Physics Unit2/3: 5.6.7.8.9

wave phase

In phase: when crest and troughs pass through same space at same time (their crest and torughs line up), can have some phase difference just not complelty opp, if complelty in sync then phase diff is 0 and the amplitude is the sum of them both Out phase: if crest is seen when other wave is at its trough point, can be expressed as λ/2 (half wave difference btw), diff ata bout 180degrees-can cancel out noises-

Propogation speed of a wave

Veloicty (m/s)=1/s(m) -this tells u how fast the wavelength (m) is going through the fixed pt (frequency at pt) frequency is just saying how many times the wave passes that pt per second, this number doesnt change going through medium bc the only thing that does change in lambda Period tells u how LONG it takes, in sec, for a full wavelngth to pass through, while frewuency tells u how how many TIMES V=FL, frequency no change but v chagnes when going through diff medium so only thing to compesnate is l so that changes -If Frequnecy were to change, E of light chnages but that is impossible so frequency doesnt change -Wave frequency is related to wave energy. Since all that waves really are is traveling energy, the more energy in a wave, the higher its frequency. The lower the frequency is, the less energy in the wave (E can not be created or destroyed) -Shorter waves move faster and have more energy, and longer waves travel more slowly and have less energy -speed of light NEVER changes, unless u are going through a diff medium so a high lambda/low lambda move at the same rate/neither are faster bc both travel at 3e8 the only time v changes is when going through diff medium,c is a constant F is a constant for a given lambda, so only way to change f is by chaning lambda (inverse) -WHEN going through diff medium, then bc n=c/v then bc your minimum refraction leaving a vaccum is always above 1 then, your speed will always decrease-for light waves -Velocity is slowest in gases, faster in liquids, and fastest in solids. (sound waves) -inensity decreases when going through aq solid bc lost E so intesnity also decreases, When sound crosses from one medium to another, a portion of the wave's energy is reflected. Therefore, sound waves lose energy (are attenuated) and their intensity decreases when passing from air to a solid structure, such as the tympanic membrane

potential difference (voltage)

W is the work needed to move charge from point A to point B (∆ in electric pot from moving pt A to pt B) -think Va and Vb are the electric pot at set distances so its the W needed to move test charge from pt a (initial) to pt b (f), so the voltage difference is: Vb-Va=∆V=Wab/q -remeber charges will spont move toward direction that results in lower U so: -poistive test charge moves from High EP to low EP results in -∆V and -Wab (↓ in PE), High EP (i) to low EP (f) so Low EP-High EP=-V=-W/+q (assuming source is positive) -negative test charge moves from Low EP to high EP results in +∆V but -Wab (so ↓ in PE) bc of the -q test charge, (both want to decrease W, just diff means of doing so, can think W and V move same diretion in postive but bc neg not thought of in electro then opp earlationshiop This shows just bc +/-∆V that doesnt mean W=U will follow, W is always want to be negative to decrease U, if moving opp direction of favorable then W will be positive, either way we want to decrease U just diff means of doing so through V (negaitve moves up, positive moves down Spont.

Sound waves and crossing a medium

When a sound wave (longitudinal wave) crosses solid medium, the sound wave looses E which means its intensity decreases

Velocity and waves

When a wave moves from one medium to another, its frequency does not change. Changes in wave velocity are only due to changes in wavelength. The propagation velocity of sound waves depends on the properties of the medium: -Velocity increases with temperature. -Velocity is slowest in gases, faster in liquids, and fastest in solids. -Within a phase of matter, velocity increases with stiffness and decreases with density.

Axons and circuits

-Axons are neg charged bc of resting pot -Myelin increases resistance (makes it more prone to dissipate the charge so that it can be rebooted at the node?) and DECREASES capacitance (ability to store AND release charges), remeber the AP is not the same one at each node, each node is a NEW AP that was made from the repolairzaation of its neighbor which caused it to depolarize -Resistance changes from increasing the area of the axon itself not the entire thing VERIFY??????????????

Capacitors in parallel

-C+C -V=V -Q+Q -Remebr only thing that is ever 1/x is resistane adn Cacpacitivance, VOLTS ARE THE SAME type (v=v or v+v)c FOR BOTH RESITIORS AND PARALLEL IN CICRUTIS bc Circuit components in parallel are connected to each other at both ends and have the same voltage across them no matter the elements in btw them

Capacitors in series

-Capactiance decreases in series bc resitance is increased (cant store as much charge bc exp same voltage drop/all go through a voltage drop) (1/C) -V+V Q=Q

Constructive/destructive interference

-Constructive: when the waves are perfectly in phase with eachother and the amplitudes add up (greater amplitude together) -Destructive: when the waves are out of phase to eachother and the amplitudes are subtracted from eachother (have lower amplitude) -Noise canceling headphones replicate wave but in out of phase perfectly to cancel it out -Partially Constructive: waves dont perfectly add up, bc not in any type of phase so amplitude is not the sum of it

spherical mirrors types

-Convex Mirrors: diverge light rays, think of looking inside cave -Concave Mirrors: Converge light rays (CONCAve CONVerge), think of looking OUTside of sphere Think of them as forming a circle either in front of behind (depending on shape)

Magnetic Materials

-Diamagnetic: no unpaired e- (e- config full) and no mag field, repelled by magnets bc of this, weak anti magentic (di-2-paired not unpaired) -Paramagnetic: unpaired e- so have mag dipole moment, weakly mag in presence of external mag field, after external lifted the thermal E of atoms will casue dipoles to reiorietn (temporary effect)-all going diff directions unless mag field applied -Ferromagnetic: unpaired e-and permanet magnetic dipoles that orient randomyl so no net mag dipole (+end to its own -end) but when exposed to mag field becomes strongly magentized-always going same direction especailly with mag field applied When two wires are placed near eachother, they will exert a NET mag field, draw out the wire and current direction (opp and same way are key) then find direction of mag feidl using cupping hand thing,-if there mag fields are same (in or out) then add, if they are opp (one in and one out) then subtract for net

electric field and force vectors

-E-field and E-Force both vectors so important to know their direction as the direction of a moving ion will be relative to the dot product of it (in btw them both) -is test q is positve: F exerted will be in same direction as field (radiate away) thus move away -if test q is negative:F exerted will be opp in direction to that of E-Field vector Remeber this is relative to charge type (+/-) and where in field you are (left right etc) --Electric charges generate electric fields, regions of space that exert an electrostatic force on charges. Electrostatic force is conservative; the total energy of a charged particle in an electric field is conserved, so U+KE=Total E -when asked how something will move, draw out the F vector from each pt charge around the pt charge of itnrest (the one moving) and cancel things out going only in the x/y fields (z is the actual value after all other forces are canceled out

