Physics

Converging lenses

Convex lens (reading glasses - needed by people who are farsighted) Always thicker at the center

sign conventions for mirrors

Focal length of converging mirrors (and converging lenses) will always be positive. Focal length of diverging mirrors (and diverging lenses) will always be negative. Image types with single lens or mirror (assuming o is positive): IR and UV: Inverted images are always Real Upright images are always Virtual

Circular loop of current-carrying wire

For circular loop of current-carrying wire of radius r, the magnitude of the magnetic field at center of circular loop is: This equation gives the magnitude of magnetic field only at the center of the circular loop of current-carrying wire with radius r.

Threshold frequency

Minimum frequency of light that causes ejection of electrons is known as the threshold frequency, which depends on type of metal being exposed to radiation. Photoelectric effect is all or nothing response: if frequency of incident photon is less than threshold frequency then no electron ejected. But if frequency of photon is greater than threshold frequency then electron ejected and maximum KE of ejected electron will be equal to the difference between hf and hfT (work function). Light beam consists of integral number of light quanta called photons. Energy of each photon is proportional to frequency of light: E=hf. Can easily find wavelength (c=wavelength*frequency). 1 angstrom = 10^-10 m

Power

The rate at which energy is dissipated by a resistor is the power of the resistor and cal be calculated:

Dielectrics in isolated capacitors

When dielectric material is placed in isolated, charged capacitor (a charged capacitor disconnected from any circuit) the voltage across capacitor decreases. This is result of dielectric material shielding the opp charges from each other. By lowering V across charged capacitor, the dielectric has increased the capacitance of capacitor by factor of k. increase in C arises from decrease in V.

Spherical mirrors

have an associated center of curvature and radius of curvature. Center of curvature is a point on the optical axis located at a distance equal to the radius of curvature from the vertex of the mirror; in other words, the center of curvature would be the center of the spherically-shaped mirror if it were a complete sphere. Focal length (f) is the distance b/w the focal point (F) and the mirror. For all spherical mirrors, f = r/2 where the radius of curvature (r) is the distance b/w C and mirror. The distance b/w the object and mirror is o; the distance b/w the image and the mirror is i. 1/f = 1/o + 1/i = 2/r *must have same units ->Using this formula can determine image distance; if image has positive distance, it is real image (in front of mirror); if has negative distance, it is virtual and located behind mirror.

Longitudinal wave

have particle oscillation parallel to the direction of propagation and energy transfer. Sound waves!

Ferromagnetic materials

have unpaired electrons and permanent atomic magnetic dipoles that are normally oriented randomly so has no net magnetic dipole. But these materials will become strongly magnetized when exposed to magnetic field or under certain temps. Iron, nickel, cobalt bar magnets

SI unit of charge

is coulomb and fundamental unit of charge is: Proton (+) and more massive than electron

Coulomb's Law

quantifies the magnitude of the electrostatic force, Fe b/w two charges:

Strings

string fixed rigidly at both ends, they are nodes. If standing wave has only one antinode b/w the two nodes, the length of string corresponds to 1/2 wavelength. if 2 antinodes then must be 3rd node b/w them. length of string corresponds to wavelength. Length L of a string must be equal to some multiple of half-length. Wavelength of standing wave and length of string L, where n is positive nonzero integer and it's called the harmonic (**for strings attached at both ends, the number of antinodes present will tell you which harmonic it is). the lowest frequency (longest wavelength) of standing wave is fundamental frequency (1st harmonic).

Phase

when analyzing waves that are passing through the same space, we can describe how in step or out of step the waves are by calculating the phase difference. 2 waves that have same frequency, wavelength, and amplitude and that pass thru same space at same time, we can say that they are in phase if their respective crests and troughs coincide (line up with each other). When perfectly in phase, the phase difference is zero. But if 2 waves travel thru same space such that crests of one wave coincide with troughs of other, then we say they're out of phase and phase diff is one-half of a wave.

change in sound level

when intensity of sound is changed by some factor, one can calculate new sound level. If/Ii is ratio of final intensity to initial intensity.

Photoelectric effect

when light of high frequency (blue to UV) is incident on metal in vacuum, the metal atoms emit electrons (photoelectric effect). e- liberated from metal by photoelectric effect will produce a net charge flow per unit time or current. when light's frequency is above the threshold frequency, the magnitude of resulting current is directly proportional to the intensity (and amplitude) of the light beam.

Reflection

when light travels thru homogeneous medium, travels in straight line (rectilinear propagation). Theory of geometric optics - behavior of light at boundary of medium or interface b/w two media. Reflection = rebounding of incident light waves at boundary of medium. Light waves reflected are not absorbed into second medium; rather, they bounce off the boundary and travel back thru first medium. Law of reflection = theta1 (incident angle) = theta2 (reflected angle) Measured from the normal - line drawn perpendicular to boundary of medium; all angles in optics are measured from normal, not surface of medium.

Open Pipes

**For open pipes, the number of nodes present will tell you which harmonic it is. End of pipe is open so supports an antinode. Open pipe has antinodes at both ends. If only one node b/w 2 antinodes at the ends, the length of pipe is 1/2 the wavelength of this standing wave. This is like string except ends are antinodes instead of nodes. second harmonic has wavelength equal to length of pipe.

