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Standing waves  one end fixed and one end free
 n=1, 3, 5, ...
 L = string or pipe length
 fixed end is a node, open/free end is antinode

Beat frequency  alternating increases and decreases in intensity
 Pitch correlates with frequency
 2 waves with constant A and different f interfere

Doppler Effect
OR
 Apparent frequency of the source is increased (apparent wavelength is decreased) as source approaches observer, and the opposite as the source leaves
 Because pitch correlates with f, apparent pitch also increased as source approaches and decreased as it leaves

Angular frequencies of a mass on a spring or a pendulum
 Whack 'em: on a spring
 Wiggle: on a pendulum

Simple Harmonic motion (mass on a spring, pendulum, planetary orbit viewed from the side, e movement in alternating current)
 Hooke's Law:
 ⇒acceleration is proportional and oppositely directed to displacement
 ⇒ acceleration is proportional to frequency squared

Wave velocity is medium dependent
 positively correlates with tension, bulk modulus, pressure (gas) & temperature (gas)
 negatively correlates with density and μ (mass per unit length)

Coulomb's law: electric force, F, as a function of Boltzmann's constant, k
 Q's are charges and r is centercenter distance
 F is repulsive if both charges positive or negative
 F is attractive if one charge positive and the other is negative

Electric field due to a point charge, q, at a distance, r
E is a vector that points away from positive toward negative charge

Electric potential energy stored between the interaction between two point charges

Electric potential, Voltage, due to a point charge
in Volts (V) or J/C

Force in a constant electric field
F is in the same direction as E if q is positive and in the opposite direction is q is negative

Electric potential, Voltage, in a constant electric field

Energy gained by a charge, q, in a constant electric field, E.
 Energy gained is force times distance traveled through the field
 Potential is the energy per unit charge

Force,F, on a charge,q, moving through a magnetic field,B, with a velocity, v.
Magnitude of the force is expressed in terms of the angle, θ, between velocity and the magnetic field

Ohm's law (electronic circuits) to relate electric potential (V) with the current (I) and the resistance (R) of the device through which it flows.

Resistance of a wire
 ρ is resistivity (experimentally determined for a given substance, units are Ω·m), L is Length of the wire, & A is the crosssectional area of the wire
 R is measured in Ohms, Ω



Total resistance in a circuit with resistors in series.

Effective resistance in a circuit with resistors in parallel.

Capacitance, C, of a capacitor
Charge per voltage

Effective capacitance of capacitors in series

Effective capacitance of capacitors in parallel

Electric energy stored by a capacitor
 Electric energy stored is given in terms of the capacitance, C, and the potential difference between the conductors, V.
 Remember in a constant electric field:

Electromagnetic wave speed in a vacuum, c
*same as any wave

Snell's Law: relating refractive indices, angle of incidence, and angle of refraction with respect to the perpendicular of the interface

Total internal reflection and the critical angle, θ_{c}
Only applies if n _{1}>n _{2} and light is traveling in medium 1

Index of refraction, n for a given medium
 c is speed of light in a vacuum
 v is the speed of light in that medium
 n_{air} is about 1
 n_{water} = 1.3
 n_{glass} = 1.5

Energy, E, of one photon and Planck's constant, h
Energy is dependent on its frequency

The lens equation and positive negative determinations for focal length, object distance, and image distance
 focal length, f, is positive for converging and negative for diverging lenses
 object distance, d_{o}, is positive if it is on the side of the lens from which light is coming and negative if on the opposite side
 image distance, d_{i}, is positive if it is on the opposite side of the lens from which the light is coming and negative if on the same side
 This also applies to mirrors but remember that light comes from the same side of a mirror as the observer and the opposite side of a lens.

Focal length of a spherical mirror
r is the radius of curvature

Lateral magnification, m, for a lens or mirror
 For an upright image, magnification is positive and for an inverted image, m is negative.
 Images and focal lengths are positive, real, & inverted on the same side as the observer.

Power of a lens, P, in diopters (m^{1})
Power is inversely proportional to the focal length, f

General nature of diffraction
 If a wave passes through an opening smaller or the same size as wavelength, it will bend (spread out).
 Smaller opening > more diffraction

Aufbau Principle
 Orbitals fill lowest energy to highest
 1s
 2s 2p
 3s 3p 3d
 4s 4p 4d 4f
 5s 5p 5d 5f
 6s 6p 6d 6f

Hund's rule
 single electrons enter each orbital of equal energy before a second electron of opposite spin enters any orbital and spin remains parallel if possible
 Ex. Nitrogen:
 N= 1s (↑↓) 2s (↑↓) 2p_{x}(↑) 2p_{y}(↑) 2p_{z}(↑)