Understanding relations of variables in electrostatics

-If F↑ by x: then r will decrease by sqrt x -If F ↓ by x: r will increase by sqrt x -if r ↑ by x: F decreases by x^2 -if r ↓ by x: F increases by x^2 Ex: r havled (2) then F increases x4 think how r effects F, r must be ^2 so its change must also be ^2, like how any changes to r will make u square the change, r is squared so so is the change done on F, in order to get F and r on the same leve, anything done on F will have to multiply the sqrt of the change to r think how F effects r, F must be sqrt (done to both sides but r side gets canceld out) Divide by Q, multuiply r to the left -if anything make F=r^2, then insert the number on one side and thing what u need to do to simplfy, if 4F=r^2 then think ok I need to sqrt to make xF=r, if r changes by then F=(r*4)^2 then think ok I need to square both sides then just apply PROPER increase/decrease -r change sqaure -F change sqrt-F root groot

Open Pipe v Closed Formulas

-Open pipes support antinodes, think normal sntanding wave formula with λ=2L/n, number of nodes tells u how many harmonics, normal f=v/2L, open pipes are the same as string like vocal cord, guitar string etc -Closed END Pipes Support nodes, one is at the end(where fixed at to end) and uses λ=4L/n and f=nv/4L not f=nv/4l, uses quarter wave lengths bc of this as n, first harmonic is the 3rdovertone, basically count each quarter that ends in a node 2 per 1 node), but when it is open at one end, then think of it has 1 so n=nodes*2+1 (nodes excluded the fixed closed pt), Hamonic=n, in open that means antinodes, the cloesd that means nodes*2+1 Think big coeffiicent on top for tboth -this formula is used for traveling waves bc travels back to u

Standing Wave

-when fixed at 2 pts, certain interfernece happens in which the wave appears to be stationary and the only movement of the wave is the ampliutudes at fixed pts along the length of the string (node) -Nodes: points that appear like remaining at rest (Nodes are no place for displacment) -Antinodes: pts midway btw nodes that have amplitude (just ampltide up 2wave) -Pipes open at both ends appear standing, pipes open at one end can support standing waves but math to work them are diff -made up of constructive and destruvie from the incident wave and reflected wave, aka when waves of same freq but traveling opp direction interfere with eachother and appear to be standing still and not propogating bc net 0

Resistors in parallel

-V: constant/what you came in with is what you are going to leave with, the V for both sides will be the same (remebr that changes after leaves parallel), this is bc wiring of cicurit, Voltage at end will be 0 and be used up throughout the entire resistor/circuit still, Voltage u come in with into a parallel ciruit will be the same in each parallel circuit BUT by the end of it, it will be all used up, this happens bc voltage drop is the same at each resistor in the parallel thing, (can add Rs together to make one guy) -I: bc branch and ohms current changes in which Itotal=Ia+Ib etc (within each branch) -these values dont matter to circuit as whole but gives u the values of V that came in and left (V=V)-------It=1a+Ib -R: as you add more resistors the total resistance decreases so 1/Rt=1/R1+1/R2 (can think that cross sectional area increased), to get actual R value do the inverse of the 1/R to plug it into formulas -use when coming into and out of parallel resistor, smush together and apply formula- can do triple way parallel resisotrs, -NOTE: when two parallel cicuits next to eachother, bc of series rule then the I top is going to go through each top resistor (so can make an I top and I bottom)

Resistors in series

-V: each time goes through resistance the voltage drops bc resistace aims to decrease voltage differece/voltage, so more R then less V so Vt=V1+V2+V3 (loop rule) -I: constant bc current only going on direction then I doesnt change (no splitting/branching), current only chanes when branches, when going through a resisotor that is increasing reistance (in series), I no change just V drops -R: bc in series total R increases with more R so Rt=R1+Rb Apply this when going down on branch and goes through multiple resitsors note the VR values as it enters and leave the series bc after it goes through it then when going through next has to use those values (E conserved) -----this is going through resistor---------

Frequency

-Wave frequency is related to wave energy. Since all that waves really are is traveling energy, the more energy in a wave, the higher its frequency. The lower the frequency is, the less energy in the wave (E can not be created or destroyed) -a bigger frequency means the wavelgnths are short, bc more amts can pass thorugh that pt -lower freq means wavelength is long bc less amt can pass through that pt -this just describes the wave, it doesnt change anything)

Change in electric potential energy

-bc change in E of system (∆U), we can use ∆U=-Wby aka ∆U=+Won , meaning the W needed to move a test cahrge from infinity to a pt in the E field, and -Wbysystem=Wdone on the system so Won.system=∆U=Wby.system (just opp magnitude) -can think of it as W bc W=F*d, and when plus ElecF*distance you cancel out the r^2 to r, when thinking about it as work think of it as ∆U=W -bc a measure of W, can think of as how much W/E needed to remove an e- (ionzation E) or E released when e- added to an atom (electron affinity), or even the E needed to break bonds (Enthalpy) bc e- being removed from bonds, change of internal E from removing a charge in which its r increases and its attraction (+protons/nucleus and -e) ∆U=W=kQq/r and this is W done by E field on to the charge -E is electric Field, so basically amount of E needed to move a charge in an E-Field at set distance -In repulsion W as spent to move molec together so W done by the system (system is E field) (+W bc +U), and that is equal to the amount of E those particles gained from being at that position, in attraction particles lose E (-W bc -U) -If moving from low to high distance then +W (work was done by the E field onto the charge to move like charges away through repulsion) -If moving from high to low distance then (-W) (Work was done on E-field by the charges to move opp charges closer bc attract and PE↓ ), thin u=Qed -------------------------------+W means work was done by the system onto the charge (work was needed to move them, aka the same charged particles, closer is high), W was done by the system onto the charges to move them in the same area (from inifinity to near eachother in E field, always wanted to be far from eachotehr but bc of formula and what we are measuring then we had to do something to move them) -W means work was done on the system by the charges, W from attraction was done by the charges onto the system

