PHYS 1010 Final Exam

You can deliver energy from one place to another using...

particles or waves

Moving energy with a wave

-energy and information are transmitted from one place to another without necessarily any material object moving between these two locations

-mathematically, a wave can represent any repeating motion such as an object rotating in a circle, a swinging pendulum, an object bouncing on a spring

Two things are true of any and all waves

they exhibit the properties of diffraction and interference

What is the difference between particles and waves?

the properties of diffraction and interference

Diffraction

occurs when waves are forced to move around objects in their path

Interference

-occurs when multiple waves overlap each other, resulting in a different final product

-no two particles can exist in the same place at the same time

-will either make the wave bigger or cancel it out

The three types of waves

1. Mechanical

-some type of physical medium transmits the waves

-water waves, sound waves, seismic waves

2. Electromagnetic

-waves in electric and magnetic fields do not require a material medium

-all electromagnetic waves travel at the speed of light

-radio waves, light, microwaves, x-rays

3. Matter

-quantum mechanical descriptions of particles

-protons, electrons

Definition of wave

-an oscillation (vibration or wiggle) that repeats in time and space

-what exactly is doing the wiggling determines the type of wave

Amplitude

-the maximum displacement from the equilibrium position (the distance from the mid-line to the top of the crest)

-is measured in units of displacement (e.g. for a water it is distance and for a sound wave it is pressure)

Wavelength

-the distance required to complete one vibration

-it can be measured as the distance between crests (or troughs)

-wavelengths are always measured in units of length

Frequency

-the number of complete vibrations occurring per unit of time

-measured in hertz

Frequency and period are related through the equation...

Frequency=1/period

The velocity of a wave

-the distance a crest (or trough) travels in a a given time

-V=wavelength/period

Transverse waves

-up and down waves

Longitudinal waves

-back and forth waves

The two different ways that a medium can be disturbed during a vibration

1. when the motion (amplitude) is at right angles to the direction of propagation it creates a transverse wave

-this is the type of wave we normally think about such as a string vibrating, a water wave, or an electromagnetic wave

2. when the motion (amplitude) is parallel to the direction of propagation it creates a longitudinal wave

-sound is a longitudinal wave

Interference of waves

-all waves obey the principle of linear superposition that states that when two or more waves are present simultaneously at the same place, the resultant wave is the sum of individual waves

-when two waves cross, they add together at the point where they cross

-at the instant they cross, the total amplitude of the wave is the sum of the two individual waves

Constructive interference

-when two waves interfere and they both have a positive amplitude, resulting in a sum that is greater than either of the individual waves

Destructive interference

-when two waves interfere and they have opposite amplitudes, causing the waves to cancel out

Standing waves

-when we add two amplitudes of waves with the same amplitude but moving in opposite directions

-commonly occurs when waves are reflected

-the waves don't stand still, the amplitude can still vary. However, there are points along the wave called nodes, where the medium stays fixed

Antinodes

points where the wave is at maximum oscillation

Resonance

-a wave that is confined between two boundaries and has a standing wave pattern achieved with large antinodes is produced at resonance

-the wave is oscillating resonance frequencies

-making atoms vibrate at resonant frequencies can shake the bonds at a frequency that we appreciate or can increase the vibrations to the point of violently rupturing the atomic bonds

Resonance frequencies on a daily basis

building resonant frequencies is what you do when you raise the octave

Sound is a ____ wave

longitudinal

The speed of sound waves can be determined by...

the medium that they travel through

The amplitude of a longitudinal sound wave is a pressure described by what equation?

-pressure=force/area

-uses the unit of Pascals

Decibels

-measures sound intensity

-orders of magnitude of power (a logarithmic scale: goes up by factors of 10)

The Doppler effect

-describes the change in frequency as a sound-emitting object moves with respect to an observer

How the Doppler effect works

-as a source approaches a stationary observer, the distance between successive waves being emit decreases

-this means that the wavelength gets smaller when it gets to the observer

-because the velocity of sound probably isn't changing, the frequency that the observers hear must increase in order to compensate for the decrease in wavelength (the closer something is to you, the higher the frequency)

-if the observer were on the other side of the sound source, they would detect the exact opposite effect: as the source moves away from an observer, the distance between successive wave fronts increases, meaning that the frequency of sound will have to decrease

Sonic booms

-the Doppler effect also causes sonic booms generated by objects that travel at or above the speed of sound

