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Click any card to expand. This guide is built to cover every Practice Q&A and Bonus question — if you read and understand all 8 sections, you'll be able to answer them all. Sections 1–4 are energy & heat; sections 5–8 are waves, sound & light.
Energy is the ability to do work or cause change. You can't make it or destroy it — you can only move it around or change its form (this is the Law of Conservation of Energy, the most important idea in this whole chapter). The unit of energy is the joule (J). One joule is about the energy it takes to lift a small apple one meter.
In science, work happens only when a force makes an object move some distance. The formula is Work = Force × distance (W = F × d), measured in joules.
The big idea students miss: if nothing moves, no work is done — no matter how hard you push. If Mary pushes a 2,000-newton couch with 500 newtons of force and it doesn't budge, the distance is zero, so the work is 0 joules. Your muscles get tired, but in physics you did no work on the couch.
Power is the rate of doing work: Power = Work ÷ time (P = W ÷ t). The unit is the watt (W), which is one joule per second.
Key trap: doing the same job in different times uses the same amount of work but a different amount of power. If a worker lifts 40 kg of flour in 5 seconds, then does the exact same lift in 10 seconds, the work is identical — but the slower lift uses half the power. Faster = more power.
Potential energy (PE) is stored energy — energy something has because of its position, shape, or chemistry. "Potential" is basically a synonym for stored. Three forms:
Kinetic energy (KE) is the energy of motion: KE = ½mv². Notice the velocity is squared. That squaring is a favorite test trap: if you double the speed, the kinetic energy becomes four times bigger (2² = 4), not twice. That's why a car at 60 mph is far more dangerous than at 30 mph.
Momentum is mass times velocity: p = m × v. People describe it as the "quantity of motion." It is a vector, meaning it has a direction as well as a size. Don't confuse it with kinetic energy: momentum depends on speed to the first power (mv), while KE depends on speed squared (½mv²).
Some things get weaker very fast as you move away — specifically with the square of the distance (1 ÷ r²). Both gravity and the brightness (intensity) of light follow this inverse-square law: move twice as far away and the effect drops to one-fourth. (Fun extra: this is also why, to double the light entering a camera, you multiply the lens opening's radius by √2 — because light collected depends on the area, πr².)
And one mind-bender: light itself carries a tiny bit of momentum. A strong laser can actually push on a very light object — this is called radiation pressure.
The Law of Conservation of Energy says energy is never created or destroyed, only transformed. The classic example is a falling object: as a rock falls, its gravitational potential energy decreases and its kinetic energy increases by the same amount. The energy isn't lost — it just changes from "stored" to "moving."
This kills a common false statement: "kinetic energy can only decrease when potential energy decreases." That's backwards — for a falling rock, KE increases exactly while PE decreases. Energy trades back and forth (think of a swing or roller coaster: highest point = most PE, lowest point = most KE).
Machines and living things constantly convert energy: a generator turns motion into electricity, your muscles turn chemical energy (food) into motion, a light bulb turns electricity into light and heat, and a coal plant goes chemical → heat → motion → electricity. In almost every real conversion, some energy escapes as heat.
Efficiency = useful energy out ÷ energy put in (written as a percent). Because energy is conserved, output can never be more than input — so a machine's efficiency is always 100% or less. The Law of Conservation of Energy is exactly what forbids efficiency above 100%.
An ideal machine is an imaginary, frictionless one where work input equals work output (100% efficient). Real machines always lose some energy to friction, which turns into heat — so they fall short of 100%. If an engine takes in 7,500 J and delivers 4,500 J of useful work, its efficiency is 4,500 ÷ 7,500 = 60%, and the other 40% leaves as heat.
Thermal energy is the total energy of all the jiggling particles in an object. Because it's a total, a bigger (more massive) object has more thermal energy than a small one at the same temperature — there are simply more particles adding up. (A swimming pool at 30°C holds far more thermal energy than a cup of coffee at 80°C.)
Temperature is the average energy of the particles — how hot or cold one particle is on average, not the total.
Heat is not something an object "has." Heat is the transfer of thermal energy from a warmer place to a cooler place. And heat always flows from warmer to cooler on its own (spontaneously), never the other way without help — that's why your hot cocoa cools down and never heats back up by itself.
Watch the spelling trap: the three real methods are conduction, convection, and radiation. "Convention" is not a method of heat transfer — it's a fake answer (a convention is a meeting or a custom).
The First Law of Thermodynamics is just the Law of Conservation of Energy again: energy can change form but is never created or destroyed.