Traveling and standing waves

A wave that travels, or propagates. Traveling waves have nodes and antinodes that move with propagation. when both ends of string are fixed and traveling waves are excited in the string. Certain wave frequencies will cause interference b/w the traveling wave and its reflected wave such that they form a waveform that appears to be stationary. The only apparent movement of string is fluctuation of amplitude at fixed points along length of string. These waves are called standing waves. Have defined nodes and antinodes. Points in wave that remain at rest (where A is zero) are known as nodes. Points midway b/w nodes fluctuate with max amplitude and are known as antinodes. Pipes open at both ends can support standing waves. math related standing wave wavelength and length of string or the open pipe are similar. Pipes open at one end and closed at other can also support standing waves, but bc closed end contains a node and open end contains an antinode, the math is diff.

Equipotential Lines

An equipotential line is a line on which the potential at every point is the same. the potential difference b/w any two points on an equipotential line is zero. No work is done when moving a test charge q from one point on an equipotential line to another. Work will be done in moving test charge from one line to another but work depends only on the potential difference of the two lines and not on pathway taken b/w them.

Total Internal Reflection

As incident angle is increased, the refracted angle also increases, and eventually a special incident angle called the critical angle is reached, for which the refracted angle equals 90 degrees. At critical angle, the refracted light ray passes along the interface b/w the two media. The critical angle can be derived from snell's law if theta2= 90, such that: theta(critical) = sin^-1(n2/n1) Total internal reflection = when all light incident on boundary is reflected back into original material, results with any angle of incidence greater than the critical angle. Total internal reflection occurs as light moves from medium with higher refractive index to medium with a lower one.

Nuclear Reactions

B/c binding E per nucleon is greatest for intermediate-sized atoms (most stable), when small atoms combine or large atoms split, a great amount of E is released. elements preceded by atomic number as subscript and mass number as superscript. Atomic number Z is number of protons; the mass number is number of protons and neutrons.

Thin Spherical Lenses

B/c light can travel from either side of a lens, a lens has 2 focal points, with one on each side - the focal length can be measured in either direction from the center.

Capacitance

Capacitance of a parallel plate capacitor is dependent upon geometry of 2 conduction surfaces. d is separation of 2 plates. The separation of charges sets up an electric field b/w the plates of parallel plate capacitor. The electric field b/w plates of parallel plate capacitor is a uniform electric field with parallel field vectors, the magnitude can be calculated as: V=Ed Direction of electric field is from positive plate toward the negative plate.

Capacitors

Capacitors are able to hold charge at a particular voltage. When 2 electrically neutral metal plates are connected to a voltage source, positive charge builds up on the plate connected to the positive (higher potential) terminal, and negative charge builds up on the plate connected to the neg (lower potential) terminal. The two plate system is a capacitor bc it can store a particular amount of charge at a particular voltage. The capacitance of capacitor is defined as ratio of magnitude of charge stored on one plate to potential difference (voltage) across capacitor. SI unit is farad (C/V).

Circuit Laws

Charge and E cannot be created nor destroyed. An electric circuit is conducting path that usually has one or more voltage sources (such as a battery) connected to one or more passive circuit elements (such as resistors). Kirchhoff's laws are 2 rules that deal with the conservation of charge and energy within a circuit. Kirchhoff's Junction Rule: at any point or junction in a circuit, the sum of currents directed into that point equals the sum of currents directed away from that point. This is expression of conservation of electrical charge and can be expressed as: I(into junction) = I(leaving junction). Kirchhoff's Loop Rule: around any closed circuit loop (but not necessarily the entire circuit), the sum of voltage sources will always be equal to the sum of voltage (potential) drops bc conservation of energy. All electrical energy supplied by source gets fully used up by other elements within the loop (if all voltage wasn't used up in each loop of circuit then voltage would build after each trip which is impossible). Consequence of law of conservation energy, but in terms of voltage (J/C) not just energy. V(source) = V(drop).

Diverging lenses

Concave lens (standard glasses - needed by people who are nearsighted) Always thinner at the center.

Conductivity

Conductance is the reciprocal of resistance. SI unit is siemens (S), given as S/m

Current

Current: the flow of charge b/w two points at diff electrical potentials connected by a conductor, such as copper wire. Current, I, is amount of charge passing through the conductor per unit time. SI unit is A (C/s). Charge is transmitted by a flow of electrons in a conductor, bc electrons - charged, they move from point of low electrical potential to higher electrical potential (reduce their electrical potential energy). But by convention, the direction of current is the direction in which positive charge would flow. A potential difference (voltage) can be produced by galvanic cell, group of cells wired into a battery, or even a potato. When no charge is moving b/w two terminals of a cell that are at diff potential values, the voltage is called the electromotive force (emf) but this is not a force; it is a potential difference and has units of J/C (voltage). Emf is a pressure to move that results in current, same way that a pressure diff b/w two points in fluid-filled tube cause fluid to flow.

Dielectric Materials

Dielectric materials = insulation. When dielectric material such as air, glass, plastic is introduced b/w plates of capacitor, it increases capacitance by factor called dielectric constant (k). The dielectric constant of a material is measure of its insulating ability and vacuum has dielectric constant of 1. A dielectric material can never decrease the capacitance; thus k can never be less than 1.