-an object traveling at the speed of sound would give all of the sound waves that it generates overlap each other, producing a resulting wave with an enormous amplitude

-the amplitude of this result wave represents a huge change in pressure emanating from the object (referred to as shock waves)

-when all of these waves reach an observer, they hear one very loud noise because all of the waves will reach them at the same time

-sonic booms are also caused by lightning heating up in the air around a flash, causing the air to expand and instigating a sound wave (thunder)

The electromagnetic spectrum

-light behaves as a traveling wave of electric and magnetic fields

-different frequencies (or wavelengths) of electromagnetic waves dictate their appearance, including visible light (although most frequencies are invisible to humans)

-the frequencies of electromagnetic waves are displayed in the electromagnetic spectrum

-the spectrum has no upper bound and is continuous

Higher frequency = ____ energy

higher

Increasing frequency = ____ wavelength

decreasing

Electromagnetic waves travel at...

-the same speed

-c

-c is the speed of light and is constant

When light strikes a surface, it can either be....

Absorbed (transparent materials), reflected, or refracted

Reflection

reflected light bounces off of the surface

Refraction

refracted light travels through the surface

Reflection and refraction occur depending on....

-the atoms that make up a substance

-electrons will absorbs some colors (frequencies) of light and emit others

-how they emit light waves determines reflection and refraction

Angle of reflection

-when light is reflected from an interface the light waves that are absorbed are re-emitted as though the light is bounced off the surface

-the angle of reflection is equal to the angle of incidence

How does refraction change waves?

-waves that are refracted continue to pass through a material, but their properties can change based on the material itself

-the waves will likely change velocity as they enter a new material

-this will alter the path of waves as they move

Snell's Law

-this equation tells us that if we have two different media at an interface (different indices of refraction), then the angle that the light travels will change

-the light ray will curve (bend) at the interface and then travel in a straight line

-any light that reaches our eyes after passing through an interface is lying to us because the light ray has not been traveling in a straight line

Density and refraction

-the phenomenon of refraction is actually due to the density of a material that the electromagnetic waves will travel through

-light will travel more slowly through denser material. It is this velocity that causes the light ray to bend

-this occurs because no matter what happens, light has to be the fastest thing in the room and will always seek the fastest path (which does not necessarily mean shortest)

If a hunter is trying to shoot a fish that he can see underwater where should he aim?

He should not shoot at where he sees the fish because that it is not where the fish actually is. The light of the fish is bending up and toward him

Chromatic dispersion

since different colors of visible light are representative of various wavelengths of light, different colors of light are refracted at different angles when incident on an interface; the light will spread out by refraction

Which frequencies are refracted more?

-higher frequencies (smaller wavelengths) are refracted more than lower frequencies (longer wavelengths)

-in the visible spectrum, this corresponds to blue light being bent more than red

Why is the sky blue?

-the atmosphere bends light the same as everything else

-light from the sun comes in

-blue light bends more than red light so it is what we see and the red light just passes by

-as the sun sets, the red light can now reach us but the blue light bends into the Earth

Total internal reflection

-the one special case that arises from Snell's law

-if n1 is greater than n2, the angle if refraction will reach 90 degrees before the angle of incidence, and the refracted light will become internally reflected

-the light is trapped

-the angle of incidence in this situation is called the critical angle

-when the angle of incidence reaches the critical angle, the ray of light is said to be subject to total internal reflection

-total internal reflection may only occur when the light source is contained in the medium of the higher index of refraction and is the driving concept behind optical fibers and similar devices

The polarization of an electromagnetic wave

a description of the angle with which the electric field oscillation is oriented in a coordinate system

Unpolarized light

-the light admitted from most common sources

-means that the electric field vector (E) changes direction randomly

Polarizing filters

-unpolarized light can be polarized by placing a special filter in the path of the incident beam

-these polarizing filters contain parallel "barrier" lines that only allow the E vectors parallel to them through the filter. All perpendicular E components are absorbed (blocked) by the filter

-the total amount of light that passes through the filter is thus half of the light that was originally striking the filter

-this helps with glare because you can't see the vertically polarized light which is the glare that comes off of water

Diffraction of light waves and diffraction patterns

-diffraction occurs when waves encounter a barrier in their path that has a very small opening through which the wave can pass

-if the opening in the barrier is on the same scale as the wavelength of the wave, when the wave passes through the opening it will spread out in all directions on the other side of the barrier

