14.1 Properties of Wave Pulses and Waves

A wave pulse is a single, nonrepeating disturbance that carries energy from one place to another (no net mass transport). A “regular” wave in the CED sense is a continuous, periodic disturbance—it has a well-defined wavelength and frequency. Both pulses and periodic waves can be mechanical (need a medium) or electromagnetic (don’t need a medium), and both transfer energy, not matter (14.1.A.1–A.2). Key practical differences: only a periodic wave has wavelength λ and frequency f; pulses are described by their shape and duration. Wave speed depends on type and medium (e.g., on a string v = sqrt(FT/(m/ℓ)) per 14.1.A.3.ii). Amplitude sets maximum displacement and energy transported (14.1.A.6). If you want a quick CED-aligned refresher, check the Topic 14.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-6/1-properties-of-wave-pulses-and-waves/study-guide/Ql0FLnrI6dIHcNlL) or the unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-14). For more practice, try the 1000+ problems at (https://library.fiveable.me/practice/ap-physics-2-revised).

Waves move energy by creating and passing along disturbances in a medium (or fields) while individual particles of the medium oscillate near their equilibrium positions instead of traveling with the wave. For a mechanical transverse wave on a string, each bit of string moves up and down while the wave shape (the disturbance) travels sideways; adjacent bits interact (via tension) and pass energy along. For longitudinal waves (sound) compressions and rarefactions carry energy through changing pressure, not mass transport. Electromagnetic waves carry energy through oscillating electric and magnetic fields and can propagate in vacuum (speed c = 3.00×10^8 m/s). Energy carried by a wave grows with amplitude, and wave speed depends on the medium (e.g., v_string = sqrt(FT/(m/ℓ)). This is exactly what the CED requires: waves transfer energy without transferring matter (14.1.A.1). For the AP review, see the Topic 14.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-6/1-properties-of-wave-pulses-and-waves/study-guide/Ql0FLnrI6dIHcNlL), the unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-14), and extra practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Short version: in a transverse wave the disturbance is perpendicular to the direction the wave travels; in a longitudinal wave the disturbance is parallel to the direction the wave travels (CED 14.1.A.4–5). What that looks like: - Transverse: a plucked string—the string moves up/down while the wave moves along the string. Amplitude = max displacement from equilibrium (14.1.A.6). - Longitudinal: sound waves—particles of the medium oscillate back and forth along the travel direction, creating compressions (high pressure) and rarefactions (low pressure) (14.1.A.5.i–ii). For longitudinal pressure waves amplitude = max pressure change. Key exam points: both transfer energy without net mass transfer (14.1.A.1). Mechanical waves need a medium; EM waves don’t (14.1.A.2). Know examples and how amplitude, wavelength, and speed depend on medium (14.1.A.3). For a quick refresher, see the Topic 14.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-6/1-properties-of-wave-pulses-and-waves/study-guide/Ql0FLnrI6dIHcNlL) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

In sound (a mechanical longitudinal wave) particles of the medium oscillate parallel to the wave’s travel direction. Compressions are regions where particles are crowded together—pressure and density are above the equilibrium—and rarefactions are regions where particles are spread apart—pressure and density are below equilibrium. The wave itself transfers energy, not matter (CED 14.1.A.1). For a longitudinal pressure wave, amplitude is the maximum pressure change from equilibrium; larger amplitude → louder sound and more energy (CED 14.1.A.6.i–iii). Remember sound needs a medium to propagate and its speed depends on the medium (e.g., speed of sound increases with temperature, CED 14.1.A.2–3.iii). These ideas show up on the AP: expect questions that link compressions/rarefactions to pressure vs. position/time graphs or to amplitude and loudness (see Topic 14.1 study guide on Fiveable: https://library.fiveable.me/ap-physics-2-revised/unit-6/1-properties-of-wave-pulses-and-waves/study-guide/Ql0FLnrI6dIHcNlL). For more practice, try problems at (https://library.fiveable.me/practice/ap-physics-2-revised).