The Second Law of Thermodynamics introduces entropy, which is a measure of disorder or randomness. The second law says the total entropy of a closed system always increases over time. A great way to picture it: a bedroom naturally gets messier on its own, and it takes energy and work to tidy it back up — the universe is the same way. This is also why heat flows hot→cold and never the reverse.
Most materials expand when heated and shrink when cooled. That's why bridges and railroad tracks are built with expansion joints — small gaps that give the material "room to grow" so it doesn't buckle or crack on hot days.
A phase change is matter switching between solid, liquid, and gas. The surprising rule: temperature stays constant during a phase change. If you put a thermometer in a melting slush of lemonade, it reads a steady temperature as long as ice remains, because the energy is being used to break the bonds holding the solid together (called latent heat) instead of raising the temperature.
Two named amounts: heat of fusion (energy to melt a solid into a liquid) and heat of vaporization (energy to boil a liquid into a gas).
Phase changes are either endothermic (absorb heat) or exothermic (release heat):
A liquid boils when its vapor pressure equals the surrounding air pressure; the bubbles in a boiling pot are pockets of water vapor (the water turning to gas), not air. Two cool consequences:
Activation energy is the minimum "push" of energy needed to start a reaction (like the spark to light a match). A catalyst (including biological ones, called enzymes) speeds a reaction up by lowering the activation energy — it gives the reaction an easier path.
About bonds: breaking bonds always needs energy (endothermic), while forming bonds releases energy. An exothermic reaction releases heat overall; an endothermic one absorbs it.
A wave is a disturbance that transfers energy from place to place without permanently moving the material itself. Bob a duck on a pond: the ripples (energy) travel outward, but the duck just bobs up and down — it doesn't get carried to shore. Waves move energy, not matter.
Water waves are actually a mix of both. (Only transverse waves can be "polarized" — more on that in Optics.)
speed = frequency × wavelength (v = f × λ). Rearranged: λ = v ÷ f and f = v ÷ λ. In a given material the speed is fixed, so frequency and wavelength are inversely proportional: shorter wavelength means higher frequency, and vice-versa. (Ocean waves with crests closer together pass a dock more often.)
The best proof that light behaves as a wave is the interference pattern made when light passes through two tiny pinholes or slits (Thomas Young's famous experiment) — only waves can interfere into bright and dark bands. Out in the ocean, the giant waves (over 100 feet, called tsunamis) are usually caused by underwater earthquakes shoving the seafloor.
EM waves are made of vibrating electric and magnetic fields that travel together. Unlike sound, they need no medium — they zip right through the vacuum of space. In a vacuum, every EM wave travels at the same speed: the speed of light, c ≈ 3.0 × 10⁸ m/s, no matter its color or frequency. (So a red photon and a blue photon travel at exactly the same speed; only their frequency, wavelength, and energy differ.) Even James Clerk Maxwell showed light is electromagnetic: a changing electric field creates a magnetic field, and a changing magnetic field creates an electric field, so the two keep regenerating each other as the wave moves.
From longest wavelength / lowest energy to shortest wavelength / highest energy:
Radio → Microwave → Infrared → Visible → Ultraviolet → X-ray → Gamma
As you move right, wavelength gets shorter while frequency and energy get bigger. Quick facts the tests love:
Within visible light, the colors run ROYGBIV: red has the longest wavelength (lowest energy) and violet the shortest (highest energy). So blue light carries more energy than yellow, and violet/UV more than red/infrared.
EM problems use the wave equation with the speed of light: c = f × λ, so λ = c ÷ f and f = c ÷ λ, where c = 3.0 × 10⁸ m/s. Know the metric prefixes for frequency: kilo (k) = 10³ (thousand), mega (M) = 10⁶ (million), giga (G) = 10⁹ (billion). Example: a station at 1000 kHz (= 10⁶ Hz) has wavelength λ = (3×10⁸) ÷ (10⁶) = 300 m; and a 30-cm radio wave has frequency f = (3×10⁸) ÷ 0.3 = 1×10⁹ Hz = 1 gigahertz.
One more rule from Einstein's relativity: the speed of light in a vacuum is constant for everyone, regardless of how the source or observer is moving. A light beam from a fast-moving spaceship still reaches you at exactly c — its speed is unaffected by the ship's motion.
Light is also made of tiny packets called photons — the smallest possible unit (a "quantum") of light. A photon has no electric charge (it's neutral), which is why X-rays and other EM waves are not bent by electric or magnetic fields. A photon's energy is proportional to its frequency: E = h × f, where h is Planck's constant. Higher frequency (toward gamma) = more energy per photon.