Torques in context of dipoles

Dipole is example of setup upon which torques can act. In absence of electric field, dipole axis can assume any random orientation. But when electric dipole placed in uniform external electric field, each of the equal and opposite charges of dipole will experience a force exerted on it by field. B/c the charges are equal and opposite the forces acting on charges will also be equal in magnitude and opposite in direction, resulting in situation of translational equilibrium. but there will be net torque about center of dipole axis. where p is the magnitude of the dipole moment (p=qd). Theta is the angle the dipole moment makes with the electric field.

Electric dipoles

Electric dipole results from 2 equal and opposite charges being separated a small distance d from each other. V = kqd(*cos(theta))/r^2 Product of charge and separation distance is defined as the dipole moment with SI units of C*m: Direction of dipole diff for physicists: define vector along line connecting the charges with the vector pointing from the negative charge toward the positive charge.

Electric Field

Electric fields are produced by source charges (Q). When a test charge (q) is placed in an electric field (E), it will experience an electrostatic force (Fe) equal to qE. Every electric charge sets up a surrounding electric field, just like every mass creates a gravitational field. Electric fields exert forces on other charges that move into the space of the field. Whether force exerted through electric field is attractive or repulsive depends on whether the stationary test charge q (the charge placed in the electric field) and the stationary source charge Q (which actually creates electric field) are opp charges or like. E = Fe/q = kQ/r^2 E is electric field magn in N/C, Fe is magnitude of force felt by test charge q, k is electrostatic constant, Q is source charge magnitude and r is distance b/w charges. Direction of E field vector given as direction that positive test charge would move in presence of source charge. If source charge + then test charge experience repulsive force and accelerate away from + Q. If Q - then the test charge attractive force and would accelerate towards neg charge. The denser the field lines, the stronger the force. If test charge within field is positive then the electrostatic force will be in same direction as the electric field vector of source charge; if test charge - then force will be in the direction app to field vector of source charge.

Ohm's Law

Electrical resistance results in E loss, which reflects a drop in electrical potential. The voltage drop b/w any two points in circuit can be calculated according to Ohm's law: V=IR; V is voltage drop, I is current, and R is magn of resistance measured in ohms. Ohms law states that for a given magnitude of resistance, the voltage drop across the resistor will be proportional to the magnitude of the current. Also for given resistance, the magnitude of current will be proportional to the magnitude of the emf (voltage) impressed upon the circuit. applies to single resistor, to any part of circuit, or entire circuit (provided that you can calculate equivalent resistance from all resistors in circuit). No charge is gained or lost thru resistor. Conductive materials act as weak resistors themselves (have internal resistance), offering some magn of resistance to current and causing drop in electrical potential (voltage). As a result of this internal resistance, the voltage supplied to a circuit is reduced from its theoretical emf value by some small amount. The actual voltage supplied by a cell to a circuit can be calculated from: V = Ecell - ir(internal). where V is voltage provided by cell, Ecell is emf of cell, i is current thru cell, and r(int) is internal resistance. If the cell is not actually driving any current (such as when switch is in open position), then the internal resistance is 0 and voltage of cell is equal to its emf. When current is not zero and internal resistance is not negligible then the voltage will be less than emf. When cell is discharging, it supplies current and current flows from positive, higher potential end to negative, lower potential end. Certain types of cells (called secondary batteries) can be recharged. When these batteries are being recharged, external voltage is applied to drive current toward the positive end of the secondary battery. In electrochemical terms, the cell acts as a galvanic cell when discharges and electrolytic cell when recharges.

Circuit problems

First thing is you need to find the total circuit values: the total voltage (almost always given as voltage of battery), the total (equivalent) resistance and total current. To find total current, first find total resistance of circuit.

Fission

Fission is process by which a large nucleus splits into smaller nuclei. Through absorption of low-E neutron, fission can be induced in certain nuclei. Releases energy

Magnetic Fields

For infinitely long and straight current-carrying wire, we can calculate the magnitude of the magnetic field produced by the current I in the wire at a perpendicular distance, r, from wire. Inverse relationship b/w the magnitude of the magnetic field and the distance from the current. to determine direction of field vectors use right-hand rule. Point thumb in direction of current and wrap fingers around current-carrying wire. Fingers then mimic the circular field lines, curling around the wire.

Resistors in series

For resistors connected in series, the current has no choice but to travel thru each resistor in order to return to cell. As electrons flow thru each resistor, energy is dissipated and there is a voltage drop associated with each resistor. The voltage drops are additive; that is, for a series of resistors, R1, R2, R3, etc. the total voltage drop is: Vs = V1+V2+V3... Because V=IR, we can also see that the resistances of resistors in series are additive, such that Rs=R1+R2+R3... The set of resistors wired in series can be treated as single resistor with resistance equal to sum, termed equivalent or resultant resistance. Rs will always increase as more resistors are added. (when only one path for current to take, the current will be same at every point including thru every resistor. Once you know current of whole circuit, you can use V=IR to solve for voltage drop across each resistor assuming you know resistances of resistors).

Fusion

Fusion occurs when small nuclei combine to form larger nucleus. Releases energy

Gamma Decay

Gamma decay is emission of gamma rays, which are high-E (high-frequency) photons. They carry no charge and simply lower the energy of parent nucleus without changing the mass or atomic number. The high-E state of the parent nucleus may be represented by an asterisk.

sound level

I is intensity of sound wave and I0 is threshold of hearing, used as ref intensity. measured in decibels (dB).

