06Unit 3 Review
Consolidate your understanding of thermal energy, thermodynamics, wave motion, sound, and electromagnetic waves with mixed problems and a student self-check.
Mastering thermal physics and waves prepares you for optics, electricity, and magnetism in Unit 4 — and these topics appear frequently on the SAT, ACT, and AP Physics exams.
Essential Question
How do energy transfer and wave behavior explain the thermal and optical phenomena we observe in everyday life — from a warm cup of coffee cooling down to the rainbow colors produced by a prism?
Unit 3 Summary — Thermal Physics and Waves
Unit 3 connects two major domains of classical physics. The first half explores thermal physics: how energy moves as heat, how temperature is measured, and the fundamental laws that govern energy conversion in engines and natural processes. The second half explores waves: the mathematical description of oscillations that carry energy through matter and space, culminating in light — the electromagnetic wave that makes vision possible.
Thermal Energy and Heat
Thermal energy, temperature scales (°C, °F, K), specific heat capacity, heat transfer by conduction, convection, and radiation.
Introduction to Thermodynamics
Zeroth, First, and Second Laws of Thermodynamics; internal energy; entropy; heat engines and the Carnot cycle.
Wave Motion
Transverse vs. longitudinal waves; amplitude, wavelength, frequency, period, and wave speed; wave equation v = fλ.
Sound Waves
Mechanical longitudinal waves; speed of sound in different media; the Doppler effect; resonance and standing waves.
Light and Electromagnetic Waves
The EM spectrum; reflection and refraction (Snell's law); index of refraction; constructive and destructive interference.
Key Equations
Heat Transfer
Q = mcΔT
Q = heat (J), m = mass (kg), c = specific heat (J/kg·°C), ΔT = temperature change (°C)
Thermal Efficiency
e = W / Q_h
e = efficiency (0–1), W = net work output (J), Q_h = heat absorbed from hot reservoir (J)
Carnot Efficiency
e_Carnot = 1 − T_c / T_h
Temperatures must be in Kelvin; sets the upper limit for any heat engine
Wave Speed
v = fλ
v = wave speed (m/s), f = frequency (Hz), λ = wavelength (m)
Doppler Effect
f' = f(v ± v_d) / (v ∓ v_s)
Use + in numerator / − in denominator when source and detector approach each other
Speed of Light
c = 3 × 10⁸ m/s
Speed of all EM waves in a vacuum
Index of Refraction
n = c / v
n = index of refraction (dimensionless), v = speed of light in the medium
Constructive Interference
Δd = nλ (n = 0, 1, 2, …)
Path difference is a whole-number multiple of the wavelength
Worked Examples
How much heat is required to raise the temperature of 2.0 kg of water from 20 °C to 80 °C? (Specific heat of water: c = 4,186 J/kg·°C)
Identify: m = 2.0 kg, c = 4,186 J/kg·°C, ΔT = 80 − 20 = 60 °C
Apply Q = mcΔT
Q = (2.0 kg)(4,186 J/kg·°C)(60 °C)
Q = 502,320 J ≈ 502 kJ
A heat engine absorbs 800 J from a hot reservoir and exhausts 560 J to a cold reservoir. (a) What is the net work output? (b) What is the thermal efficiency?
(a) By the First Law: W = Q_h − Q_c = 800 J − 560 J = 240 J
(b) Efficiency: e = W / Q_h = 240 J / 800 J = 0.30
Convert to percent: e = 30%
A wave on a string has a frequency of 5.0 Hz and a wavelength of 0.40 m. What is the wave speed?
Use v = fλ
v = (5.0 Hz)(0.40 m)
v = 2.0 m/s
An ambulance siren emits a tone at 800 Hz. The ambulance moves toward a stationary observer at 30 m/s. The speed of sound is 340 m/s. What frequency does the observer hear?