Standing wave formula/for strings

-in a 2pt node(fixed at 2pts-closed) the wavelength is 2x the Length of the strong bc it it only has one amplitude not 2, 2 would create the wavelength and be double the sting -and if two antinodes there must a a third node (pt inteserction/no displace) essetially Nodes=antinode +1 -basically the harmonic corresponds to how may antiodes there are (3anti then harmonic number 3 ad 4 nodes total) aka harmonic motion is the number of half wavelnegths that resulted in antinodes -this applies to both closed or both open lambda=2L/n , L is length of pipe

Circuit formula (capacitance in parallel plates)

-increases plate overalp (A) increases C -closer plates are to eachother (smaller d) increases C C=sigma0(A/d) (sigma constant) sigma guy is permabiltiy of free space -when a dielecttric mateiral (insulator like plastic ceramic etc) used is increases capacitance C'=kC (k is the factor that it increased it by and since never decrease it then k always greater then 1) note the oppositeness to resistance A increases C (decrease R), d aka L decreases C but increases R

angular frequency

-measured in radians/sec w=2πf or w= 2π/T -used in considaeration in simple harmoic motion of springs and pendula -dont need to know about harmonic motion just know overall cocept

EMF (electromotive force)

-remeber current happens bc of the pot diff. (wants to move spont high to low for +), but when no charge is moving btw each sides that are diff pot values the volatge is called emf -an emf is the pot diff generated btw 2 charges to move: basically pressure to move -uses Volts but emf is J/C bc just E/q (singular)

electromagnetic spectrum

-spans from radio waves(long waves, low freq/E) to gama rays (short waves, high E/freq) All of the frequencies or wavelengths of electromagnetic radiation -Radio Waves: long waves, low freq, low E -Gamma rays: short waves, high freq, high E lowest to highest E waves: microwaves<infrared<visisble light (400nm-700nm)<UV light Visaible spectrum: 400-700 with BGR in terms of wavelength -Blue Green Red but rememebr opp for E, higher E means shorter wavelength so blue>green>red aka UV>green/visible>IR Radio-micro-IR-Visible-UV-xray-gamma ^from long to short waves -electromag waves vary in freq and wavelength but in vaccum all travel at 3e8

Sinusodial waves

-transverse -longitudinal -In any waveform, E is is delviered in the direction of the wave travel when think of waves, think of waves as E and E waves

Waves

-wavelength (nm): the distance between two maximum points (crests) NOT amplitude, think of it as the V between peaks -frequency(Hz or SI units:1/s-1): the number of wavelengths that pass through a fixed pt per second -Period: the number of seconds it takes to reach one wavlength cycle (Crest to crest), amount of time that ONE wavelength needs to pass through a fixed point -central pt: equilibrium position (0), and any displcemet is the distance from this position -Amplitude: the peaks of crest to equi postion aka the max magnitude of displacments-basically from pt 0 to max above OR below not both (from top of crest or bottom of trough), it is the max extent of vibration measured from the crest position to equi position, so basically the max amt of E exerted to surrounding, measured in m but thats m due to E displacment from equi not due to length of wave

Snells law tells us

-when going from bigger index of refractin to smaller (n1>n2) then light will bend AWAY from the normal and Θ2>Θ1 -when going from small index of refraction to bix index refraction (n1<n2), then light will bend TOWARD the normal and Θ2<Θ1 -high to low n->bend AWAY -low to high n-> bend TOWARD going from high money to low amt money makes me want to runaway

total internal reflection.

-when going from high to low n, the angle is larger (bends away- Θ2>Θ1), and the refreacted angle is larger then the incidnet angle, as incidence angle increase so does angle of refraction (further from normal) until it reaches the point in which NO REFRACTION happens but reflection happens back into same medium light came from -as incident angle icreases the refreacted angle also increases until recahes critical angle, -when angle of incidence=crtical angle then reflection starts to happen in which the refracted angle is 90 (Θ2=90º), when angle of incident is above 90 then total internal reflection happens -internal reflection is the pt where there is NO refreaction, ONLY HAPPENS WHEN GOING HIGH TO LOW

Traveling Waves

-when one end of wave is fixed, a wave will form and propogate toward the fixed pt, bc moving away then traveling wave -when the wave reaches the fixed pt, it is refelcted and inveted -if cont, moved then will have original incident wave and reflceted wave moving away from fixed pt toward u and these waves will interfere -uses the lamda=4L/n formula

Ray Diagrams concve mirrors

1) Ray parallel to axis from pt, then hits mirror and reflects back to focal pt 2) Ray through focal pt then reflects back parallel to axis ----no dotted lines except when before F---- -Obj btw focal pt and C/r-> inverted and real and magnififed (when ur btw something Cming and fking IdontReally know what to do IR) -obj at focal pt->no image formed bc rays are parallel to eachother -obj in front of focal pt-> upright virtual and magnified (WHEN btw F and L (FL) there lots of UV) (L being mirror but in terms of nuemonic Lnes) ALWAYS Magnify/make bigger UNLESS BEYOND C -IF obj beyond C then image will be SMALLER and IR (CRIS- beyond C Real Inverted and Small), makes sense beyond C means u are far so itll be smaller, i live beyond myslef/expsnese lol -ALWAYS MAGNFIED before C, unless past C then reduced -anything before focal pt is UV, anything after it is IR (think closer to mirror more UV like tanning) -Anything before C is magnified (btw c and mirror) anything after is reduced

Ray diagram for convex mirror

1) Ray parallel to axis, then hits mirror and reflects back to focal pt 2) Ray through focal pt then reflects back parallel to axis 3) Ray to center of mirror then reflects back at same angle (wants to hit but gets hit first) -ALWAYS UV and SMALL, father away from obj smaller the obj (SUVs have convex features) -vex sex suv -think how the father away u go from convince store mirrors harder it is to see -think diverging makes it look smaller