KE of ejected electrons

If frequency of photon incident on metal is at threshold frequency for metal, the e- barely escapes from metal. But if frequency is above threshold the photon will have more than enough energy to eject a single electron and excess E will be converted to KE in ejected electron. Can calculate the maximum KE of ejected e-: KEmax=hf-W where W is work function of metal. The work function is the minimum E required to eject an electron and is related to threshold frequency of that metal: W=hf(threshold) --> like activation energy solve for maximum KE rather than exact bc actual energy can be b/w 0 and KEmax. Light energy causes increased in electrical potential energy in atom - enough to allow e- to escape and anything left over is transferred into KE of ejected electron.

Shock waves

In special case of Doppler effect, an object that is producing sound while traveling at or above speed of sound allows wave fronts to build upon one another at front of object. when the source is moving at or above speed of sound, shock waves (sonic booms) can form.

Lenses

Lenses refract light while mirrors reflect it. 2 surfaces that affect light path. Light is refracted twice as it passes from air to lens and from lens back to air. To find where image is (for a lens), draw the following rays and find a point where any two intersect. This point of intersection marks the tip of image. If rays drawn do not appear to intersect, extend them to the same side of lens from which the light came, creating a virtual image. *Ray parallel to axis -> refracts thru focal point of front face of lens *Ray thru or toward focal point before reaching lens -> refracts parallel to axis *Ray to center of lens -> continues straight thru with no refraction

Attenuation

Like nonconservative forces, attenuation is generally negligible on test day. If it is important for question, the MCAT will make it clear that you should consider effects of damping (attenuation) on an oscillating system. Intensity decreases over distance and some energy is lost to attenuation (damping) from frictional forces. Damping does not have an effect on frequency of wave, so pitch will not change.

Magnetic Forces

Magnetic fields exert forces only on other moving charges (charges do not sense their own fields). Force on a moving charge: when a charge moves in a magnetic field, a magnetic force may be exerted on it, the magnitude of which can be calculated: q is charge, v is magnitude of velocity, B is the magnitude of the magnetic field, and theta is the smallest angle b/w the vector v and the magnetic field vector B. Charge must be perpendicular component of velocity in order to experience magnetic force. If charge moving parallel or antiparallel to the magnetic field vector, it will experience no magnetic force. 2nd right-hand rule: to determine direction of magnetic force on moving charge, first position right thumb in direction of velocity vector then put your fingers in direction of magnetic field lines. your pal will point in direction of force vector for positive charge, whereas back of hand will point in direction of force vector for neg charge. v and Fb will always be perpendicular to each other; this implies that uniform circular motion will occur in this field, with Fb pointing radially inward toward center of circle. Fc=Fb

Nuclear Binding Energy and Mass Defect

Mass of nucleus is thought to be sum of masses of the protons and neutrons within it, the actual mass of every nucleus (other than hydrogen) is slightly smaller than that. this diff is the mass defect. E=mc^2 shows equivalence of mass and energy. The mass defect is a result of matter that has been converted to energy. When protons and neutrons (nucleons) come together to form the nucleus, they are attracted to each other by the strong nuclear force, which is strong enough to more than compensate for the repulsive electromagnetic force b/w the protons. Although the strong nuclear force is the strongest of 4 fundamental forces, it only acts over extremely short distances, less than a few times the diameter of a proton or neutron. The bound system is at lower energy level than the unbound constituents and this difference in energy must be radiated away in form of heat, light, or other electromagnetic radiation before mass defect becomes apparent. This energy, called binding energy, allows nucleons to bind together in the nucleus. Given strength of strong nuclear force, amount of mass that is transformed into the dissipated E will be a measurable fraction of initial total mass. Binding E peaks at Fe ->most stable atom. Intermediate sized nuclei more stable than very large or small nuclei. Weak nuclear force also contribute to stability of nucleus but much less than strong nuclear force. 4 fundamental = strong and weak nuclear forces, electrostatic and gravitational forces. so mass defect will be diff bw protons and neutrons and then the true mass of nucleus. and this mass defect is the mass that contribute to binding energy of nucleus (E=mc^2)

Resonance

Natural (resonant) frequencies of objects. Any solid object when struck will begin to vibrate. If natural frequency is within the frequency detection range of human ear, the sound will be audible. The quality of the sound, called timbre, is determined by natural frequency or frequencies of object. Some objects vibrate at a single frequency, producing a pure tone. Other objects vibrate at multiple frequencies that have no relation to one another. These sounds are called noise. Still other objects vibrate at multiple natural frequencies (a fundamental pitch and multiple overtones) that are related to each other by whole number ratios, producing a richer, more full tone. The frequencies b/w 20 and 20,000 Hz are audible to healthy young adults. If periodically varying force is applied to a system, the system will then be driven at a frequency equal to the frequency of the force, this is called forced oscillation. If the frequency of applied force is close to that of natural frequency of system, then the amplitude of oscillation becomes much larger. The amplitude is increasing bc the force frequency is nearly identical to natural frequency. If frequency of the periodic force is equal to a natural (resonant) frequency of system, then the system is said to be resonating, and the amplitude of oscillation is at maximum. If oscillating system were frictionless, the periodically varying force would continually add energy to system, and the amplitude would increase indefinitely, but bc no system is completely frictionless, there is always dampening, which results in finite amplitude of oscillation. In general, damping is a decrease in amplitude of a wave caused by an applied or nonconservative Many objects cannot withstand large A of oscillation and will break of crumble. *Applying a force at natural frequency of a system change the system - the object will resonate bc force frequency = natural (resonant) frequency. The A of oscillation will increase.