Source approaches, observer stationary: use f' = f · v / (v − v_s)
f' = 800 Hz × (340 m/s) / (340 − 30) m/s
f' = 800 × 340 / 310
f' = 800 × 1.0968 ≈ 877 Hz
A ray of light travels from air (n₁ = 1.00) into glass (n₂ = 1.50) at an angle of incidence of 30°. What is the angle of refraction?
Apply Snell's Law: n₁ sin θ₁ = n₂ sin θ₂
(1.00) sin 30° = (1.50) sin θ₂
0.500 = 1.50 sin θ₂
sin θ₂ = 0.500 / 1.50 = 0.333
θ₂ = arcsin(0.333) ≈ 19.5°
Guided Practice
A 0.50 kg aluminum block (c = 900 J/kg·°C) is heated from 25 °C to 125 °C. How much heat energy is absorbed?
Hint: Use Q = mcΔT. Calculate ΔT first: 125 − 25 = 100 °C.
A Carnot engine operates between a hot reservoir at 600 K and a cold reservoir at 300 K. What is its maximum possible efficiency?
Hint: Use e_Carnot = 1 − T_c / T_h. Make sure both temperatures are in Kelvin.
A sound wave travels at 340 m/s and has a wavelength of 0.85 m. What is its frequency?
Hint: Rearrange v = fλ to get f = v / λ.
A train whistle emits a 500 Hz tone. The train moves away from a stationary observer at 20 m/s. The speed of sound is 340 m/s. What frequency does the observer hear?
Hint: Source moves away: use f' = f · v / (v + v_s). The denominator increases, so the observed frequency is lower.
Light travels from water (n = 1.33) into air (n = 1.00) at an angle of incidence of 20°. Find the angle of refraction.
Hint: Apply Snell's Law: n₁ sin θ₁ = n₂ sin θ₂. Solve for θ₂ = arcsin(n₁ sin θ₁ / n₂).
Key Vocabulary
Thermal Equilibrium
The state reached when two objects in contact have the same temperature and there is no net heat flow between them.
Example: A cold drink left on a table eventually reaches room temperature.
Specific Heat Capacity
The amount of heat energy required to raise the temperature of 1 kg of a substance by 1 °C (or 1 K).
Example: Water has a high specific heat (4,186 J/kg·°C), so it resists temperature changes.
Entropy
A measure of the disorder or randomness of a system. The Second Law states that entropy of an isolated system never decreases.
Example: Ice melting in warm water increases the total entropy of the system.
Wave
A disturbance that transfers energy through matter or space without permanently displacing the medium.
Example: A ripple on a pond carries energy outward from the point of disturbance.
Frequency
The number of complete wave cycles that pass a fixed point per second, measured in hertz (Hz).
Example: Middle C on a piano has a frequency of 262 Hz.
Wavelength
The distance between two consecutive points that are in phase on a wave (e.g., crest to crest), measured in meters.
Example: Visible light has wavelengths between about 400 nm (violet) and 700 nm (red).
Doppler Effect
The change in observed frequency of a wave when the source or the observer is moving relative to the medium.
Example: A siren sounds higher-pitched as an ambulance approaches and lower-pitched as it moves away.
Refraction
The bending of a wave as it passes from one medium into another due to a change in wave speed.
Example: A straw appears bent when placed in a glass of water because light refracts at the water–air boundary.
Workbook Quiz
Interactive Practice — 5 Questions
A 1.0 kg sample of iron (c = 450 J/kg·°C) absorbs 9,000 J of heat. By how much does its temperature increase?
Which statement best describes the Second Law of Thermodynamics?
A wave has a frequency of 200 Hz and a speed of 340 m/s. What is its wavelength?
A fire truck moves toward you at 25 m/s while its siren emits 600 Hz. The speed of sound is 340 m/s. Which best describes the sound you hear?
Light passes from air (n = 1.00) into a medium with index of refraction n = 2.00. Compared to its speed in air, the speed of light in this medium is: