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⚡ Chapter 5: Energy, Thermal Physics, Waves, Sound & Light

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Chapter 5 — Energy, Thermal Physics, Waves, Sound & Light

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.

⚡ 5.1 — Energy, Work & Power

What energy is

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.

Work — force that actually moves something

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 — how fast you do the work

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.

Two kinds of mechanical energy: potential and kinetic

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:

  • Gravitational PE — stored by lifting something higher (formula PE = mgh). Raising a bucket from the floor to a shelf increases its gravitational PE.
  • Elastic PE — stored by stretching or squeezing a springy object, like a pulled-back rubber band or a compressed spring.
  • Chemical PE — stored in the bonds of atoms and molecules, like the energy in food, gasoline, or a battery.

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 — the "quantity of motion"

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).

The inverse-square law (a sneaky bonus idea)

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.

⚖️ 5.2 — Conservation, Machines & Efficiency

Energy is conserved — follow it as it changes form

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).

Energy transformations everywhere

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.

Machines and efficiency

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.

🌡️ 5.3 — Temperature, Heat & Heat Transfer

Three words people mix up: thermal energy, temperature, and 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.

The three ways heat travels

  • Conduction — heat moving through direct contact, as fast-jiggling particles bump slower ones. A metal spoon left in hot soup heats up by conduction.
  • Convection — heat carried by a moving fluid (liquid or gas). Warm fluid rises, cool fluid sinks, making a loop (a "convection current") — how boiling water churns and how a room heater warms the air.
  • Radiation — heat carried by electromagnetic waves (like infrared). It's the only kind that works through the vacuum of empty space, which is how the Sun's heat reaches Earth.

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).

🧊 5.4 — Thermodynamics, Phase Changes & Reactions

The Laws of Thermodynamics

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.

Heat changes matter: thermal expansion

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.

Phase changes and "hidden" (latent) heat

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):

  • Endothermic (absorb): melting, boiling/vaporizing, sublimation (solid→gas).
  • Exothermic (release): freezing, condensation, deposition (gas→solid). For example, liquid water freezing into ice releases heat.

Boiling: it's about pressure, not just "hot"

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:

  • High altitude lowers the boiling point. On a tall mountain like Mount McKinley (Denali), air pressure is low, so water boils at about 90°C instead of 100°C — which is why food takes longer to cook up high.
  • "Boiling" doesn't mean "hot." Liquid nitrogen boils at about −196°C. Boiling just means changing to gas at that liquid's boiling point.

Chemical reactions and energy

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.

🌊 5.5 — Wave Fundamentals

What a wave does

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.

Two types of waves

  • Transverse wave — the material vibrates at right angles (perpendicular) to the direction the wave travels. It has high points (crests) and low points (troughs). Light is transverse.
  • Longitudinal wave — the material vibrates back and forth in the same direction the wave travels. Instead of crests/troughs it has compressions (squeezed-together, high pressure) and rarefactions (spread-out, low pressure). Sound is longitudinal. A compression matches a transverse crest; a rarefaction matches a trough.

Water waves are actually a mix of both. (Only transverse waves can be "polarized" — more on that in Optics.)

The parts of a wave

  • Frequency (f) — how many waves pass each second, measured in hertz (Hz). One hertz = one cycle (one vibration) per second, so 890 kHz means 890,000 vibrations per second.
  • Wavelength (λ) — the distance from one crest to the next.
  • Amplitude — how tall the wave is (how far the material moves from rest). Amplitude carries the wave's energy: bigger amplitude = louder sound or brighter light. Importantly, amplitude is completely separate from frequency and wavelength — making a wave taller does not change its frequency or wavelength.
  • Period (T) — the time for one full wave. It's just the flip of frequency: T = 1 ÷ f (so a 2,000 Hz wave has a period of 0.0005 s).
rest position crest trough wavelength (λ) amplitude
Anatomy of a transverse wave: wavelength is crest-to-crest; amplitude is height from rest to crest.

The wave equation (use it constantly)

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.)

How waves behave

  • Superposition & interference — when waves overlap, they add together (superposition). Constructive interference lines crests up to make a bigger wave (two pond ripples making one larger ripple; what changes is the amplitude). Destructive interference happens when waves are a half-wavelength out of step, so a crest meets a trough and they cancel — giving a flat line or silence. (This is how noise-canceling headphones work.)
  • Diffraction — waves bend and spread around edges or through openings, which is why you can hear someone around a corner. Huygens' Principle explains this by saying every point on a wavefront acts like a tiny new source of wavelets.
  • Reflection — a wave bounces off a surface (its frequency doesn't change).
  • Refraction — a wave bends when it changes speed entering a new material (covered in Optics).

