## Formulas 3

#### Oscillations and Waves:

Harmonic motion:
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

Doppler effect:
f = f0(v - vobs)/(v - vs)  (velocity components in the direction of v are positive)

#### Temperature and Heat

Ideal gas:  PV = (2/3)N(m<v2>/2) = (2/3)U,  PV = NkBT = nRT
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

#### Thermodynamics:

First law:  ΔU = ΔQ - ΔW
Second law:  Qhigh/Thigh = Qlow/Tlow
Entropy:  S = kB lnΩ,  ΔS = ΔQ/T

#### Conversion:

Cal = 1 kcal = 4186 J