas: PV = (2/3)N(m<v2>/2) = (2/3)U, PV = NkBT =
kB = 1.381*10-23 J/K, R = 8.31 J/(mol K)
Linear expansion: ΔL = αLΔT
Thermal conductivity: ΔQ/Δt = -kA ΔT/Δx
Stefan-Boltzmann Law: Radiated power = emissivity * σ * T4 * Area
Wien Law: λmax(nm) = 3*106/T(K)
Specific heat: c = ΔQ/(m ΔT)
Latent heat: ΔQ = mL
First law: ΔU = ΔQ - ΔW
Second law: Qhigh/Thigh = Qlow/Tlow
Entropy: S = kB lnΩ, ΔS = ΔQ/T
1 Cal = 1 kcal = 4186 J