Wave evidence and big waves

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.

🌐 5.6 — The Electromagnetic Spectrum & Light

What electromagnetic (EM) waves are

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.

The spectrum, in order

From longest wavelength / lowest energy to shortest wavelength / highest energy:

Radio → Microwave → Infrared → Visible → Ultraviolet → X-ray → Gamma

Radio Micro IR Visible UV X-ray Gamma longer wavelength higher frequency & energy →
The EM spectrum: left = long wavelength & low energy (radio); right = short wavelength & high energy (gamma).

As you move right, wavelength gets shorter while frequency and energy get bigger. Quick facts the tests love:

  • Radio — longest wavelength, lowest energy; used for communication. AM = Amplitude Modulation, FM = Frequency Modulation (two ways to put a signal on a radio wave). The ionosphere (a charged layer high in the atmosphere) reflects certain radio waves back down, allowing long-distance radio.
  • Microwaves — longer wavelength than visible light; made in your oven by a device called a magnetron.
  • Infrared — the heat we feel as radiation; lower energy than visible light.
  • Ultraviolet (UV) — higher energy than visible light; it causes sunburn by damaging skin cells, and most of it is absorbed by the ozone layer.
  • X-rays — high energy; pass through soft tissue to image bones.
  • Gamma rays — highest frequency and energy, and the most penetrating because their photons have no mass or charge.

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.

Doing the math with EM waves

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 as particles: photons

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.

What is NOT an EM wave

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).

Spectra, lasers, and scattering

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.

🔊 5.7 — Sound & Acoustics

What sound is

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.)

How fast sound travels

Sound's speed depends on the medium's temperature, density, and elasticitynot 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, loudness, and the decibel

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

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.

Echoes, earthquakes, and pipes

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.

🔭 5.8 — Optics: Reflection, Refraction, Lenses & Color

Reflection

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 — bending by a speed change

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).

air (fast light) water (slower light) normal incoming ray reflected refracted (bends)
At a boundary, light partly reflects (equal angle) and partly refracts — bending toward the normal as it slows entering water.

Mirrors and lenses (real vs. virtual images)

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.

Convex (converging) focus Concave (diverging)
A convex lens bends parallel rays together to a focal point; a concave lens spreads them apart.
  • Plane (flat) mirror — virtual, upright, same size.
  • Concave mirror (curves inward) — can make a real, inverted image; if the object sits between the focal point and the center of curvature, the image is real, inverted, and larger.
  • Convex mirror (curves outward, like the back of a spoon) — always a smaller, upright, virtual image (wide view).
  • Convex (converging) lens — thicker in the middle; can form real inverted images, but when the object is inside the focal length it acts as a magnifying glass (virtual, upright, enlarged). A convex lens is also the kind that focuses parallel rays to a bright spot. It's the only one here that can make a real image.
  • Concave (diverging) lens — thinner in the middle; has a negative focal length and makes only virtual, smaller images.

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.

Color

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:

  • Additive (mixing light, RGB): red, green, and blue are the primaries of light. Green + blue = cyan, red + green = yellow, red + blue = magenta, and all three together = white. Colors made from two primaries are secondary colors. This is how TV and phone screens work — more light = brighter.
  • Subtractive (mixing pigments/paint, CMY): pigments work by absorbing light, so more pigments mixed together = darker, heading toward black.

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 and lasers

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).

🌟 Themes & Strategy

Built from all 217 Q&A

Click any card to expand. Every tip here is pulled straight from the patterns in the Practice and Bonus questions.

⚡ Energy is always conserved — follow the conversion

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%.

🧾 Square the velocity, remember the units

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).

🌡️ Heat vs. temperature vs. thermal energy

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.

🌊 Use v = fλ and its rearrangements

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.

🌐 Order the EM spectrum cold

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 needs a medium; light does not

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).

🔭 Mirrors & lenses: real vs. virtual

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.

🎨 Color rules show up everywhere

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.

🔭 Mirrors & lenses: a quick decision tree

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.