Light has a dual nature — it acts like both a wave and a particle. The wave side shows up in interference; the particle side shows up in the photoelectric effect, where light knocks electrons off a metal. Einstein explained the photoelectric effect (and won the Nobel Prize for it), proving light comes in particle-like packets.
EM waves include radio, microwave, infrared, visible, UV, X-ray, and gamma. The following are NOT electromagnetic: sound and ultrasound (mechanical waves), cathode rays and beta particles (streams of electrons), alpha particles (helium nuclei), cosmic rays (high-speed particles), and phonons (vibrations in a crystal).
A glowing gas like neon gives off an emission (line) spectrum — specific bright color lines, not a smooth rainbow, and not an absorption spectrum. Hydrogen, with its single electron, shows four visible lines (the Balmer series). A laser — the word stands for Light Amplification by Stimulated Emission of Radiation — makes coherent light (one color, one direction, waves in step). And clouds look white because their water droplets scatter all colors of light equally, even though the water itself is clear.
Sound is a mechanical, longitudinal wave — a traveling pattern of compressions and rarefactions (pressure squeezes and stretches). Because it needs particles to pass the vibration along, sound must have a medium (solid, liquid, or gas) and cannot travel through a vacuum. That's why explosions in space movies are scientifically wrong — space is empty, so there's nothing to carry the sound. (Sound is a wave, so it has no mass of its own.)
Sound's speed depends on the medium's temperature, density, and elasticity — not on the wave's frequency or amplitude. Surprisingly, sound is fastest in solids, slower in liquids, and slowest in gases (for example, fastest in aluminum, then water, then air), because the tightly-connected, springy particles in solids pass the vibration along quickly. In air, warmer = faster: a handy estimate is v ≈ 331 + 0.6 × T(°C), so sound is about 331 m/s at 0°C and around 343 m/s at 20°C.
Pitch is how high or low a sound is — it's set by frequency (higher frequency = higher pitch = crests closer together). Loudness is set by amplitude and is measured in decibels (dB). The decibel scale is logarithmic: every +10 dB means 10× more sound intensity. So a sound 10,000× (that's 10⁴) more intense is 40 dB louder. Humans hear roughly 20 Hz to 20,000 Hz; above 20,000 Hz is ultrasonic (too high to hear), below 20 Hz is infrasonic. A pure tone is a single sine wave (an electronic synthesizer can make one); real instruments add extra overtones, giving each its own sound.
The Doppler effect is the change in the perceived frequency when the source and listener move relative to each other. When an ambulance approaches, its sound waves bunch up — shorter wavelength, higher pitch. As it moves away, the waves stretch out — longer wavelength, lower pitch. It works for all waves, not just sound. For light, it gives redshift (a source moving away, light stretched toward red — how we know distant galaxies are receding) and blueshift (a source moving closer). A police radar gun uses the Doppler shift of radio waves bouncing off a car to measure its speed.
An echo is reflected sound. Since the sound travels to a wall and back, the distance to the wall is (speed × time) ÷ 2. You can also estimate how far away lightning or fireworks are: sound travels ~340 m/s, so a 3-second delay means about 3 × 340 ≈ 1,000 m away. A seismograph detects earthquake waves using a heavy mass that stays still (due to inertia) while the ground shakes around it; the first waves to arrive are P-waves (primary waves), which are longitudinal — they compress and stretch the ground.
Reflection is light bouncing off a surface; its frequency doesn't change. Mirrors are made by coating glass with a thin layer of silver ("silvering"). When a sound or light wave reflects back into the same material, its speed stays the same too — only its direction changes.
Refraction is the bending of light when it changes speed moving from one material to another. The wave's speed and wavelength change, but its frequency stays the same (frequency is set by the source). Light travels fastest in a vacuum/air, slower in water, slower still in glass. The refractive index (n = c ÷ v) tells you how much a material slows light (a vacuum is exactly 1.0).
Refraction explains lots of everyday illusions: a straw or pencil looks "broken" where it enters water (the underwater part's light bends, so our eyes trace it to the wrong spot), a fish sees the Sun higher in the sky than it really is, and desert mirages appear when light bends through layers of hot and cool air.
A prism splits white light into a rainbow by dispersion: each color bends a slightly different amount, and violet bends the most (highest frequency) while red bends the least. A diffraction grating spreads white light into its colors in order (red, orange, yellow, green, blue, indigo, violet).
Total internal reflection: when light tries to leave a dense material at a steep enough angle — past the critical angle — it can't escape and reflects entirely back inside (this is how fiber-optic cables and sparkly gems work). The critical angle is found from sin⁻¹(n₂ ÷ n₁).
A real image is formed where light rays actually meet — it can be projected on a screen and is always inverted (upside down). A virtual image is where rays only appear to come from — it can't be projected and is upright.