Mechanical waves need a medium because they’re disturbances of matter—particles of the medium oscillate (longitudinal for sound, transverse for a string) and that motion carries energy from one place to another. The CED’s essential knowledge 14.1.A.2 says just that: mechanical waves require a medium. Electromagnetic (EM) waves don’t need a medium because the wave is an oscillation of electric and magnetic fields themselves. A changing electric field produces a magnetic field and a changing magnetic field produces an electric field (Maxwell’s equations), so the fields sustain each other and the disturbance travels through vacuum at the universal speed c = 3.00×10^8 m/s (14.1.A.3.i). No mass motion is required—only field energy moves. If you want a quick review tied to the CED, see the Topic 14.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-6/1-properties-of-wave-pulses-and-waves/study-guide/Ql0FLnrI6dIHcNlL). For more practice, check the Unit 14 overview (https://library.fiveable.me/ap-physics-2-revised/unit-14) and the practice problems collection (https://library.fiveable.me/practice/ap-physics-2-revised).

Short answer: yes—in a vacuum all electromagnetic waves travel at the same speed, c = 3.00 × 10^8 m/s (this is Essential Knowledge 14.1.A.3.i in the CED). Quick extra detail that matters on the AP: that common speed is only true in a vacuum. In materials (glass, water, air) different wavelengths can travel at different speeds because the medium’s index of refraction depends on wavelength (dispersion). Mechanical waves, by contrast, need a medium and their speed depends on the medium’s properties (e.g., string tension or temperature for sound)—see 14.1.A.2 and 14.1.A.3. If you want to review this CED point, check the Topic 14.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-6/1-properties-of-wave-pulses-and-waves/study-guide/Ql0FLnrI6dIHcNlL). For extra practice, Fiveable has lots of practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

The speed of a transverse wave on a string depends on the string’s tension and its linear mass density: v = sqrt(FT / (m/ℓ)). Here FT is the tension and m/ℓ (often written μ) is the mass per unit length. So increasing the tension increases wave speed—specifically, if you double the tension, the speed increases by a factor of sqrt(2). Increasing the mass per length (heavier string) decreases speed. Why? Higher tension gives a stronger restoring force on a displaced segment, so neighboring bits pull back faster and the disturbance travels quicker. Heavier strings have more inertia, so the same restoring force accelerates them less and the wave moves slower. This is exactly the CED essential knowledge (14.1.A.3.ii). For a quick review, check Topic 14.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-6/1-properties-of-wave-pulses-and-waves/study-guide/Ql0FLnrI6dIHcNlL) and try practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Amplitude is the maximum displacement of the medium from its equilibrium position—for a transverse wave that’s the tallest peak height, for a longitudinal (sound) wave it can be the largest pressure change from atmospheric (CED 14.1.A.6 and 14.1.A.6.i). Amplitude tells you how “big” the disturbance is; energy carried by a wave depends on that size. For most mechanical waves (strings, springs) and for sound, energy or intensity grows with the square of the amplitude—double the amplitude → about four times the energy or intensity. That’s why louder sounds (greater pressure amplitude) carry more energy (CED 14.1.A.6.ii–iii). For exam work, remember amplitude is not frequency or speed—it’s independent of wavelength and v, but it controls energy. For a quick topic refresher check the Topic 14.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-6/1-properties-of-wave-pulses-and-waves/study-guide/Ql0FLnrI6dIHcNlL) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Sound is a mechanical longitudinal wave, so its speed depends on the medium’s properties (CED 14.1.A.2–A.3). In air (approximated as an ideal gas) the speed of sound v ≈ sqrt(γRT/M), so v increases with temperature T—roughly v ∝ √T. Physically, warmer air means the molecules have higher average kinetic energy and move faster, so pressure disturbances (compressions and rarefactions) propagate more quickly through collisions and pressure forces. Numerically, a 1% increase in absolute temperature gives about a 0.5% increase in speed (because of the square root). This idea is part of Essential Knowledge 14.1.A.3.iii for the AP course. For a quick review, see the Topic 14.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-6/1-properties-of-wave-pulses-and-waves/study-guide/Ql0FLnrI6dIHcNlL) and more practice problems at (https://library.fiveable.me/practice/ap-physics-2-revised).

Short answer: waves move energy by making the medium oscillate locally, not by hauling chunks of matter along with them. That’s exactly what the CED says: “Waves transfer energy between two locations without transferring matter” (14.1.A.1). Think of a rope pulse: you flick one end and a pulse travels to the other end. Individual bits of rope move up and down (transverse), but after the pulse passes each bit returns to equilibrium—no net transport of rope mass. For sound (longitudinal), air molecules oscillate back and forth creating compressions and rarefactions; the pattern (and energy) moves, the air doesn’t flow across the room. For electromagnetic waves, fields carry energy with no medium at all (14.1.A.2). Key tie-in for the exam: energy carried grows with amplitude (14.1.A.6) and pulses vs continuous waves are treated differently (14.1.A.1.i–ii). For a quick refresher, check the Topic 14.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-6/1-properties-of-wave-pulses-and-waves/study-guide/Ql0FLnrI6dIHcNlL) and practice questions (https://library.fiveable.me/practice/ap-physics-2-revised).