🧮 Calculation shortcuts & metric prefixes

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).

📐 Formulas & Practice

Ch5 — Energy, Heat, Waves, Sound & Light

Each card shows the formula, what it means in plain English, and practice problems. Write your work, then click Show Answer to check.

🧾 Kinetic Energy
KE = ½ m v²
KE = kinetic energy (J)  |  m = mass (kg)  |  v = speed (m/s)
📚 In plain English: energy of motion. Because speed is squared, going twice as fast gives four times the energy — that's why high-speed crashes are so destructive.
✍ Practice Problems:
Q1. A 2 kg melon flies at 20 m/s. Find its kinetic energy.
Q2. A car doubles its speed from 25 m/s to 50 m/s. By what factor does its KE change?
⚖️ Gravitational PE, Work & Power
PE = m g h  |  W = F × d  |  P = W ÷ t
g ≈ 9.8 m/s²  |  h = height (m)  |  W = work (J)  |  P = power (W)
📚 In plain English: lift something higher and you store more potential energy. Work happens only when a force moves something. Power is how fast you do that work.
✍ Practice Problems:
Q1. You push a stalled car with 300 N over 20 m. How much work do you do?
Q2. The same 6000 J of work is done in 10 s. What is the power output?
⚙️ Efficiency
Efficiency = (useful output ÷ input) × 100%
Always ≤ 100% — lost energy usually leaves as heat
📚 In plain English: how much of the energy you put in actually does the job you wanted.
✍ Practice Problems:
Q1. An engine uses 7500 J and produces 4500 J of useful work. Find its efficiency.
🌊 Wave Speed & Period
v = f λ  |  λ = v ÷ f  |  f = v ÷ λ  |  T = 1 ÷ f
v = speed (m/s)  |  f = frequency (Hz)  |  λ = wavelength (m)  |  T = period (s)
📚 In plain English: a wave's speed equals how often it cycles times how long each cycle is. At fixed speed, more frequency means shorter wavelength.
✍ Practice Problems:
Q1. A sound wave in water travels 1450 m/s at 2900 Hz. Find its wavelength.
Q2. A radio wave has a frequency of 100 MHz (100×10⁶ Hz). Find its period.
⚡ Speed of Light & Photon Energy
c = f λ  |  E = h f  |  n = c ÷ v
c ≈ 3.0×10⁸ m/s  |  h = Planck's constant  |  n = refractive index
📚 In plain English: all light travels at c in a vacuum. A photon's energy rises with frequency, so blue/violet photons pack more punch than red. The refractive index says how much a material slows light.
✍ Practice Problems:
Q1. A radio station broadcasts at 1000 kHz (10⁶ Hz). Find the wavelength (use c).
Q2. Light travels through glass with index n = 1.5. Find its speed in the glass.
🔊 Speed of Sound in Air
v ≈ 331 + 0.6 T
v = speed of sound (m/s)  |  T = air temperature (°C)
📚 In plain English: warmer air makes molecules move faster, so sound travels faster. At 0°C sound moves about 331 m/s.
✍ Practice Problems:
Q1. Find the speed of sound in air at 20°C.
Q2. A cliff echo returns in 2.0 s; speed of sound is 340 m/s. How far away is the cliff?
🔭 Refractive Index & Critical Angle
n = c ÷ v  |  critical angle θc = sin⁻¹(n₂ ÷ n₁)
n = refractive index (vacuum = 1.0)  |  c = speed of light  |  v = speed in the material
📚 In plain English: the refractive index says how much a material slows light. Past the critical angle, light can't escape a dense material and totally reflects inside (fiber optics, sparkly gems).
✍ Practice Problems:
Q1. Light slows to 2×10⁸ m/s in a glass. What is the glass's refractive index?
Q2. Light goes from material A (n=1.5) to air (n=1). Write the critical angle.
📷 Mirror & Lens Equation
1/f = 1/d∅ + 1/dᵢ  |  Magnification M = −dᵢ ÷ d∅
f = focal length  |  d∅ = object distance  |  dᵢ = image distance  |  M > 0 upright/virtual, M < 0 inverted/real
📚 In plain English: this links where an object sits to where its image forms and how big it is. A convex lens or concave mirror can make a real, inverted image; placing the object inside the focal length makes a magnifying-glass (virtual, upright, bigger) image.
✍ Practice Problems:
Q1. An object sits 10 cm from a convex lens with focal length 20 cm. Is the image real or virtual, upright or inverted?
🔊 Echo Distance & Decibels
distance = (speed × time) ÷ 2  |  +10 dB = 10× intensity
Echo: sound goes to the wall and back  |  Decibels are logarithmic
📚 In plain English: an echo travels twice the distance to the wall, so halve it. On the decibel scale, every 10 dB step multiplies the sound intensity by 10.
✍ Practice Problems:
Q1. An echo returns in 0.5 s; speed of sound is 340 m/s. How far is the wall?
Q2. A jet (100 dB) is 10,000× more intense than a train. What is the train's level in dB?