Frequency of hearing

20-20,000Hz -decreases with age the sounds things make can be changed by chanig the obj (filling glass more), sound comes from vibration -vibrating material causes sound, can be air (vocal chords) or something phsyical -pitch is our perception of frequency aka pitch=ercived freq, so higher pitch means higehr percived freq -high pitch is squeaky while low pitch is bass like -males have thicker vocal cords so lwoer pitch (denisty increased so lower v, lower v means lower frequency and higher λ) -high pitch: higher freq, lower wave length -low pitch: low freq, higher wave length -resonant frequency of an object is the frequency that causes relatively large oscillations compared to other frequencies. The resonant frequency depends on the physical characteristics and geometry of the object., natural frequency of vibration determined by the physical parameters of the vibrating object

Solving circuits

Add= resistors and batteries in series, and capacitors in parallel Inverse= resistors and batteries in parallel, and capacitors in series Parallel: can smush them together to essentially be one to then be used in a series For anything that stays "constant" that just means what you go in with is what you leave with goal is to make series In parallel: can have different values of I that went through each R, use those values to find the Voltage as a whole etc-so using I1 and I2 WITH RESPECTIVE R1 AND R2 can find Vt to plug into VIR T formula to solve for the VIR that left this parallel resistor ------------------------------------------- From kaplan, find total R first then bc series has no I change then total I given starting V , (ony time V decreases is when in total loop aka in series) so after combo parallel then find thier V, bc cant find the V going into other stuff until all has been solved into a series, voltage going thorugh each parallel branch is equal only thing that does change is I ----------------------------- Basically, push anything that is inside the loop out to be a series, if a series runs inside which is next to 1 resistor in paralle then solve for the series and then from there solve the parallel-goal is to have eveything out

Sound formula

B is bulk modulus: resistance to compression-highest in solids>liq>gas so sounds travel faster through solids and slower through gas (more resistace from molec not moving in solid) Density of object is in denom, but bulk modulus outweighs this Speed of sound 343m/s higher debsity less fast (has to travel through more mass) When sound crosses from one medium to another, a portion of the wave's energy is reflected. Therefore, sound waves lose energy (are attenuated) and their intensity decreases when passing from air to a solid structure, such as the tympanic membrane

Farday AND e-

F+9.65*10^4 C/mol e- so F=Q/mol e- or Q=F*mol e- Can use Q from I or from C

spherical mirrors

Mirrors reflect light, lenses refract light -R: radius=center of curvature -f=focal length: distance from focal point and mirror (f=r/2), think it is the halfway distance from r -I=image distance from mirror to image -O =distance from mirror to obj Remember foir in forumla 1/f=1/o+1/i=2/r aka f=r/2 -most often be asked to find image distance -all same units of eachother, so as long as all m, mm etc when inputting ur all gucci

uniform electric field and non-uniform

More field lines represents a higher field strength. In a non-uniform electric field, the field lines tend to be curved and are more concentrated near the charges. In a uniform electric field, since the field strength does not vary, the field lines are parallel to each other and equally spaced. Uniform fields are created by setting up a potential difference between two conducting plates placed at a certain distance from one another. The field is considered to be uniform at the center of the plates, but varies close to the edge of the plates

Path of a moving charge

Moving charged particles are accelerated in a magnetic field by the Lorentz force. The direction of the force is always perpendicular to the particle's velocity. As a result, the particle's trajectory is forced into a curved path. In the figure, the path of the proton is bent to the left in the presence of the external magnetic field. This means that the Lorentz force initially points to the left for positive charges in the magnetic field. Because the mass and inertia of an electron is much lower than that of a proton, the electron will be more greatly affected by the magnetic field, and its path will curve more.

Frequency in motion

Periodic motion is modeled in terms of wave motion, where the time required to complete one cycle of motion is defined as the period (T). The frequency (f) of oscillations per interval of time, which is often expressed in units of cycles per second (hertz), is the inverse of the period Periodic motion occurs when an object moves in a cyclical fashion, returning to the same location after a certain period of time. Classic examples of periodic motion are the oscillatory behavior of a clock pendulum, or a mass located on the end of a perturbed spring. -Basically, frequency= time^-1 (1/time) that it takes for one full revolution or compelte cycle

Real v Virtual Image

Real: lighta actually converges at the postion of the image Virtual: light only appears to be coming from image but does not converge there(diverge), light rays appear to be oriented together but not actually

Conductivity/Conductance

Reciprocal of resistance, want to pass charge along, measured in Siemens (S) or S/m does NOT want to store it like capacitance, 2 categories -Metallic: free flow of electirc charge within them, from metalic bonds (low ionizatoin E) in which a metal gives away its outer e- more easily and can turn into cation, and e- pass to to non-metal, e- move free to move in metal and conduct charge (pass it along), more molarity of ionc solution higher conductivity -Electrolytic: depends on strength/concetration of solution, basically how solutions can conduct charges, helps bc solution allows ionic bonds in lattice strucutre to be broken allow its ions to pass along a charge, think what dissolves easier (ionic usually better, but acids poten also) (higher molarity better) -the ability for electrolytes to conduct depends on their [moles], the more moles they have the better conductotrs -Note becareful with mocle like HNO3 tech only 2 ion moles not 3 bc its a polyatomic , if needed highlight it when doing probs bc tend to forget (polayatomic)-moles are in terms of ionic moles not just the molec

Colors/wavelengths of light

Red: ~ 700-635 nm (65) Orange ~ 635-590 nm (55) Yellow ~ 590-560 nm (30) -closer to top, bigger gap Green ~ 560-490 nm (70) -490 to little over 550 is green Blue: ~ 490-450 nm (40) Violet: ~ 450-400 nm (50) -think 400~500 blue/purple When color is seen with naked eye, that means everyother color wavelenghts are being abs and is only reflecting the color you want/see Aka: u reflect what you want and other wavelengths are abs/kept Think colors of rainbow -as you abs more of the other wavelnegths, the brighter/more distinct the reflected color that u see is, so if u abs lots of waeleneths at 700 then u SEE more of the other color (ex maybe blue?) -Compliment Colors: Orange-Blue, G-R, Yellow-Violet (both have the V in it like Y has teh V in the Y)

Ultrasound

Sound waves with frequencies above the normal human range of hearing -high freq sound waves

resonant frequency

The frequency at which standing waves are made, natural frequency of vibration determined by the physical parameters of the vibrating object -The resonant frequency of an object is the frequency that causes relatively large oscillations compared to other frequencies. The fundamental frequency is the lowest resonant frequency, and each subsequent harmonic frequency is a multiple of the fundamental frequency. -Resonant frequency waves are known as standing waves because the locations of the nodes and antinodes do not change. Nodes occur at the locations of zero displacement, and antinodes occur at the locations of maximum displacement.