Electrical PE

PE that is dependent on the relative position of one charge with respect to another charge or collection of charges: If charges are like charges then PE will be positive; if unlike then the PE will be negative. Electrical PE is work necessary to move a test charge from infinity to a point in space in an electric field surrounding a source charge. PE for 2 opp charges becomes increasingly negative as charges brought closer together. Increasingly neg numbers are actually decreasing values bc they're moving left of 0 so decrease in energy represents increase in stability. Like charges: closer they are to each other, less stable. Become more stable the further apart they move bc magn of electrical PE becomes smaller positive number.

Measuring Power

Power is work to time. In electric circuits, energy is supplied by cell that houses spontaneous oxidation-reduction rxn which when allowed to proceed (by closing of switch) generates flow of electrons. Current delivers energy to various resistors, which convert this energy to some other form.

Capacitors in parallel

Produce resultant capacitance equal to sum of individual capacitances. Voltage across each parallel capacitor is same and equal to voltage across entire combination.

Potential energy stored in capacitor

Regardless of particular geometry of capacitor, the function of a capacitor is to store an amount of energy in form of charge separation at particular voltage. Potential energy stored in capacitor is:

Voltmeters

Requires a circuit to be active. Also use magnetic properties of current-carrying wires but they're used to measure voltage drop across 2 points in circuit. They are wired in parallel to these two points. Bc the goal with any meter is to minimize its impact on the rest of the circuit, and voltmeters are wired in parallel, an ideal voltmeter has infinite resistance.

Resistance

Resistance is opposition within any material tot he movement and flow of charge (kinda like friction). Materials that offer almost no resistance are called conductors and those that offer very high resistance are insulators. Conductive materials that offer amounts of resistance b/w these two extremes are called resistors. *on MCAT most common resistors outside of generic, unlabeled resistors are light bulbs, although all appliances fun as resistors.

Metallic conductivity

Some materials allow free flow of electric charge within them; these materials are called electrical conductors. Metal atoms can lose one or more of outer electrons, which are then free to move around in larger collection of metal atoms. This makes most metals good electrical and thermal conductors. The metallic bond - sea of electrons flow over and past rigid lattice of metal cations. Metals have lowest ionization energies, it is easier for these atoms to lose electrons.

Sound

Sound is a longitudinal wave transmitted y oscillation of particles in a deformable medium. So it can travel thru solids, liquids, and gases but not thru vacuum. Speed of sound is given by: where B is bulk modulus, a measure of medium's resistance to compression (B increases from gas to liquid to solid) and p is density of medium. **The speed of sound is fastest in a solid with low density, and slowest in very dense gas. Fastest thru solids, then liquids, then gas. Within a medium, as density increases, the speed of sound decreases.

Battery

The "plus" end of battery is high potential end and minus end of battery is low-potential end. Positive charge moves from + to - (definition of current) and negative charge moves from - to +.

Describing waves

The distance from one maximum (crest) of wave to next is wavelength. The frequency is the number of wavelengths passing a fixed point per second and measured in Hz. Can calculate speed of wave: v = f*wavelength If frequency defines the number of cycles per second, then its inverse - period (T) - is number of seconds per cycle: T = 1/f

Intensity and Loudness of Sound

The loudness or volume of a sound is the way in which we perceive its intensity. Sound intensity is objectively measurable. Intensity is the average rate of energy transfer per area across a surface that is perpendicular to the wave. The SI units of intensity are therefore watts per square meter (W/m^2), where P is power and A is area. Intensity is power transported per unit area. Power delivered across a surface is equal to produce of I and surface area. Amplitude of sound wave is related to intensity: intensity is proportional to the square of amplitude - so if amplitude doubled -> intensity 4x Intensity also related to distance from source of sound wave. as sound waves go outward from source, the waves are pushing against spherical balloon and bc surface area of sphere is 4*pi*r^2, sound waves transmit their power over larger and larger areas the farther from source. So intensity is inversely proportional to square of distance from source. so sound waves traveled 2 m from source have spread energy cut over surface area that is 4X larger than that for identical sound waves that have traveled 1 meter from source.

Transverse Waves

Transverse waves have particle oscillation perpendicular to direction of propagation (movement) and energy transfer. Like the wave. Include electromagnetic waves, such as visible light, microwaves, and x-rays.

Ultrasound

Ultrasound uses high frequency sound waves outside the range of human hearing to compare the relative densities of tissues in the body. Ultrasound machine consists of transmitter that generates a pressure gradient, which also functions as receiver the processes the reflected sound. Doppler ultrasound si used to determine the flow of blood within the body by detecting the frequency shift that is associated with movement toward or away from receiver. Can be used therapeutically - ultrasound waves create friction and heat when act on tissues, which increase blood flow to site of injury in deep tissues and promotes faster healing.

Ammeters

Used to measure current at some point within circuit, which has to be on. Ammeters inserted in series where current being measured and use magnetic properties of current-carrying wire to cause visible needle movement. If high current a special low resistance shut used in parallel to allow reading. Ammeters must have extremely low resistance (ideal have 0 resistance and no voltage drop across them).