📚 Vocabulary

Ch5 — All Key Terms

All essential definitions for Chapter 5. Use the highlighter toolbar to mark terms you need to review.

⚡ 5.1/5.2 — Energy, Work & Momentum
Energy
The capacity to do work. Measured in joules (J). Can be transformed but never created or destroyed.
Work
Force applied over a distance (W = F×d). No displacement means no work, regardless of force.
Power
The rate of doing work (P = W/t). SI unit: the watt (W) = 1 joule per second.
Potential Energy
Stored energy due to position, shape, or chemical bonds. Types: gravitational, elastic, chemical.
Kinetic Energy
Energy of motion: KE = ½mv². Proportional to the square of speed.
Conservation of Energy
Energy cannot be created or destroyed, only transformed from one form to another.
Momentum
Quantity of motion: p = mv. A vector quantity, conserved in all collisions.
Elastic / Inelastic Collision
Elastic: both momentum and KE conserved. Inelastic: momentum conserved, some KE becomes heat/sound.
Efficiency
Useful energy output divided by energy input. Always 100% or less; lost energy usually becomes heat.
Activation Energy
The minimum energy needed to start a chemical reaction or transformation.
🌡️ 5.3/5.4 — Heat & Thermodynamics
Thermal Energy
Total internal kinetic energy of all the particles in a substance. Depends on mass.
Temperature
Average kinetic energy per particle — how hot or cold something is. Not total energy.
Heat
Transfer of thermal energy from a warmer region to a cooler one.
Conduction
Heat transfer through direct molecular contact (a metal spoon in hot soup).
Convection
Heat transfer by the bulk movement of a fluid; warm fluid rises, cool fluid sinks.
Radiation
Heat transfer by electromagnetic waves; the only mode that works through a vacuum.
Heat of Fusion / Vaporization
Energy to melt a solid (water: 334 J/g) / to boil a liquid. Temperature stays constant during the change.
Entropy
A measure of disorder. The 2nd Law says total entropy of an isolated system always increases.
First / Second Law of Thermodynamics
1st: energy is conserved. 2nd: entropy increases; heat flows hot→cold spontaneously.
Thermal Expansion
Most materials expand when heated; bridges use expansion joints to prevent buckling.
🌊 5.5 — Wave Fundamentals
Transverse Wave
Particles vibrate at right angles to wave travel (e.g., light). Has crests and troughs; can be polarized.
Longitudinal Wave
Particles vibrate along the direction of travel (e.g., sound). Has compressions and rarefactions.
Frequency
Number of cycles per second, measured in hertz (Hz). Heard as pitch in sound.
Wavelength (λ)
Distance between two consecutive crests. Inversely proportional to frequency.
Amplitude
Maximum displacement from rest. Sets loudness (sound) or brightness (light); independent of frequency.
Period (T)
Time for one complete cycle. T = 1/frequency.
Interference / Superposition
Overlapping waves add. Constructive = bigger; destructive (½λ out of phase) = cancellation.
Diffraction
Bending/spreading of waves around edges or through openings.
Refraction
Bending of a wave as it changes speed entering a new medium. Frequency stays constant.
Polarization
Restricting a transverse wave to a single plane. Sound (longitudinal) cannot be polarized.
🌐 5.6 — EM Spectrum & Light
Electromagnetic Wave
Oscillating electric & magnetic fields. Needs no medium; travels at c in a vacuum.
Speed of Light (c)
≈ 3.0×10⁸ m/s in a vacuum — the same for all EM waves regardless of frequency.
EM Spectrum Order
Radio → Microwave → Infrared → Visible → UV → X-ray → Gamma (increasing frequency & energy).
Photon
The smallest, electrically neutral quantum of light. Energy E = hf.
Planck's Constant (h)
The constant linking a photon's energy to its frequency (E = hf).
Wave–Particle Duality
Light acts as both wave and particle. Wave evidence: interference; particle evidence: photoelectric effect.
Magnetron
The vacuum-tube device that generates microwaves in a microwave oven.
Ultraviolet (UV)