-the spreading out of the resulting waves on the right side of the barrier is consistent with the opening behaving as a point source, as described in Huygens principle

-this effect occurs in the same manner for any wave and any obstacle, provided that the size of the obstacle and the wavelength of the wave is on the same "scale"

-high frequencies do not bend as much as low frequencies e.g. the sound waves passing over sound barriers on the highways are usually only large wavelengths (low frequency) sound waves

-when waves fan out in this manner, they can interfere with each other (over short distances) and produce what's referred to as a diffraction pattern on a nearby surface

-the diffraction pattern is made up of points where the light waves constructively and destructively interfere, giving a pattern of bright and dark lines which depends on the shape and size of the opening they pass through

-diffraction patterns can be created by a wide range of shapes

Young's interference experiment

-generally regarded as the first definitive experimental proof that light was a wave, and was later used to prove more abstract concepts of quantum mechanics

-monochromatic plane waves of light are diffracted by the single slit on barrier A, the diffracted waves then travel to barrier B where they are diffracted through two separated slits

-the waves diffracted independently from the two sources begin to overlap each other as they travel toward the final barrier C

-the interference resulting from this overlap creates bright and dark regions (fringes) on barrier C

-the pattern of bright and dark fringes constitutes the interference pattern produced by the two small slits in barrier B

The discovery of the photoelectric effect

-there was a well known experiment that could not be explained using Maxwell's description of light waves

-the two issues that arose were that the kinetic energy of the ejected electrons did not depend on the intensity of the electromagnetic waves and some of the colors didn't produce any ejected electrons at all, regardless of intensity

-in 1905, Albert Einstein was able to provide a description of these results (now called the photoelectric effect) by assuming that light is not continuous and instead is made up of indivisible particles, called photons

-Einstein's proposal suggested it was the frequency (or wavelength) of the electromagnetic waves that determined the energy they transferred, not the intensity

Photon

-the quanta of quantum particles (packets) of light

-quanta are the most basic of particles

The energy of a particle is determined by...

the frequency

The quantum of a light wave of frequency has energy E according to the relation

-E=hf=hc/wavelength

-h is Planck's Constant

-this tells us that the smallest amount of energy that a wave of frequency can have is hf

-if the wave's energy is greater than hf, then it has to be a multiple of hf, containing more than one photon

-since the photon is the basic carrier of electromagnetic energy, energy is also quantized

When do absorption or emission of light from matter occur?

-when a subatomic particle absorbs or emits an individual photon

-when light is absorbed by an electron, the energy of the electron increases by one photon energy

-when light is emitted by an electron, the electron's energy decreases by one photon energy

-the energy of the light transferred to the electron had to be enough to overcome the work function of the atom

-any excess energy was observed as kinetic energy (seen in the photoelectric equation)

Wave/particle duality

-waves can behave as particles

-light behaves as a wave but also as a particle, like colliding billiard balls

-light also has momentum like particles do

-particles can also behave as waves

Wave/particle duality and the double slit experiment

-when individual photons are subject to the double slit experiment one at a time, you would still see an interference pattern

-if light were only particles, this would suggest that the particles can interfere with themselves

-this effect also occurs when electrons are sent through the double slit experiment

The initial work that led to the discovery of the atom

-1827: Robert Brown postulated the presence of atoms when he noticed the random motion of pollen grains on the surface of a liquid

-1887: JJ Thompson discovered the cathode-ray tube when he noticed a beam of light passing between high-voltage plates

-the importance of this was that the light beam behaved exactly like an electric current, it could be bent by electric or magnetic fields

-this led Thompson to the conclusion that the beam of light he created was the result of a stream of elemental electric charges, which is essentially the discovery of an electron

-he was also able to measure the ratio of an electron's charge to its mass

-25 years later: Robert Millikan was able to measure the elemental charge of an electron, and thus the electron's mass

-the electron was added to the model of the atom

-1909: Ernest Rutherford gave a menial task to his students who discovered the positively-charged nucleus of atoms doing the task

-Using what was already known about the atom, Rutherford postulated that the positive charge of the nucleus was due to an elementary particle called the proton

-1932: the neutron was discovered

The Bohr Model

-electrons orbit the centrally positioned nucleus in specific paths, much like planets orbit the sun in our solar system

-the amount of energy that an electron has is determined by the orbit in which they are located

-they cannot exist between levels

-closer orbits have less energy than farther away orbits

How do electrons move between orbits?