Wave anatomy

Waves oscillate about a central point called the equilibrium position. The displacement (x) in a wave describes how far a particular point on wave is from equilibrium position. The max magnitude of displacement in a wave is called its amplitude (A).

Capacitors in Series

When capacitors are connected in series, the total capacitance decreases in similar fashion to the decreases in resistance seen in parallel resistors. This is bc capacitors must share the voltage drop in the loop and therefore cannot store as much charge. A group of capacitors in series acts like one equivalent capacity for much larger distance b/w plates (distance equal to those of each capacitor added together) - increase in d means smaller capacitance. Cs decreases as more capacitors added. The total voltage is sum of individual voltages just like resistors in series.

Dielectric in circuit capacitors

When dielectric material is placed in charged capacitor within circuit - that is still connected to V source - the charge on capacitor increases. V must remain constant bc it must be equal to that of the voltage source. By increasing the amount of charge stored on capacitor, the dielectric has increased the capacitance of the capacitor by factor of k. When dielectric material is introduced into circuit capacitor, the increase in capacitance arises from increase in stored charge.

Snell's law

When light is in any medium besides a vacuum, it's speed is less than c: n = c/v v is speed of light in medium, and n is dimensionless quantity called index of refraction of medium. The index of refraction of a vacuum is 1; for all other materials, the index of refraction will be greater than 1 Refracted rays of light obey Snell's law as they pass from one medium to another: n1 and theta1 refer to medium from which the light is coming and n2 and theta2 refers to medium into which the light is entering. When light enters a medium with a higher index of refraction (n2>n1), it bends toward normal (sintheta2<sintheta1) ***when light enters medium with higher index of refraction, it bends toward normal. When light enters medium with lower index of refraction, it bends away from normal.

Absorption and emission of light

an electron can jump from lower energy to higher energy orbit by absorbing photon of light of precisely the right frequency to match energy difference b/w orbits (E=hf). When e- falls from higher E to lower E level, photon of light is emitted with energy equal to energy diff b/w 2 orbits. Changes in molecular structure can cause dramatic shifts in absorption patterns of substance (pH indicators). Have diff absorption patterns based solely on protonation state of compound.

Magnetism

any moving charge creates a magnetic field. SI unit for magnetic field strength is the tesla (T). 1 T = 1 (N*s)/(m*C)

Paramagnetic materials

atoms have unpaired electrons so do have net magnetic dipole moment, but atoms in these materials are usually randomly oriented so that material itself creates no net magnetic field. Will become weakly magnetized in presence of external magnetic field, aligning the magnetic dipoles with the external field. copper, gold, Al

Electromagnetic waves

can travel through vacuum unlike sound waves. Transverse waves bc oscillating electric and magnetic field vectors perpendicular to direction of propagation. all electromagnetic waves travel at same speed, speed of light (3.0 x 10^8 m/s). R(~700 nm)OYGBIV(~400 nm)

Electron capture

capture an inner e- that combines with proton to form a neutron. Atomic number is now one less than original but mass number is same.

Conductors

charges will distribute approximately evenly upon surface. They are able to transfer and transport charges and are often used in circuits or electrochemical cells. Conceptualized as nuclei surrounded by sea of free electrons that able to move rapidly throughout material and are only loosely associated with the positive charges. Generally metals but ionic (electrolyte) solutions are also effective conductors.

Closed Pipes

closed end = node open end = antinode **have to actually count the number of quarter-wavelengths contained in pipe to determine the harmonic. First harmonic consists only of the node at closed end and antinode at open end. there can ONLY BE ODD HARMONICS. The first harmonic has a wavelength that is four times the length of the closed pipe. 3rd harmonic has a wavelength that is 4/3 the length of closed pipe. n can only be an odd integer.

Force on a current-carrying wire

current-carrying wire placed in magnetic field may also experience a magnetic force. L is length of wire in the field, B is magnitude of magnetic field and theta is angle b/w L and B. **current is considered the flow of positive charge.

Electrolytic conductivity

depends on strength of a solution. Conductivity in electrolyte solution is measured by placing solution as a resistor in a circuit and measuring change in voltage across solution. Bc concentration and conductivity are directly related, this method is used to determine ionic concentrations in solutions, such as blood.

Doppler effect

describes the difference b/w the actual frequency of a sound and its perceived frequency when the source of the sound and the sound's detector are moving relative to one another. If source and detector are moving toward each other, the perceived frequency is greater than actual frequency. If source and detector are moving away from each other, the perceived frequency is less than actual frequency. f' is perceived frequency, f is actual emitted frequency, v is speed of sound in medium, vD is speed of detector, and vS is speed of source. Top sign for "toward" and bottom sign for 'away" Upper sign should be used when the detector or source is moving toward the object. The lower sign should be used when detector or source is moving away from other object.

Magnification

dimensionless value that is ratio of image distance to object distance: a negative magnification = inverted image a positive magnification = upright If absolute value of m is less than 1, the image is smaller than object; if greater than 1 the image is larger than object (enlarged); if = 1 the image is same size as object.

Ohmmeters

doesn't require circuit to be active. Ohmmeters will often have their own battery of known voltage and then function as ammeters thru another point in circuit. Bc only one circuit element is being analyzed, Ohm's law can be used to calculate resistance by knowing the ohmmeter's voltage and the current created thru another point in circuit.