Pauli Exclusion Principle
no two electrons in an atom can have the same set of four quantum numbers, each orbital of specific quantum numbers (n,l,m) can hold at most two electrons with opposite spins (m_{s}=1/2 for one and +1/2 for the other)

Heisenberg Uncertainty Principle
position and momentum of a particle cannot both be exactly known at the same time

Chemistry: Quantum numbers
 Principal, n = shell level (higher n means increased size and energy)
 Azimuthal, l = subshell (s, p, d, & f); l=0 means subshell s (for each new shell, n, l=n1)
 Magnetic, m_{l} = precise orbital numbered l to +l (for n=1; l=0 and m=0; for n=3, l=2 and m=2, 1, 0, +1, or +2, 5 orbitals)
 Electron spin, m_{s} = 1/2 or +1/2 (unpaired electrons in same shell have parallel spins, paired electrons in same orbital have opposite spins)


Standard Molar Volume of an Ideal Gas at STP
 22.4L/mol
Standard Conditions: 25 ^{o}C and 1atm

Partial Pressure of a Gas in a mixture

Dalton's Law: Total Pressure of a mixture of gasses

Average Kinetic Energy of one mole of gas (or liquid) molecules

Graham's Law: average rms velocities of two gasses in a mixture

Effusion rates of 2 gasses in a mixture through a pinhole
M represents molecular weights

Van der Waal's Equation: behavior of a Real Gas
Where a relates to the strength of intermolecular interactions and b is the volume of one mole of the gas

General (qualitative) characteristics of a Real gas compared with an Ideal gas
because of the volume of the gas molecules
because of attractive intermolecular forces

Types of Solids and descriptions of each
 Molecular solid: molecules held in place by dispersion forces, dipole interactions, and/or hydrogen bonds
 Metallic Solid: atoms held in place by delocalized bonding
 Network Solid: contains an array of covalent bonds linking every atom to its neighbors
 Ionic Solid: Contains cations and anions attracted to one another by coloumbic interactions (charge forces)

Intermolecular Forces: Hydrogen Bonding
Involves the lone pair of electrons on an electronegative atom of one molecule and a polar bond to hydrogen in another molecule, generally confined to molecules that contain O, N, and F atoms

Intermolecular Forces: Dipole Interactions
Describe the attraction between the negatively charged end of a polar molecule and the positively charged ends of neighboring polar molecules

Intermolecular Forces: Dispersion Forces or London Dispersion Forces
Attraction between the negatively charged electron cloud of one molecule and the positively charged nuclei of neighboring molecules

Rate law of an elementary chemical reaction: dependence of reaction rate on [reactants]
*If reaction is not elementary replace orders with α,β, etc and determine orders experimentally:

Arrhenius equation for temperature dependence of reaction rate constant, k
 z is the number of collisions, p is the fraction of collisions occurring in the correct orientation, and e is the fraction of collisions containing sufficient energy to carry out the reaction (higher Ea means lower reaction rate, higher temperature means higher reaction rate)

The law of mass action: forward and reverse reaction rates are equal at equilibrium so, for the following elementary reaction:
*This applies to nonelementary reactions as well.

Reaction quotient, Q, for a nonequilibrium state predicts which direction a reaction will proceed.
 Q=K @ equilibrium
 Q>K then reverse reaction predominates
 Q<K then forward reaction predominates

Le Chatelier's principle regarding a reaction at equilibrium that is stressed in one of three ways:
 1) addition or removal of a reactant or product
 2) changing the pressure of the system
 3) heating or cooling the system


Molarity; Molality; Mole fraction (χ); mass percent; parts per million
 Molarity, M = moles solute/volume solution
 Molality, m = moles solute/kg solvent
 mole fraction, χ = moles solute/total moles
 mass percent = mass solute/total mass of solution * 100%
 parts per million, ppm = mass solute/total mass of solution * 10^{6}


Henry's Law: Solubility of Gas in a Liquid
 is directly proportional to the partial pressure of the gas above the liquid
 Think: CO_{2} leaves soda after pressure is released.
 Mathematically: (p is partial pressure, c is concentration of gas in liquid and k is a constant)

Thermochemistry State Variables
 Conditions that must be specified to establish the state of a system
 Pressure (P)
 volume (V)
 Temperature (T)
 amounts of substances (n)

Standard Enthalpy of Formation
 Enthalpy change accompanying the formation of one mole of a chemical substance from pure elements in their most stable forms under standard conditions
 Symbol:

Hess's Law of heat summation
The enthalpy change for any overall process is equal to the sum of enthalpy changes for any set of steps that leads from the reactants to the products (ΔH is path independent)

Enthalpy (definition and equation)
 A thermodynamic quantity whose change equals the heat flow at constant pressure

Henderson Hasselbalch Equation for calculating the pH of solutions of weak acids (or bases)

Relate Equilibrium and ΔG