Snells Law

The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for a given frequency.-given freq u wont change your angle (just saying u can measure the angle effectvly) -1 refers to the medium from which the light is coming from, and 2 is new medium it is entering ito -Θ refers to angle from normal -high n to low n→bend away from normal, more room to bend away -low to high n→ bend closer to normal, more dense so less angle

Time period formula

The time it takes to get from crest to crest -also 1/freq bc freq is jsut the amount of times something goes through a fixed pt period looks at how long it takes to get one full wave length, period is measured in seconds while frequency is measured in s^-1 (1*s/1=s) -moving up and down straight basically takes no time/is negligible, but moving btw the crests does so to calc period all need to do is calc the time between each crest and add together, so its just the time between peaks and dont have to account for the time it takes to go down, if box like waves then the flat part between peaks are not counted as the flat lines are just the up and down part f and t are inverse

Columbs Law

This just tells you how strong the elctric Force is based on its magnitude (Newtons), the Force of the electric charge btw two charges -k=9e9 -Note the similarity btw that and the force of gravity -the direction of force depends on whether charges attract or repel (repsective to the situation) -Remebr FE and UV -Pay attention to if they want magnitude or actual value -vector, important to know how the F vector and E Field vector are in relation -force/strength of electric force between charges, while E is the strength of electric field per unit charge (each inidi charge -also remeber Newtons 3rd law: the F exerted on a charge from another will be equal but opposite direction so F on a froom b then -F on b from a (magnitude is same just diff signs)

Traveling and standing waves

Traveling waves- if string fixed on one end and free on another, moving it will get you a traveling wave. If fixed on both ends, standing wave. Node and antinode.-basicallt when u can tell when a wave is traveling (like constructive), looks liek going one direction Standing waves: fixed at both pts, Transfer no energy. They have the same amplitude and are in phase. Happens when a wave & its reflection interfere (or just 2 waves), A pattern of vibration that simulates a wave standing still, standing waves looks like its still bc two waves coming from both pts are moving toward eachother at each end (basically wave from left and wave from right meeting) the incident and reflected waves merge to form one wave in which the only appernt movemtn is the flux of amplitudfe at fixed pts (from node)

Shock waves

a moving region of crowded molecules produced when the source is traveling faster than sound -causes highly condesnded shock wave, as it passes through object causes high P then sudden very low P: sonic boom -sonic boom can heard when traveling at or higher then speed of sound when passing a detector skiped

Longitudal Wave

a wave that moves the medium parrelel to the direction in which the wave travels -particle ossicilation moves parallel to the direction of propogation and E transfer -moves WITH the direction of E transfer (not perp) -think sonar can go long -seen in sound waves, think the waves are long since they are going one direction like sonar -happens through cycles of comrpession and rarefaction (decompression) along the direction of motion of the wave

Resistance

aims to slow down and make charge less strong -resistivity is the p and changes per mateiral measured in ohms -Length: longer length greater resistance (more charge dissipated) -Cross Sectional Area: bigger it is the less resistance (less charge dissipated) so to have high resistnace want thin -Temp: higher temps higher reistance (think e- more prone to move bc excited), they are proportional any change in temp will cause that same change in the resistance Ex raise by 2.3 (600/293=2.3) then resistnace raised by 2.3, T1/R1 = T2/R2 (any linear relationship) and since I and R are inversely related T1*I1 = T2*I2 -Resistors convert elctric E to thermal E, thermal E is heat and that can come from friction etc so (friction leads to heat) so think of it that way.-Electric E-Friction in R-Thermal E

Intensity

average rate of E transfer (Power) per area across a surface that is perpendicular to the wave (hitting the obj at 90degree) W/m^2 -Intensity is also proportional to the SQAURE(^2) of the amplitude-double ampltiude 4x the intenstiy******* -A^2=I -bc intesnity also realted to distance, think of source as radiating a sphere of sound and bc sphere the Area then use sphere of rea formula= 4pir^2, so larger areas lower intesntiy, realted by a square, so if radius (Pt where u here sound) increased by 4, then intensity decrease by 2 -Softest intensity: 1e-12 W/m^2 -Pain Intensity of sounds: 1e4 W/m^2 -Intenstiy=P/A, A=4pir^2 -intesnity is not related to doppler bc doppler is about PERCIEVED freq not actual while this is based on actual E and waves

Ohm's Law

basically resistance results in E loss which drops electric pot, so higher resistance means more V drop and I does not change when resitance increases bc of this -when discharging the current supplied will move from high EP to low Ep (galvnoic) (normal spont) -When charging, external voltage applied so move from loe EP to high EP (electrolytc)

Potential Energy in capacitors

bc function to store charge it holds PE Note the V is voltage not velocity NOTE!!!!: If solving for charge, then bc C=Q/V then u can cancel out the V^2 -Note: bc of math properties, u ONLY 1/2 of the C or V^2 not both, ex":100*12^2/2=50*12^2

Electric Field of Capacitor

bc sep charges (+ and -) you have E field btw plates -the e field moves from + end to - end Volts/d btw -this a uniform electric field bc the e field lines are equally spaced and moving in the same direction

Plane Mirrors

bc surface is flat, then follows law of reflection -if parallel indicent ray then parllel reflecting ray -ALWAYS creates virtual images -image appears to be same distance from mirror as the actial obj

dielectrics in circuit capacitors

charged capacitor w/in circuit still connected to voltage source charge on capacitor increases voltage constant (= source) increase capacitance -C'=kC (k is the factor that it increased it by and since never decrease it then k always greater then 1) A dielectric (or dielectric material aka k) is an electrical insulator that can be polarized by an applied electric field.

