Physics 8: Final Exam Study Guide

Spring Term, 2006

The final exam will cover lecture material from Tuesday, 05/02 on Sound (Lecture 10) through the lecture on Thursday, 06/08 (Lecture 20). You will also want to remember basic definitions from the first part of the quarter dealing with forces, work, energy, power, etc.

You may also want to study the transmitter questions (PDF |PPT) we've had in class.

Below are the topics that are likely to appear in some form on the exam. The exam will consist of 40 multiple choice, 10 true/false, and 5 short answer questions. I'll give you a bucket of equations on the exam (See example front page). It may help you to know that I construct the exam from this study guide. I make the study guide by scanning the lectures and asking: "What do I want the students to take away from this?" Then I create exam questions by looking at each item and asking: "What can I ask to see if a student understands this concept?" This suggests a study strategy: ask yourself if you understand the concepts on the page: this can be more than remembering what the page says.

• Sound is fluctuation of air pressure: a series of compressions and rarefactions. These disturbances travel through the air at a speed of approximately 345 m/s (at sea level).
• Sound can be represented by a waveform characterized by a wavelength, frequency (or period, which is 1/freq.), and amplitude. The wavelength and frequency are related through the speed of sound: λf = c
• Sound waves are longitudinal in nature, meaning that the direction of wiggling of the air molecules is along the direction of propagation.
• Sound travels through all media (except vacuum, which is the absence of all media), and generally is faster in liquids than in gases, and even faster in solids.
• Our range of hearing spans from 20 Hz to 20,000 Hz: an impressive range of frequency compared to our eyes.
• A speaker produces sound waves by pushing and pulling a cone of material in and out to compress and rarefy (anti-compress) the air. This modulation then travels away from the speaker at the speed of sound.
• A speaker's size is related to its wavelength: higher frequency needs a smaller speaker.
• A simple sinusoidal sound waveform is a pure tone, at a single, well-defined frequency. More complicated waveforms involve higher harmonics, or multiples, of the fundamental frequency. The exact frequency structure determines what our ears perceive, and is what makes a trumpet sound different from a violin and that different from a voice.
• Understand how binary numbers (positive ones only) are constructed out of ones and zeros. For example, be able to express the number 97 in binary, and tell me what 010001110 is in decimal.
• Be able to add binary numbers, showing the work (carry operations).
• Digital audio recording involves sampling the sound intensity (pressure) at uniform instances in time, and assigning to each time a waveform amplitude (positive or negative), then representing this amplitude as a digital number.
• Understand the basic scheme behind CDs: are the pits the actual bits? Do non-pits also contain information? How is it that CD players can ignore small scratches? Know why the laser wavelength limits the density of information that can be stored on a CD (pits can't be smaller than wavelength).
• Digital is often preferred over analog because it offers unambiguous preservation and transfer of data. Precision equipment is not needed to tell the difference between a zero and a one (or zero volts vs. 5 volts; or a pit vs. a non-pit), whereas in analog systems, precise voltage or mechanical aspects (like subtle wiggles in vinyl record grooves) place higher demands on manufacturing tolerances.
• Digital information is represented electronically as voltages. Typically, a 1 is represented by 5 V, and a zero by 0 V.
• Transistors act like switches, either closed or open depending on the voltages they see (you won't have to remember the precise operation of n-channel vs. p-channel).
• Transistors can be combined to make more complicated logic, like AND, OR, XOR, NAND, etc. We explicitly developed a NAND gate out of 4 transistors in lecture. You need not know more than the general idea that logic is created by transistor combinations.
• We used NAND gates to construct other logic types. Be able to follow the logic of multiple gate arrangements. The basic logic tables will be provided: just be able to construct a new table from gate combinations. If you can follow the 6-gate arrangement that adds binary digits, you should be totally prepared for anything.
• Understand, in broad terms, what the in-class infrared transmitters are doing to communicate data to the receiver. In broad terms, this is is the same as a TV remote control (bursts of IR light to make ones and zeros). I don't intend for you to know particulars of how each device encodes information (egad), just the basic ideas.
• Understand that electromagnetic radiation is an oscillation of electric and magnetic fields transverse to the direction of propagation. Radio waves, microwaves, infrared, visible, ultraviolet, x-rays, and gamma rays are all forms of electromagnetic (EM) radiation. All forms of EM radiation travel at the speed of light (about 300,000,000 m/s).
• Just like with sound waves, light waves can be described by wavelength and a frequency, with the usual relation: λf = c describing the relationship of frequency and wavelength. Be able to use this to calculate one from the other.
• Any time a charge (e.g., an electron) accelerates, an electromagnetic wave is generated. A transmitting antenna wiggles electrons back and forth to create the oscillating electric and magnetic fields.
• A radio wave emitted from an antenna is polarized so that the electric field is aligned with the direction of the antenna. A receiving antenna will work best if it is in this same orientation, so that the electric field can efficiently wiggle charges in the receiving antenna (you want the electric field to point along the antenna direction). An antenna is most efficient if its length is one fourth of the wavelength of the signal it is receiving.