Electrical Potential

electrical potential is the ratio of the magnitude of charge's electrical potential energy to the magnitude of the charge itself. 1 V = 1 J/C Even if no test charge q, can calculate V by knowing magnitude of source charge and distance from charge to point in space in the field. Electrical potential is scalar - sign determined by sign of source charge Q. Total electrical potential at point is scalar sum of electrical potential due to each charge. A potential difference will exist b/w two points that are at diff distances from the source charge. If Va and Vb are the electrical potentials at points a and b then the potential difference b/w them, the voltage, is Vb-Va = Wab/q where Wab is the work needed to move test charge q thru electric field from a to b. Work is independent of pathway b/w a and b (conservative). Charges will move spontaneously in direction that results in decrease in electrical potential energy. For + charge this means moving from position of high electrical potential to lower electrical potential. Voltage is neg in this case; bc q is positive, Wab must also be neg (represents decrease in electrical PE). Neg test charge will move from position of lower electrical potential to position of higher electrical potential. Voltage is positive; bc q is neg, Wab must also be negative which represents decrease in electrical PE. Positive charges spontaneously move in direction that decreases their electrical potential (neg voltage); neg charges move in direction that increases their electrical potential (positive voltage) but both electrical PE decreases.

Resistors in Parallel

have common high-potential terminal and low-potential terminal. Electrons can follow diff parallel paths and can choose which path they will take. No matter which path is taken the voltage drop experienced by each division of current is the same b/c all pathways originate from a common point and end at a common point within the circuit. Vp=V1=V2=V3... While the voltage is same for all parallel pathways, the resistance of each pathway may differ. Electrons prefer the path of least resistance; the current will be largest thru the pathways with lowest resistance. *Remember Kirchhoff's loop rule: if every resister in parallel then voltage drop across each pathway alone must be equal to voltage of entire circuit. There's inverse relationship b/w cross-sec area of resistor and resistance of that resistor. The configuration of resistors in parallel allows for a greater total number of conduction paths, and the effect of connecting resistors in parallel is reduction in equivalent resistance. We could replace all resistors in parallel with single resistor that has resistance that is less than the resistance of the smallest resistor in circuit. Equivalent resistance of resistors in parallel is calculated by: 1/Rp = 1/R1 + 1/R2... Rp will always decrease as more resistors are added. Bc V drop across any one circuit branch must be same as V drop across each of other parallel branches, magn of current in each branch will be inversely proportional to resistance by that branch. *When n identical resistors are wired in parallel, the total resistance is given by R/n. V across parallel resistors is equal and for equal resistances, the I flowing thru each resistor is also equal. Current of I(total)/n runs thru each.

Plane mirrors

image is real if the light actually converges at position of the image - real images can be projected onto a screen. image is virtual if light only appears to be coming from the position of the image but does not actually converge there. Parallel incident light rays remain parallel after reflection from a plane mirror; plane mirrors - being flat and reflective surfaces - cause neither convergence nor divergence of reflected light rays. B/c light does not converge at all, plane mirrors ALWAYS create virtual images. Image appears to be same distance behind mirror as object is in front of it. Plane mirrors can be thought of as spherical mirrors with infinite radius of curvature. Plane mirrors produce visual, upright images; these images are always the same size as the object. spherical mirrors w/ infinitely large focal distances so r = f = infinity, and equation becomes 1/o + 1/i = 0 or i = -o; virtual image is distance behind mirror equal to distance the object is in front of the mirror.

Half life

in sample of radioactive particles, the half-life (T1/2) of sample is the time it takes for half of the sample to decay. in each subsequent half-life 1/2 of remaining sample decays sot act remaining amount asymptotically approaches zero.

Refraction

is bending of light as it passes from one medium to another and changes speed. Speed of light thru any medium is always less than its speed thru a vacuum.

Alpha decay

is emission of alpha-particle, which is 4/2He nucleus that consists of 2 protons and 2 neurons and 0 electrons (so carry 2+ charge). Alpha particle massive compared to beta particle and carries double the charge. Alpha particles interact with matter very easily, they do not penetrate shielding (such as lead sheets) extensively. Emission of alpha particle means atomic number of daughter nucleus will be 2 less than that of parent and mass number will be 4 less.

Beta decay

is emission of beta-particle, which is an electron and is given the symbol e- or beta-. Electrons do not reside in nucleus but they're emitted by the nucleus when a neutron decays into proton, a beta particle, and an antineutrino. Bc electron is negatively charged and a lot smaller than proton, the beta radiation from radioactive decay is more penetrating than alpha radiation. During beta- decay, a neutron is converted to proton and electron/beta- particle (Z=-1, A=0) is emitted. So the atomic number of daughter nucleus will be one higher than that of parent and mass number will not change. In positron emission, a positron is released which has the mass of an electron but carries a positive charge (e+ or beta+). During beta+ decay, proton is converted into a neutron and a beta+ particle (Z=+1, A=0) is emitted. The atomic number of daughter nucleus will be 1 lower than that of parent and mass number doesn't change.