Circuit Laws

depend on notion that charge and E can not be destroyed or created -Kirchoff Junction Rule: when current moves to junction they will be split by number of pathways possible (cant pick one), the I for each can be different (dont have to be equal) just needs to add up with you came in with (charge conserved by I=q/t) Ex: I going in gets split into Ia+Ib=Itotal at branch, the branched values of I are based on whatever I is after it passes next through next circuit thing in that branch (sum of enter=sum of leaving the junction) -Kirchoff Loop Rule: in cloesd circuit, bc of conserving E you can not have more Voltage (J/C) than the source provided (Voltage Source=Voltage Drops through entire circuit), all of the voltage must be used up by end of circuit, so as you go through something your V constanly decreases as it goes through, total potential difference will always be 0 in a lopp Note: each elemtn incircuit needs to apply V=IR formula,voltage and I changes depending in situation just sayin Vtotal and I total can not change so basically when solving these probs use the total to then work your way to specfic elemnts and their VIR numbers Circuit E: kinetic E of e- (moving) converted to themal E, light or sound

Doppler effect

describes the diff btw actual frequency of sound from sources and its perceived (relative to eachother)-think Doppler D/S (cardiac is S/D) -the top bottom is realtive to eachother, so can both be coming toward and both use top or one top (toward) other away (bottom) or away away (bottom) -D is detecter, S is source -V is speed of sound in medium -Vd and Vs is speed of detecor/source,can be 0 if nobody is moving, watch out for conversions -Toward->Top -Bottom->away F' is the perceived, F is the actual frequency -applies to all waves includig sound and light -if detector is getting closer to source (toward) then F perceived is higher (sounds louder) (denom decreases and numb increases net increase in perceived), father away less perscived, then think how this applies to wavelgnth in which freq and lmnda are inverse -Think +/-, then reciprocal in denom -stationary then 0 vd/vs (either) is 0 -v is speend of sound (3e2) -Doppler shift is the change in freqency (actual) due to the source/obs velocities, which leads to observed freq -doppler effect=doppler shift from the velocity onto the freq -no doppler shift=no veolcity =v=0 ---v must be 0 when no shift bc vd and vs are 0 then speed of sound is 1+0/1+0 (aka 1/1) *f=f' in whicf f'=f, and speed of sound cant be 0 SO vd or vs must be 0 -Note: when the source is an imaging tehcnique (ultrasound) the source is 0 -u essentiallly also have a percived velocity (by the things inside the ( ), so bc of that also have a percieved wavelgth

Speed of light formula

f=c/λ c=3e8

electric potential energy

form of PE (hence U) that depends on distance btw charges, the lower value of U the more stableand less reactive (think want -U or lowest possible U+), measured in Joule U=KQq/r=W -like charges will have a high U (+U) and repluse (less stable) (+U tells repulse), far apart more unstable(+U↑) but closer less stable(+U↓) (think like +100 v +1) -unlike chages will have small U (-U) and attract (more stable) (-U tells attract), and as r increases become more stable (U becomes more negative and makes stable) -when thinking about it as work think of it as ∆U=W can think of it as W bc W=F*d, and when pluGGING IN ElecF*distance you cancel out the r^2 to r -when thinking of W think of it as W needed to move a test cahrge from infinity to a pt in the E field, NOTE: this is not eletric pot (v) electric pot E is U, W done on a charge to move it +W means work was done by the system onto the charge (work was needed to move them, aka the same charged particles, closer is high), W was done by the system onto the charges to move them in the same area (from inifinity to near eachother in E field, always wanted to be far from eachotehr but bc of formula and what we are measuring then we had to do something to move them) -W means work was done on the system by the charges, W from attraction was done by the charges onto the system -Aso remeber that W=KE=1/2mv^2 so can find v/speed of charge by U AFTER the charge has moved, bc before the charge has moved then U>KE the speed upon imapct will be when KE=U- bc no U anymore all that E has been changed into KE

Force on a current in a B Field

happens bc a moving charge creates a mag field that exerts force on other moving charges -if charge is parallel to the moving cahrge then no F exerted on it bc sin180=0 -remebr when multiplying vector the product will be from the palm (v*b=F product so F in hand) -I current direction (+q) is thumb, fingers are B, palm F

Force on moving charge

happens bc a moving charge creates a mag field that exerts force on other moving charges -if charge is parallel to the moving cahrge then no F exerted on it bc sin180=0 -remebr when multiplying vector the product will be from the palm (v*b=F product so F in hand) -velocity of cahrge(+/-) direction is thumb, fingers are B, palm F of pos charge bak hand s force of neg charge electrons use left hand rule same shit

Transerves waves

have particle osscilation perpendicular to the direction of propogration and E transfer( wave dirction is left but the ossicaltion is up and down) -basically classical ex -think of wave in stadium: people go up and down (perpindcular) to the direction of the wave, -think transverse between the x plane -seen in electromagentic waves: light waves, microwaves, xrays -can form a transverse wave by attaching a string to a fixed pt and moving hand up and down -bc E is delvied in the direction of wave travel, then the wave not only ossicaltes perpendicular to the direction but also to its direction of E transfer

insulator v conductor

insulator- valence electrons tightly bound to its atom and nucleus, so holds charge and doesnt want to transfer charge to a neutral obj-hold q from being dissipated-NON-metals conductor- delocalized electrons, metallic bonds, charge is distrubuted evenly on surface and able to transfer charges (circuits or electrochem cells), think e- able to move loosly and freely and loosly bound to nucleus-wants to spread q-METALS and IONIC solutions - sea of e- to loosley move charge over Electrons within metals are weakly attracted to their corresponding nuclei because the atomic number of many metals is such that the distance between positively charged protons and negatively charged valence electrons is relatively great. Consequently, electrons within metallic materials may be easily dislodged following exposure to an external electric field. Therefore, most metals are electrical conductors whereas most nonmetals are electrical insulators (materials that do not readily transmit electrical energy).