• Amplitude modulation is a technique for encoding information on a "carrier" electromagnetic wave. This technique involves changing the amplitude, or strength, of the radio signal. For instance, you push your speaker out when the amplitude is high, and pull it back when the amplitude is low. Thus the "amplitude envelope" looks like the sound waveform being transmitted.
• Frequency Modulation is a technique for encoding information on a "carrier" electromagnetic wave. This technique involves changing the frequency (slightly) of the carrier signal. For instance, you push your speaker out when the frequency is higher than normal, and pull it back when the frequency is lower than normal. The amplitude of the radio wave is unchanged throughout this process.
• AM and FM are techniques for encoding information, and are not strictly tied to the frequency ranges implemented for radio broadcast in our country. For instance, TV and aeronautical broadcasts are in the 100 MHz range (like FM radio), but use amplitude modulation. It's just a choice.
• Radios perform the task of listening to the carrier and its modulations (be it amplitude or frequency), and driving the speaker accordingly. Thus the sound that comes out of your radio is generated there: the sound is not broadcast through the air from the radio stations. The radio station sends the information needed to reconstruct the sound in the form of electromagnetic waves traveling at the speed of light.
• All radio transmissions are centered at some "carrier", or center frequency, but needs room on either side to "fit" the information that is being encoded. This is called bandwidth, and is easiest to imagine in the FM context (need to vary frequency over some range, without intruding on next station's turf). If an electromagnetic wave doesn't vary in frequency or amplitude, then it can carry no information. Bandwidth is synonymous with information content. AM radio broadcasts take up 9 kHz of bandwidth, FM uses 150 kHz (more information means better sound quality & stereo), and TV broadcasts use up 6 MHz per channel (way more than radio).
• Microwaves are used to transmit communications (telephone, internet) across the country, for cell phones, for microwave ovens, for weather radar. In the context of information transmission, microwaves beat the pants off of radio because they can support greater bandwidth. This is simply a consequence of their higher frequency: a 6 MHz-wide TV station barely makes a dent in the available space at several GHz, whereas it's a real space hog at 60 MHz. Optical communications (via fiber) do even better in the bandwidth context.
• Faraday Cages work because electrons are free to move through any metal (conductor). In the presence of an electric field, electrons will move wherever they need to until they cancel the electric field within the conductor. As long as any electric field is left, more electrons will flow until no field is left. So the interior of a conductor (solid or hollow) will have zero field, with electrons redistributed on the surface to make this so.
• Even a mesh (or other conductor with hole in it) acts like a solid sheet of metal for electric fields that vary slowly enough—giving the electrons time to move into the canceling position. The rule of thumb is that if the holes are significantly smaller than the wavelength of EM radiation, the cancellation will be good, and the shield effective. This connection to wavelength is valid because electron distributions change at about the speed of light, and distance = rate × time parallels the λf = c rule.
• Microwave ovens, operating at a frequency of 2.45 GHz, take advantage of the polar nature of water molecules to flip them back and forth (via the oscillating electric field). The wiggling water molecules bump into other molecules in the food and transfer energy into kinetic energy (heat) of all the molecules in the food.
• Ice doesn't get hot directly in a microwave oven because the molecules are locked into a lattice and cannot flip back and forth. When defrosting, ice must be heated by conduction from neighboring hot-spots (where water is liquid).
• Microwaves are effective because the microwave power is absorbed throughout the food, directly heating it inside and out. Conventional cooking relies on the slow transfer (conduction) to the inside of heat applied on the outside.
• Metal can be a problem in a microwave, but doesn't have to be. The metals that have problems are thin metals (foil, twist-tie, decorative trim) because they heat up too much conducting current (the oscillating electric field drives free electrons in the metal). Pointy metals are also problematic, in that the electric field gets concentrated at their tips, and may make sparks in the air (potentially causing fire). But thick, smooth pieces of metal are just fine.
• TVs have the job of painting a picture on the screen. A new picture is drawn 30 times per second. The picture is drawn by shooting a tightly focused electron beam at phosphors on the screen, which light up when hit. The electron beam is steered (deflected) by electric or magnetic fields to control where it falls on the screen, and the intensity of the spot is controlled by the instantaneous intensity of the electron beam. The picture is drawn by "rastering" the beam across the TV one line at a time. 525 lines 30 times per second means this sweep is 15.75 kHz, and this is what makes the high-pitched whine from a TV set.
• Color TVs use three electron beams, and three types of phosphors that glow red, green, and blue. A mask makes sure that the "green" electron beam only sees the green phosphor spots on the screen, and likewise for red and blue.
• The radio signal to tell a TV how to draw each line is just an amplitude-modulated signal where the amplitude dictates the electron beam intensity as a function of time.
• Understand the law of reflection in terms of equal angles, least time, or image formation.
• Refraction is a bending of light by the effect of retarding light's speed in a medium (like glass, water). Refraction also follows the principle of least time, so the direction of bending is into the slower medium. The analogy with a pair of wheels on an axle moving from the sidewalk (fast medium) into grass (slow medium) gets the behavior exactly right.