Radioactive decay

is naturally occurring spontaneous decay of certain nuclei accompanied by emission of specific particles. Need to be able to answer 3 gen types of radioactive decay probs: 1) The integer arithmetic of particle and isotope species 2) Radioactive half-life problems 3) The use of exponential decay curves and decay constants Sum of atomic numbers must be same on both sides of equation and sum of mass numbers must be same.

Diamagnetic

made of atoms with no unpaired electrons and that have no net magnetic field. Slightly repelled by magnet and so can be called weakly antimagnetic. Wood, plastics, water, etc. (don't get stuck to magnet).

Concave mirrors/converging mirrors

make-up mirrors - everything appears bigger and closer the center of curvature and radius of curvature are located in front of the mirror. Ray diagram: 3 important rays - A ray that strikes the mirror parallel to axis is reflected back thru focal point. - A ray that passes thru focal point before reaching the mirror is reflected back parallel to axis. - A ray that strikes the mirror at point of intersection with axis is reflected back with same angle measured from normal. Object placed b/w F and C -> image is real, inverted, and magnified. Any time object is at focal point of converging mirror, the reflected rays will be parallel and image will be at infinity. Object placed b/w F and mirror, image is virtual, upright, and magnified.

angular frequency

measured in radians per second and used in consideration of simple harmonic motion in springs and pendula.

rate of nuclear decay

n is number of radioactive nuclei that have not yet decayed in a sample. Rate at which nuclei decay is proportional to the number that remain (n). lambda is decay constant.

exponential decay

n0 is number of undecided nuclei at time t=-. The decay constant (lambda) is related to half life by: lambda = ln2/T(1/2) = 0.693/T(1/2)

Perpendicular bisector of the dipole

one very important equipotential line to be aware of is the plane that lies halfway between +q and -q called the perpendicular bisector of dipole. B/c angle b/w this plane and the dipole axis is 90 and cos90 = 0, the electric potential at any point along this plane is 0. Magnitude of electric field on the perpendicular bisector of the dipole can be approximated as: The electric field vectors at the points along the perpendicular bisector will point in direction opposite to p

Frequency and pitch

our perception of frequency of sound is pitch. lower frequency = lower pitch. Sound waves with frequencies below 20 Hz are infrasonic waves and those with frequencies above 20,000 Hz are ultrasonic waves.

Convex mirrors/diverging mirrors

passenger mirrors - everything appears smaller and further away the center of curvature and radius of curvature are behind the mirror A single diverging mirror forms only a virtual, upright, and reduced image, regardless of position. Further away object, the smaller image will be.

Properties of Resistors

resistance of resistor dependent upon certain characteristics of resistor: resistivity, length, cross-sectional area, and T. (p) is resistivity, L is length, and A area. Resistivity: some materials just better conductors of electricity. number that characterizes the intrinsic resistance to current flow in material is the resistivity (p) SI unit is ohm-meter. Length: A longer resistor means electrons will have to travel a greater distance thru a resistant material. if resistor doubles length, it also doubles resistance (directly proportional to resistance). Cross-sect area: inverse relationship b/w resistance and cross-sec area of resistor. Bc increase in area increases number of pathways thru resistor, called conduction pathways. Temperature: most conductors have greater resistance at higher temps. Bc increased thermal oscillation of the atoms in the conductive material, which produces a greater resistance to electron flow.

Production of sound

sound is produced by mechanical disturbance of a material that creates an oscillation of the molecules in the material.

Standing waves

standing waves are produced by the constructive and destructive interference of a traveling wave and its reflected wave. A standing wave will form whenever two waves of same frequency traveling in opp directions interfere with one another as they travel thru same medium. Appear to be standing still bc interference of wave and its reflected wave produce a resultant that fluctuates only in amplitude. the points in standing wave with no fluctuation in displacement = nodes (nodes are places of no displacement) and points with maximum fluctuation are called antinodes. Objects that support standing waves have boundaries at both ends. Closed boundaries are those that don't allow oscillation and that correspond to nodes. The closed end of pipe and secured ends of string are both considered closed boundaries. Open boundaries are those that allow maximal oscillation and correspond to antinodes (open end of pipe).

Principle of superposition

the principle of superposition states that when waves interact with each other, the displacement of the resultant wave at any point is the sum of the displacements of the two interacting waves. When waves are perfectly in phase, the displacements always add together and amplitude of the resultant is equal to the sum of the amplitudes of 2 waves: constructive interference. When waves perfectly out of phase, the displacements always counteract each other and amplitude of the resultant wave is difference b/w the amplitude of the interacting waves. This is destructive interference. *If 2 waves perfectly in phase, the resultant wave has an amplitude equal to sum of amplitudes of the 2 waves. If two equal waves are exactly 180 degrees out of phase, then the resultant wave has zero amplitude. If waves are not perfectly in or out of phase with each other, partially constructive or partially destructive interference can occur.

Real Lenses

thickness cannot be neglected, the focal length is related to curvature of lens surfaces and index of refraction of lens by lens maker's equation: n is the index of refraction of the lens material r1 is radius of curvature of first lens surface and r2 is radius of curvature of second lens surface.

Insulators

will not easily distribute a charge over its surface and will not transfer that charge to another neutral object very well - esp not to another insulator. electrons of insulators tend to be closely linked with their respective nuclei. Most nonmetals are insulators. Insulators serve as dielectric materials in capacitors as well as in isolating electrostatic experiments from the environment to prevent grounding **will not distribute charge over surface