Amplitude

is essentinally the mesaure of E, high E means high amplitude, think amplitiude as E needed to push off against the medium to create the wave -Remember that sound looses E, but that happens from hc/lambda not hf

Electric Field Lines

lines that represent both the magnitude and the direction of the electric field -more there are stronger the field -vector quantity, and conventially the direction of the electric field comes from how a poistive test charge would move near its source -if source is also positive then repulse and test charge would accerlate away from source but if negative then would acc toward source-gives convection of field lines -Assumes + middle source -When drawing in presence of other things, its easier to draw one line per attraction or repulsion to other moelc (although radial), and then cancel things moving in opp direction to know where itll flow Ex: pyrmaid of charges bottom left + bottom right - then top is +. Top will have 2 forces attract and repulse so attract moving right and moving away from other, then do the same for each molec then cancel out things going, (if diff value of charges then draw a line for each value +2 then 2 rright 2 down etc)-essential;yl draw out the vectors of the field, just think how each cahrge exerts on eachother (remebr attraction pulls while repulstion makes u go opp way)???????AAMC material REVIEW REVIEW

E=HF aka E=HC/l

longer wavelgnth, more time then E has to didpisate so lower E it has shorter wavelnght, less time E has to dissipate so higher E Xray/gamma ray do NOT abs photons, they damage tissue bc they abs E of the photons and cause ionzation in tissues (so thats why high E gamma rays aka low lambda are most bad for u? -be careful with h*c bc that gives u 21e-26 aka 2.1e-25 (so when doing calcs keep them straight)

Magnetic field of straight wire

measured in Tesla (N* s/m *C), happens bc a moving charge creates a mag field that then exerts force on other moving charges -the mag field is circular and cocnentric -to find direction of mag field point thumb to were POSITIVE charge is moving and act like grabbing wirse -bc mag field is circular then use pi

Magnetic Field of loop

measured in Tesla (N*s/m*C), happens bc a moving charge creates a mag field that then exerts force on other moving charges -the mag field only found inside wire not outside, bc of this dont use pi, i is the current (I) -Mag field only inside bc since a circle moves that has centripetal accelration and Force that drive the mag field inside (hold hand and go in XXX: goes in OOO: goes out page -same formula as straight just change based on pi bc of where magfield is located)

Charges

proton (+) and e- (-) -opp charges attract -similar charges repel Regardless if+/-: -magnitude of charge is 1.6e-19 Columbs****** -if positive then +1.6e-19, if negative -1.6e-19 Remeber the mass of the proton>mass e- -(e-) mass: -(p+) mass: Charges measured in Coulmbs If Value of something is given, then just plug and chugg that number dont need to 2q it, ex +2uC then use 2uC (that was already solved for u) no need to 2q=q(1.6e-19) it, only do that when its 2Q etc

Quantity of Charge formula

q = ne -q= charge produced -n: nyumber of electrons/protons -e: 1.6e-19 This is the product of charge, so depdenign on ur charge then u input the opp values, if +product that means e- remvoed, inf neg product that means protons added

Timbre

quality of sound from vibes at same freq

Power

remeber power is measure of E transfer over time (W/t or E/t) so in cicruits same concept with I supplying time V supplying E -this measure the rate of E transfer from ElecE to KE as e- flows and moves in ciruit, think PIV and PIIR(I^2, Piiiier) and V^2/R -Electric Power is dissipiated as heat and light (heat usually for resisitors bc of the friction they have)

Farday's constant

remebr units and how Q=mol e-*F constant (F constant=9.7e4 C/mol e-)

Special Cases in Electrostatics

skippped abt equipotential lines, electric diploes

Standing waves and nodes

standing waves will form whenever two waves of same freq traveling in opp direction interfere as they travel through same medium (going toward eachother) -obj that support standing waves: closed boudnries-allow nodes (no room for displace and appear like no fluctuation) or open ends at both -boundires that allow maximal ossicaltion-correspond to antinodes (btw nodes that have amplitudes)

Electric field strength

strength of force per unit charge(F/q), essentially the stregnth of the electric field that is created from the force? or can be E=KQ/r^2 -electric charges create a surrounding circular e-field (why we use radius) and these fields exert forces on other charges that move into its space -measured in Newton/Coumb (N/C) bc force over charge (test q), and in pic gives us a ratio of how Force and charge are related- if using test charge can measure force exerted on this test charge (through this formula) (q) -if given source charge (Q) and use FE UV eqn -a collection of charges will exert a net Electric Field at a pt in space that is equal to the vector sum of all the E fields, bascailly if on beads on string can add the realtionships between Ato B, B to C , and A to C to find the total -vector quantity, and conventially the +/- of E field gives the direction of the electric field comes from a poistive test charge would move in the presense of of the source charge, ALWAYS remember electrostatics is based on + charge so..... -if source (Q) is positive then repulse and test charge would accerlate away from source but if negative then would acc toward source-gives convection of field lines -important to know how the F vector and Field vector are in relation -also remebre F:ma (so can tell direction of movement by force) given from E field, if -E then attracting and going toward but if positive E then repulsing and moving away, but do note that F and E are vectors to eachother and so the F and E can add together or cancel eacother out? -+F and +E means the F vector and E vector going in same direction -but if -F and -E then attract and F vector and E vector are opposite to eachother (F vector is the direction of the movement if not stationary anymore while E field normally applied F on that charge) -Electric charges generate electric fields, regions of space that exert an electrostatic force on charges. Electrostatic force is conservative; the total energy of a charged particle in an electric field is conserved, so U+KE=Total E

Capacitance

the ability of a conductor to store energy in the form of electrically separated charges to then use them later (Defirbulator) -measures in Farrads (1F=C/V)-remebr units and how Q=mol e-*F constant (F constant=9.7e4 C/mol e-) -more voltage difference harder to store and capacitance decreases -bigger charge easier to store then smaller -increases plate overalp (A) increases C -closer plates are to eachother (smaller d) increases C C=sigma0(A/d) (sigma constant) -when a dielecttric mateiral (insulator like plastic ceramic etc) used is increases capacitance C'=kC (k is the factor that it increased it by and since never decrease it then k always greater then 1)