-by gaining or losing energy. The way that electrons do this is by absorbing or emitting light, respectively

The two specific rules for how electrons fill the energy levels

1. all electrons want to be in the 1st level

2. exclusion rule: no two particles can be in the same place at the same time

Spectroscopy

-when an electron changes energy levels, it emits or absorbs a single photon, the energy of which has to match the energy difference between the atomic energy levels

-spectroscopy measures the photons that are emitted by atoms, different colors of light imply photons of different energies

-more specifically, the electron levels of an atom can be mapped by measuring the photons that are given off by electrons that move from level to level

-there is no "in-between" for electron transitions, it is either a single, complete transition or nothing at all

-if there were "in-between" energy amount, we would see a gradual spectrum of colors for every transition

Do atoms look the Bohr model?

-no, but it is still useful for demonstration

-quantum physics showed us that the position and motion of everything is based on probability

-from this, we know that atoms look like a mess

-atoms contain a nucleus surrounded by a cloud of probability which provides the possible positions and energies of the electrons because we cannot know exactly where they are

Atoms

-considered to be the basic elements of everything in the universe

-even though we know that there are things that are smaller than atoms, these objects do not arrange themselves to make larger objects the way that atoms do (e.g. electrons are smaller but you cannot build with them)

Elements

-there are currently 115 discovered types of atoms, known as elements, but we can reasonably assume that there are at least 118 elements

-many of the largest elements (and those most recently discovered) don't appear naturally and must be created in a lab. Nearly all of these are incredibly unstable and only last for millionths of a second

-which elements are which, and the properties of elements, are determined by the number of protons within the atomic element

-all elements want to be in the column the farthest to the right on the periodic table

What is the primary element of the universe?

-hydrogen

-hydrogen atoms are the first that were created in the universe, and it is doubtless that all other hydrogen atoms that exist in the universe currently are remnants of the first few minutes of the creation of the universe

-all other natural elements are created through the process of fusing multiple hydrogen atoms together to make larger elements

What is the largest element (highest number of protons) that can be produced by a star such as our sun?

-iron

-all other elements were formed from other stellar phenomena, specifically supernovae (exploding stars)

Can we see atoms?

-atoms are the smallest object that we have been able to see

-atoms are too small to be see using visible light because the wavelength of visible light is hundreds of times larger than the atoms themselves

-thus, tricks need to be used in order to develop pictures of individual atoms

How do atoms arrange themselves?

-atoms arrange themselves to form larger objects using very structured patterns

-how strongly these bonds hold determines whether the molecule (the object) will be a solid, liquid, or gas, among a large range of other properties

What determines the properties of an atom?

its protons

What state do all atoms tend toward?

-being neutrally charged

-to do this, there must be an equal number of protons and electrons

-however, there is an also an issue with how the electrons are placed in the energy level and whether their electron spins are paired (up and down)

-because of this, many atoms would rather have more or fewer electrons than protons in order to satisfy these other issues

-will achieve this by gaining, losing, or sharing electrons

Covalent bonding

atoms share electrons by sticking together

Ions

an atom or molecule with a net electric charge due to the loss or gain of one or more electrons

Ionic bonding

when positive ions and negative ions attract each other

Ionization

-the amount of energy required to remove an electron

-depends on the number of protons and electrons in the atom and how the electrons are arranged

How do we instigate chemical changes?

-by removing one electron from the atom

Quarks postulate

-it was postulated that because electrons were so much smaller than other particles, that maybe protons and neutrons were made up of even smaller particles

-suggested that protons and neutrons were each composed of three of these hypothetical (at the time) particles

-Murray Gell-Mann named these particles quarks

The Stanford Linear Accelerator experiment

-in 1968, a group of scientists at the Stanford Linear Accelerator effectively discovered the presence of quarks by running electrons into protons

-further experiments of ramming things together provided an increase amount of info about these sub-sub-particles

How many quarks are there?