• The special phenomenon of total internal reflection happens when a light ray inside a denser medium (the one with the higher refractive index) approaches the surface at an angle (relative to the surface normal) greater than the critical angle. For glass, the critical angle is 42°, and 49° for water.
• Total internal reflection is responsible for piping light through fibers, for deflecting light inside right-angle prisms (45° incidence), and for mirages seen off the interface between hot and cool air over a road.
• Associated with any step (abrupt change) in the refractive index will be a reflection. The amount of reflection is greater the greater the step, and follows the formula: R = [(n₂ - n₂)/(n₂ + n₂)]².
• Lenses work by refraction. If you know how light is expected to bend when it hits a refractive step (look at slides 7, 9, 10, 11, 13 in Lecture 16), then you should be able to identify appropriate ray paths through lenses.
• Most of the refraction in the eye happens at the surface of the cornea because this is where the step (change) in refractive index is greatest. Thereafter, only small changes in the refractive index are seen.
• We can't see well underwater because when our cornea is immersed in water, the refractive step is all but gone, and we have no focusing ability. Goggles fix the problem by restoring the air-cornea interface.
• What we call light is a small portion of the electromagnetic spectrum, ranging from 400 nm to 700 nm in wavelength. Know what a nanometer is. How big is green light in millimeters? Know that 400 nm is violet, and 700 nm is red.
• White light is the equal combination of all colors (wavelengths). A piece of paper looks white because it reflects well at all wavelengths.
• Red, Green, and Blue sources of light can be combined in different amounts to reconstruct virtually any perceivable color, making RGB the primary additive colors.
• Understand subtractive color: if a shirt absorbs blue light, green and red are left, which together look yellow. If the shirt absorbs green, blue and red are left, looking magenta.
• If we use W, R, G, B, C, Y, M to represent white, red, green, blue, cyan, yellow, magenta, respectively, then W = R + G + B; C = W - R = G + B; Y = W - B = R + G; M = W - G = R + B.
• Spectra are dissections of light by wavelength content, and are a powerful way to see the true nature of color.
• Know how to distinguish the spectra of various items, a la Lecture 17. For sources, be able to pick out a laser spectrum, an LED, a fluorescent light, the solar spectrum, an incandescent spectrum. For reflected light, be able to identify different colors of paper, and recognize fluorescence when you see it (more than 100% at some wavelength)
• The fact that we can draw a color wheel (unlike the linear spectrum seen via a prism or grating) is a result of our eye physiology. The phenomenon of after-images confirms that our receptors are complementary in nature: we have blue/yellow receptors and red/green.
• Metals are shiny because electrons move freely on their surfaces. This enables them to reflect any EM wave hitting the surface, and is really the same thing that governs how Faraday Cages work.
• Even though solid ice, large sugar and salt crystals, and quartz are clear, when you pulverize them into crushed ice, table salt/sugar, and sand, they look white. The reason is the myriad reflections off the great number of surfaces.
• Coating an otherwise rough surface with a liquid of similar refractive index suppresses the reflections (smaller step in index). So the substance (scratched plexiglass, rough sidewalk) becomes more transparent. Polishing rocks is similar: replace a hazy, washed out surface with a rich, deep tone after eliminating the rough surface.
• The sky is blue because air molecules more readily deflect (scatter) blue light than red light. UV is even more efficiently scattered than blue (can get sunburn from blue sky, even out of direct sun). The same scattering is what results in orange/red sunsets: all the blue is gone when the sunlight travels through lots of air.
• Rainbows are seen in a direction roughly opposite the sun, in a 42° arc surrounding the anti-solar point. Understand what this means in terms of where you should look to see a rainbow.
• The green flash is a real effect sometimes seen in the setting sun due to the slightly different refractive index of air for different wavelengths. In essence, the green image of the sun is higher in the sky than the red/orange image, and sets a few seconds later. There would be a blue flash, except the air is so aggressively scattering the blue light that this doesn't survive the trip to our eyes.
• The photons that make up ultraviolet (UV) light have a high enough energy to break chemical bonds, resulting in faded pigments, death to microbes, and skin cancer.
• Sunscreen is rated by SPF: sun protection factor. SPF 15 means you can tolerate 15 times the sun exposure as you could without the sunscreen. Be aware that some clothing can have SPF as low as 4, and that the blue sky contains damaging UV as well as the sun.
• Tides act by gravity. The fact that the side of the earth nearer the moon is pulled more strongly than the center of earth, and the far side is pulled more weakly means that a bulge forms on both near and far sides. As the earth rotates under the moon, the bulge (high tide) appears to move around the earth so that a given spot gets two high tides and two low tides per day. Solar tides are 45% the strength of lunar tides. They add at new and full moon, and partly cancel at quarter moons. Tidal strength is proportional to mass (of sun or moon, for instance) divided by distance cubed. Thus while the sun is 27 million times more massive than the moon, it is 400 times further. 400 cubed is 64 million, so 27 million divided by 64 million comes out near 45%.
• We are starting to build a large catalog of planets around nearby stars. Planets seem to be common companions of stars. With 100 billion stars in our galaxy, and over a hundred billion galaxies in the visible universe, the number of planets inferred is truly astounding. This has obvious implications for how we view the specialness of life here on our speck of a planet.