Law of reflection

the angle of incidence is equal to the angle of reflection Θincident=Θ reflected -Reflection: happens when light waves are not refelcted and not abs when hitting a new medium and bounce off, reboudning icidnet light, the reflected light goes back into the same medium (back to the air) -Θincident is the angle FROM the normal, if something strikes the mirror that is not stated as from the normal (perp to the mirror) such as "strikes the mirror at 35 degrees" that means it hits the mirror at that angle BUT the Θincident is compliment to what it hit bc Θincident is based off the normal which is parallel to the plate and since coming in at an angle then you need to find the angle in which the normal is parallel aka just fidn the compliment Ex: angle of diffraction struck at 35 so Θincidentis at 55-compliment to 90 to get the perp normal line-draw out helps understnad better

Critical angle

the angle of incidence that produces an angle of refraction of 90 degrees -this is the bare minimum angle in which anything above this angle would result in total itnernal reflection -critical angle changes per medium but only happens when going high to low -refracted angle is another angle not the same one that bends in, it is the one that is in the other medium -Critical angle is just when the refraction angle is 90 (Θ2=90º), when beyond that angle, then no refraction and TOTAL INTERNAL REFLECTION -Θc←Θ1=Θ2→90º -when agle of incidence is equal to at crtical angle reflection AND refraction happens Θc<Θi→total internal reflection

Refraction

the bending of light as it goes through one medium to another, bc speed of light is always the fastest (bc going through vacuum) then speed of something going through medium will ALWAYS be less then speed of light (3e8) -n is the index of refraction, in vaccum its 1 and bc air in vaccum is 1 that means the index of refraction will ALWAYS be greater then 1 (To make velocity smaller bc othng faster then speed of light) -even when refraction is happening, reflection is also happening!(reflection never goes away but refraction can at total internal reflection) note ratio of speed c/v

Current

the flow of a charge btw two points at diff EP per time (how fast a charge passes aka charge flow rate) -Measured in Amps (A=C/s) -current measures the flow of a postive charge (high EP to low EP) although protons dont actually move, so to find direction that e- moving just opp direction of current -this also means, that a charge has a vlaue of current aka amps per second -remeber current happens bc of the pot diff. (wants to move spont high to low for +), but when no charge is moving btw each sides that are diff pot values (V) the volatge is called emf (1V=J/C)

natural (resonant) frequencies

the frequency at which an object vibrates most easily and with the largest amplitude

Sound level

the logarithmic scale that measures the amplitudes of sounds that humans can hear -measured in dB -I is the intenstiy of the sounds -Io is threshold of hearing: 1e-12, constant use this formula as a reference if not given muliple intesntiies -dB is the decimal log scale of meausing intensrity If sound 1 is 10 decibels louder than sound 2, it is 10 (10^1) times as intense. If sound 1 is 20 decibels louder than sound 2, it is 100 (10^2) times as intense. If sound 1 is 30 decibels louder than sound 2, it is 1000 (10^3) times as intense Looking at the formula u will see that dB is its own value called sound level, and the inteity are a part of sound levels so that means to find intensity u have 10^x db AND THEN muliply Io is lowest intensity sound , so if intensity chagnes that means u have to find the new value of the log10 of it then multiply it by 10 so increased by a magnitdue of 4 (10^4) then that means 4*10=db raised ---------------------------------------- think like ur solving for the intesity ratio, B=10*log10(x), remember log2(8)=3 which is 2^3=8 (to undo log), so 10^B/10=x=Intesity ratio -so 10db then 10^10/10=10^1 aka 10x more intense etc

fundamental frequency

the lowest frequency of vibration of a standing wave v is wave speed n is harmonic the overtone in the hamoic -1, the n=3 has harmonic of 3 but secondary overtone v=fl, so just rearrange in whiich f=v/l and apply the 1/2 wavelength to it so f=v/2L

frequency of sound wave formula

the number of complete wavelengths that pass a point in a given time Speed of sound 3.4e2m/s, spped light 3e8 m/s -when electromagnetic (radio, micorwaves, IR, UV etc) then use 3e8 but when soudnwave the use 3.4e2 m/s

Harmonic

the number of half wavelengths

Focal Point

the point at which rays parallel to the optical axis reflect and meet the point at which rays or waves meet after reflection or refraction, or the point from which diverging rays or waves appear to proceed.

Electric Potential

the ratio btw the magnitude of a charges Electic-PE (∆U=W or just U) to the magnitude of the test charge, this gives the electric pot for a single charge -measured in volts (1V=J/C) -if no test charge then use V=kQ/r -potential to move (but dont actually) -scalar so sign matters and depends on the source charge, minus charges flip relationships -its the potential to move if given the chance? FE related UV related eith E and V being singular and based on per unit charge bc V=U/q and E=F/q so only difference is the top aka V is based on E while E is based on F (Fe strong, UV is E from sun) while FU based on things together

Velocity of light after refraction

the speed of a wave/light does not change until after it enters a diff medium -the only time the speed changes is when in diff medium (but remeber never faster then 3e8) n=c/v

Magnification equation

this gives the ratio of size of image to size of obj -m: (-m) means image inverted but (+m) is upright-this makes sense +m is right -m value: m smaller then 1 (ImI<1) then smaller, m bigger then 1 (ImI>1) then bigger, this is based on magnitude/value not signs Remember UV IR (if upright then virtual, if inverted then real) -m tells u both size and orientation, think big M (big magnitude) tells u big and vise versa, and +m tells u upright like normal but -m tells u inverted (neg bad) -can also use hi/ho for the height of an image over the height of the object, so if hight of image is bigger then biger m and thus M (bigger) etc the sign just tells u inverted or upright aka i/o=hi/ho

Intensity sound change

to calc new sound level when intenstiy has changed -Note: If/Ii is a ration of final to intiail intsnity -sound usually decreases in intesntiy as time passes as a result of damping/attenuatio -any nonconserattive forces acting, decreases amplitude which then decreases intensity and sound level-it does not decrease frequency however (attenuation usually neglible)

noise

vibration at mulitple frequencies