-protons and neutrons are made up of 3 quarks, each of them having a combination of 1/3rds of an electron charge

-the number of quarks has been firmly established at 6, with each associated with an anti-particle (12 total quarks)

-each quark also has three possible colors

Quark possibilities

UP (+2/3e)

DOWN (-1/3e)

STRANGE (-1/3e)

CHARMED (+2/3e)

TOP (-1/3e)

BOTTOM (+2/3e)

-the first two make up protons and neutrons

-the last four only existed naturally for a fraction of a second after the Big Bang

Quark/anti-quark colors

-Quark Colors: Red, Green, Blue

-Anti-Quark Colors: Cyan, Magenta, Yellow

-colors must add up to be white

What particles are their own quark?

-electrons

-neutrinos

-muons

-tau particles

-all belong to a class of particles known as leptons

What specifics don't fit in the Standard Model of Particles?

-gravity

String Theory

-considers everything in the universe based on vibrations in energy similar to that of vibrations in a string which cause matter and charge to exist

-it may involve as many as 11 dimensions, although at least 7 are wrapped together so tightly that they are (somewhat) immeasurable

Relativity

-is concerned with where and when events happen and how the events are separated in space and time

-this includes how events appear from different reference frames (different situations of viewing an event)

Spacetime coordinates

-x, y, and z: tell us where an event happens

-t: tells us when an event happens

The relativity of simultaneity

-when reference frames move at different velocities, the issue of simultaneous events becomes a problem

Example

-suppose a person standing still (Sam) sees two events that happen at the same time (simultaneously)

-if another person is moving with some velocity past the first observer (Sally), they generally will not describe the event as being simultaneous

-depending on the velocities of travel for the light (which is finite) and the observer, the event will occur at different times

-remember that from the moving observer's point of view, he is standing still, and the other person is moving backward

-neither of these observations is correct. They are both equally valid descriptions that took place

-simultaneity is not an absolute concept

-there is no such thing as simultaneous events

-it is relative and depends on the motion of the observer

Postulate 1 of the Special Theory of Relativity

-the laws of physics are the same in any inertial reference frame

-whether you are moving with constant velocity or standing still, the laws of physics will be the same in either situation

-it doesn't say that the measured values of physical quantities will be the same, only the relations between them are

Postulate 2 of the Special Theory of Relativity

-the speed of light in a vacuum has the same value (c) in all directions and inertial frames

Example

-imagine someone traveling in a car at a velocity relative to the ground who then "throws" the light forward

-the second postulate tells us that the speed of light thrown relative to the car is c and the speed of light relative to the ground is c. Someone would see the light travel at the same speed as someone in the car

Relativity of time

-time is not absolute

-time is different for people in different reference frames

The time dilation equation

-tells us that an object traveling at velocity v experiences a different time interval than one standing still

-the relation in this equation is that time slows down the faster you travel

-things that move quickly live longer

The relativity of length

a moving object shrinks (but only in the direction of motion)

Relativistic momentum

-in classical mechanics, the total momentum of objects (defined as the product of mass and velocity) involved in a collision would be conserved by all observers, in any reference frame

-the momentum of an object increases as the particle moves faster relative to an observer (v increases)

-the mass of an object increases as it moves faster

-as v approaches c, the mass approaches infinity. Since it would take an infinite force to accelerate an infinite mass, no particle can be accelerated to the speed of light

Relativistic energy

-mass and energy are the same things

-simply by existing, if a particle has mass it also has energy

Can energy turn into matter?

-yes

-this is how all matter in the universe was created. It is also a process that can be recreated in high-energy physics labs and occurs when huge amounts of energy are released from supernovae and other cosmological phenomena

Matter/anti-matter

-whenever matter is created, it is always created in matter/anti-matter pairs to preserve charge neutrality

-anti-matter is sort of the opposite of matter, like the hole that is left over when a marble is removed from a bucket of marbles

-the anti-matter particle of an electron is a positron, which has the exact same properties as an electron but is positively charged

-whenever matter and anti-matter come into contact, they annihilate each other and give off a burst of gamma rays

The General Theory of Relativity

-unlike the special theory of relativity, which only dealt with inertial reference frames, general relativity also covers non-inertial (accelerating) reference frames

-the basis of this theory is the principle of equivalence which states that there is no difference between a uniformly accelerating reference frame and one which is in a uniform gravitational field

General Theory of Relativity and deflection

-light can be deflected by a gravitational field

-if this is true, then light would not be taking the shortest path

-Einstein solved this by saying that light actually is taking the shortest path, but the path is not flat, it is curved

-on a curved surface, the shortest distance between two points will also be a curve

-these curves in space only appear in an acceleration reference frame, which is the same as a gravitational field