Wave Equation: $y(x,t) = A \sin(kx - \omega t + \phi)$
Wave Speed: $v = f\lambda = \frac{\omega}{k}$
Speed of transverse wave on string: $v = \sqrt{\frac{T}{\mu}}$
Speed of sound in fluid: $v = \sqrt{\frac{B}{\rho}}$
Speed of sound in solid rod: $v = \sqrt{\frac{Y}{\rho}}$
Intensity: $I = \frac{P}{A} \propto A^2 \omega^2$
Doppler Effect: $f' = f \left(\frac{v \pm v_o}{v \mp v_s}\right)$
Standing Waves:
- String fixed at both ends: $\lambda_n = \frac{2L}{n}$, $f_n = \frac{nv}{2L}$
- Open organ pipe: $\lambda_n = \frac{2L}{n}$, $f_n = \frac{nv}{2L}$
- Closed organ pipe: $\lambda_n = \frac{4L}{2n-1}$, $f_n = \frac{(2n-1)v}{4L}$
Beats: $f_{beat} = |f_1 - f_2|$

Coulomb's Law: $F = k \frac{|q_1 q_2|}{r^2}$ where $k = \frac{1}{4\pi\epsilon_0}$
Electric Field: $\vec{E} = \frac{\vec{F}}{q_0} = k \frac{q}{r^2} \hat{r}$
Electric Field (continuous charge dist.): $\vec{E} = \int d\vec{E}$
Electric Potential: $V = \frac{U}{q_0} = k \frac{q}{r}$
Relation between E and V: $\vec{E} = -\nabla V = -\left(\frac{\partial V}{\partial x}\hat{i} + \frac{\partial V}{\partial y}\hat{j} + \frac{\partial V}{\partial z}\hat{k}\right)$
Electric Dipole Moment: $\vec{p} = q\vec{d}$
Torque on a dipole: $\vec{\tau} = \vec{p} \times \vec{E}$
Potential Energy of a dipole: $U = -\vec{p} \cdot \vec{E}$
Gauss's Law: $\oint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\epsilon_0}$

Current: $I = \frac{dQ}{dt} = nAve_d$
Ohm's Law: $V = IR$
Resistance: $R = \rho \frac{L}{A}$
Resistivity (temperature dependence): $\rho_T = \rho_0 [1 + \alpha(T - T_0)]$
Resistors in Series: $R_{eq} = \sum R_i$
Resistors in Parallel: $\frac{1}{R_{eq}} = \sum \frac{1}{R_i}$
Kirchhoff's Laws:
- Junction Rule: $\sum I_{in} = \sum I_{out}$
- Loop Rule: $\sum \Delta V = 0$
Electrical Power: $P = VI = I^2R = \frac{V^2}{R}$
Cells in Series (same polarity): $E_{eq} = \sum E_i$, $r_{eq} = \sum r_i$
Cells in Parallel (same E): $E_{eq} = E$, $\frac{1}{r_{eq}} = \sum \frac{1}{r_i}$
Wheatstone Bridge (balanced): $\frac{R_1}{R_2} = \frac{R_3}{R_4}$
Meter Bridge: $\frac{R}{S} = \frac{l}{(100-l)}$
Potentiometer:
- Comparing EMFs: $\frac{E_1}{E_2} = \frac{l_1}{l_2}$
- Internal Resistance: $r = R(\frac{l_1}{l_2} - 1)$

Biot-Savart Law: $d\vec{B} = \frac{\mu_0}{4\pi} \frac{I d\vec{l} \times \hat{r}}{r^2}$
Magnetic Field (long straight wire): $B = \frac{\mu_0 I}{2\pi r}$
Magnetic Field (circular loop at center): $B = \frac{\mu_0 I}{2R}$
Magnetic Field (solenoid): $B = \mu_0 n I$
Magnetic Field (toroid): $B = \frac{\mu_0 N I}{2\pi r}$
Ampere's Law: $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}$
Lorentz Force: $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$