AE1241-I Physics

Doing my best to NOT shit myself!!!

Simple pendulum period

2π √(L/g)

Critical damping coefficient

2√(mk)

Wave speed

√(T/μ), μ = m/L

Time for wave to travel a hanging rope of length L?

√(2L/g)

Sound intensity level in decibels?

10 log₁₀(I / I₀)

Total dB level from N identical sources?

β_single + 10 log₁₀(N)

Beat frequency between two sources?

|f₁ − f₂|

Wavelength & frequency in an open-open tube?

λₙ = 2L/n, fₙ = (nv)/2L

n = harmonics (number of HALF-wavelengths present)

Wavelength & frequency in an open-closed tube?

λₙ = 4L/n, fₙ = nv/4L

n= harmonics (number of QUARTER-wavelengths present)

Doppler effect (SOURCE)?

f / (1 ± M(source))

Ratio of Doppler frequencies (approach vs. depart)?

f_app / f_dep = (v + v_s) / (v − v_s)

Mach cone angle for shock wave?

sinθ = 1/M(source)

General wave relation?

v = f λ

Linear thermal/volume expansion?

ΔL =* (α/β) * (L₀/V0) * ΔT

Number of molecules in a speed range (Maxwell)?

N = ∫ f(v) dv from v₁ to v₂

How does molecular speed scale with temperature?

v ∝ √T

Internal energy from degrees of freedom?

U = (f/2) NkT

f = degrees of freedom

Relative humidity?

RH = p_vapor / p_sat(@ T) × 100%

COP of a Carnot refrigerator?

COP = T_c / (T_h − T_c)

Heat extracted by Carnot refrigerator?

Q_c = COP · W

Adiabatic process relations?

TV^(γ−1) = const, PV^γ = const

Latent heat absorbed/released?

Q = mL

Entropy change during heating?

ΔS = mc ln(T₂/T₁)

Split from phase change entropy!

Entropy change during a phase transition?

ΔS = Q / T

Rate of heat conduction?

Q̇ = kAΔT / d

Ideal gas law?

PV = nRT

Work in an isothermal process?

W = nRT ln(V₂/V₁)

Work in an isochoric process?

W = 0

Work in an adiabatic process?

W = (P₁V₁ − P₂V₂) / (γ − 1)

First Law of Thermodynamics?

ΔU = Q − W

Thermal efficiency of a heat engine?

η = W_net / Q_in

Electric field from electric potential?

E = -∇V

Coulomb's Law?

F = (1/4πε₀) · q₁q₂/r²

Electric field outside a charged cylinder?

E = ρR₀² / (2ε₀R)

Superposition of electric fields?

E_T = ∑E_i

Electric potential from a charge element ?

V = (1/4πε₀) · ∫dq/r

Capacitance of a parallel plate capacitor?

C = εA/d

Permittivity with a dielectric?

ε = K ε₀

K = dielectric constant

Equivalent capacitance in series?

1/C_eq = Σ 1/Cᵢ

Equivalent capacitance in parallel?

C_eq = Σ Cᵢ

Charge on a capacitor?

Q = CV

Energy stored in a capacitor?

U = ½CV²

Capacitance with layered dielectrics? (Series application)

C = ε₀A / (d₁/K₁ + d₂/K₂)

Gauss law?

∫E dot dA = Q(encl.)/ϵ0

Voltage from electric field

V= -∫E dot dr

Doppler (observer moving)?

f(1 ± M source)

Method for calculating total dB FROM different intensities

1. Convert each dB level back to intensity:

2. Sum all intensities:

3. Convert back to dB (known equation)