Higher energy than visible light; causes sunburn. Mostly absorbed by the ozone layer.
🔊 5.7 — Sound & Acoustics
Sound Wave
A mechanical, longitudinal pressure wave. Requires a medium; cannot travel through a vacuum.
Compression / Rarefaction
High-pressure (compression) and low-pressure (rarefaction) regions of a sound wave.
Pitch
How high or low a sound is — determined by frequency.
Decibel (dB)
Logarithmic unit of sound intensity/loudness. +10 dB = 10× the intensity.
Doppler Effect
Change in perceived frequency due to relative motion. Approaching = higher; receding = lower. Applies to all waves.
Redshift / Blueshift
Doppler shift of light: receding source → redshift; approaching source → blueshift.
Ultrasonic
Sound above the human hearing limit (> 20,000 Hz). Human range is 20–20,000 Hz.
🔭 5.8 — Optics
Reflection
A wave bouncing off a surface. Frequency is unchanged.
Total Internal Reflection
All light reflects back when it hits a boundary beyond the critical angle (dense to less-dense medium).
Refractive Index (n)
Factor by which a material slows light: n = c/v. Vacuum = 1.0.
Dispersion
Splitting of white light into colors by a prism; violet bends most, red least.
Convex (Converging) Lens
Thicker in the middle; focuses light, can form real inverted images; acts as a magnifying glass.
Concave (Diverging) Lens
Thinner in the middle; spreads light; forms only virtual images.
Real vs. Virtual Image
Real: formed by converging rays, can be projected, inverted. Virtual: appears behind the optic, upright.
Coherent Light
Light of one wavelength, one direction, all waves in phase — e.g., a laser.
⭐ Extra Key Terms (across all sections)
Inverse-Square Law
Gravity and light intensity weaken with the square of distance (1/r²). Twice as far → one-fourth as strong.
Activation Energy
The minimum energy needed to start a chemical reaction.
Catalyst
A substance that speeds up a reaction by lowering its activation energy (enzymes are biological catalysts).
Endothermic / Exothermic
Endothermic absorbs heat (melting, boiling). Exothermic releases heat (freezing, condensation, burning).
Superposition
When waves overlap, their displacements add together, producing interference.
Huygens' Principle
Every point on a wavefront acts as a source of new wavelets; explains how waves spread and diffract.
Photoelectric Effect
Light ejecting electrons from a metal. Einstein explained it (Nobel Prize), proving light's particle nature.
Emission (Line) Spectrum
Bright color lines given off by a glowing gas (e.g., neon; hydrogen shows 4 visible lines). Not an absorption spectrum.
Scattering
Light bouncing in many directions off tiny particles. Cloud droplets scatter all colors → clouds look white.
AM / FM (Modulation)
Amplitude Modulation and Frequency Modulation — two ways to put a signal onto a radio wave.
Ionosphere
A charged upper layer of the atmosphere that reflects certain radio waves, enabling long-distance radio.
Critical Angle
The angle beyond which light can't leave a dense medium and totally reflects inside: θc = sin⁻¹(n₂/n₁).
Additive Color (RGB)
Mixing light. Red+Green=Yellow, Green+Blue=Cyan, Red+Blue=Magenta, all=White. Two-primary mixes are secondary colors.
Subtractive Color (Pigments)
Mixing paints/dyes. Pigments absorb light, so more pigments = darker (toward black).
Complementary Colors
Colors opposite each other (blue/yellow, red/cyan). If a surface reflects one, it transmits/absorbs its complement.
Magnification
How many times bigger an image is than the object: M = −dᵢ/d∅. Positive = upright/virtual, negative = inverted/real.
Refracting vs. Reflecting Telescope
Refracting uses a lens to gather light; reflecting (Newtonian) uses a curved mirror.
P-wave / Seismograph
A seismograph detects earthquake waves with a still mass (inertia). P-waves (primary) are fast, longitudinal ground waves.
Radiation Pressure
The tiny push light exerts because photons carry momentum (p = E/c).

⭐ Review List

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