Telescopes: a refracting telescope uses a lens to gather light, while a reflecting telescope (Newtonian) uses a curved mirror instead. A radio telescope lets us "see" stars in radio waves, not just visible light.
An object's color is the light it reflects; it absorbs the rest. So a red object looks black in blue light (there's no red to reflect), and a white object reflects every color (it looks blue in blue light, red in red light). Two ways colors combine:
Colors directly across from each other (like blue and yellow, or red and cyan) are complementary — if a glass reflects blue, it transmits its complement, yellow.
Polarization means lining up a wave's vibrations into a single plane — and it only works for transverse waves, which is why light can be polarized but sound cannot. Sending ordinary light through one polarizing filter cuts it to half intensity; adding a second filter turned 90° to the first blocks the light completely (no light gets through). Coherent light (from a laser) is special: one wavelength, one direction, all the waves perfectly in step. And because light carries momentum, a strong beam can even gently push a very light object in a vacuum (radiation pressure).
Click any card to expand. Every tip here is pulled straight from the patterns in the Practice and Bonus questions.
The single most-tested idea: energy is never created or destroyed, only transformed. When a question describes a falling object, a pendulum, or a roller coaster, track PE↔KE. As something falls, PE decreases and KE increases. Watch for the classic trap claiming "KE only decreases when PE decreases" — it's false.
Trap watch: raising an object at constant speed adds potential energy, not kinetic (speed isn't changing). Friction in any real machine converts useful energy into heat, so efficiency is always under 100%.
KE = ½mv² — the velocity is squared, so doubling speed quadruples kinetic energy. Momentum (p = mv) is only linear in velocity, so don't mix them up. Energy and work are both measured in joules; power is in watts (J/s); force is in newtons.
Trap watch: a question may give time to tempt you into a power calculation when it only asks for work (work is the same regardless of how fast you do it).
These three are the most common wording traps in the thermal section. Temperature = average KE per particle. Thermal energy = total KE of all particles (depends on mass). Heat = energy in transit from hot to cold. Remember: only radiation transfers heat through a vacuum, and during a phase change the temperature holds constant.
Most wave calculations come from v = fλ, λ = v/f, f = v/λ, and T = 1/f. For EM waves use v = c = 3×10⁸ m/s. Keep frequency and wavelength inversely related in your head. Amplitude is independent of both — it only changes energy/loudness/brightness.
Trap watch: frequency is set by the source and never changes during reflection or refraction — only speed and wavelength change.
Memorize Radio → Microwave → Infrared → Visible → UV → X-ray → Gamma (increasing frequency & energy, decreasing wavelength). Energy E = hf, so gamma > X-ray > UV ... and red is the lowest-energy visible color, violet the highest. Know the "NOT EM" list: sound, ultrasound, cathode rays, cosmic rays, alpha/beta particles, phonons.
Sound is mechanical & longitudinal — no vacuum travel, fastest in solids. Light is EM & transverse — vacuum travel, can be polarized. The Doppler effect works for both: approaching = higher frequency (blueshift for light), receding = lower (redshift). Pitch = frequency, loudness = amplitude (decibels, logarithmic).
Converging optics (concave mirror, convex lens) can make real, inverted images when the object is far enough away; otherwise virtual & upright. Diverging optics (convex mirror, concave lens) make only virtual, upright, smaller images. Object inside the focal length of a convex lens → magnifying glass (virtual, upright). Color appears from what is reflected; absorbed colors are missing.
An object's color = the light it reflects (it absorbs the rest). So a red object looks black in pure blue light, and a white object reflects whatever color shines on it. Mixing light is additive (Red+Green=Yellow, Green+Blue=Cyan, Red+Blue=Magenta, all=White); mixing pigments is subtractive (more pigment = darker). Watch for "complementary" pairs like blue/yellow.
Ask two questions: is it converging (convex lens / concave mirror) or diverging (concave lens / convex mirror)? And is the object inside or outside the focal length? Diverging optics only make virtual, upright, smaller images. Converging optics make a real, inverted image when the object is far out, but a magnifying-glass (virtual, upright, bigger) image when the object is inside the focal length. Real images are always inverted; virtual images are always upright.
Most number problems come from v = fλ (use c = 3×10⁸ m/s for light) and T = 1/f. Memorize prefixes: kilo = 10³, mega = 10⁶, giga = 10⁹, nano = 10⁻⁹. For echoes, distance = (speed × time) ÷ 2. For decibels, every +10 dB = 10× the intensity. For the speed of sound in air, v ≈ 331 + 0.6×T(°C).
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