Short answer: light waves are electromagnetic and transverse, so they don’t need a medium and travel at c = 3.00×10^8 m/s in vacuum (slower in materials); sound waves are mechanical and longitudinal, so they require a material medium and propagate via compressions and rarefactions. Key CED points to remember: mechanical waves transfer energy through a medium (sound), electromagnetic waves don’t require one (light) (14.1.A.2). Sound’s speed depends on the medium and its temperature (14.1.A.3.iii); light’s speed in vacuum is the constant c (14.1.A.3.i). In transverse vs longitudinal language: light’s disturbance is perpendicular to propagation, sound’s disturbance is parallel (14.1.A.4–5). Amplitude relates to energy; for sound amplitude → loudness (14.1.A.6). On the exam you might be asked to compare or describe these differences (use CED task verbs like “describe” or “compare”). For a quick refresher, see the Topic 14.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-6/1-properties-of-wave-pulses-and-waves/study-guide/Ql0FLnrI6dIHcNlL), the Unit 14 overview (https://library.fiveable.me/ap-physics-2-revised/unit-14), and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Use v = sqrt(FT / (m/ℓ)). Think of m/ℓ as the linear mass density μ (kg/m), and FT as the tension in newtons. Steps: 1. Find μ = m/ℓ (e.g., a 0.020 kg, 0.50 m string → μ = 0.040 kg/m). 2. Put FT in N (not grams or kg·m/s^2 mistakes). 3. Compute v = sqrt(FT / μ). Units: N/(kg/m) = (kg·m/s^2)/(kg/m) = m^2/s^2, sqrt → m/s. Quick facts useful for the AP: v scales as sqrt(FT) and as 1/√μ, so doubling FT → v increases by √2; doubling μ → v decreases by √2. This is exactly EK 14.1.A.3.ii in the CED. For more examples and practice problems, check the Topic 14.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-6/1-properties-of-wave-pulses-and-waves/study-guide/Ql0FLnrI6dIHcNlL) and the unit review (https://library.fiveable.me/ap-physics-2-revised/unit-14). You can drill many practice questions at (https://library.fiveable.me/practice/ap-physics-2-revised).

Amplitude is the maximum displacement from equilibrium. For sound (a mechanical longitudinal wave) that displacement shows up as pressure changes—bigger amplitude means larger compressions and rarerfactions (larger ΔP). Your ear (or a microphone) senses those pressure variations; larger pressure swings move the eardrum more, so the brain interprets the sound as louder. Physically, higher amplitude also means the wave carries more energy (CED 14.1.A.6.ii–iii), so more energy reaches your ear per second. Frequency and wavelength set pitch and tone, but loudness correlates with amplitude (not frequency). If you want to study this with AP-style framing, review Topic 14.1 in the Fiveable study guide (https://library.fiveable.me/ap-physics-2-revised/unit-6/1-properties-of-wave-pulses-and-waves/study-guide/Ql0FLnrI6dIHcNlL) and try practice problems (https://library.fiveable.me/practice/ap-physics-2-revised) to see amplitude → energy → perceived loudness in questions.

A wave is transverse if the disturbance of the medium is perpendicular to the direction the wave travels; it’s longitudinal if the disturbance is parallel to the travel direction (CED 14.1.A.4–5). Examples: a wave on a string is transverse—the string moves up/down while the pulse travels along the string (string wave speed depends on tension: v_string = sqrt(FT/(m/ℓ))). Sound in air is a mechanical longitudinal wave—air parcels oscillate back and forth along the direction the sound moves, creating compressions and rarefactions. Electromagnetic waves (light, radio) are transverse and don’t need a medium; mechanical waves do (CED 14.1.A.2). Amplitude: for transverse waves it’s max displacement; for longitudinal (sound) it’s max pressure change—loudness increases with amplitude (CED 14.1.A.6). This topic is tested in Unit 14 (waves, sound, optics) on the AP exam—review the Topic 14.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-6/1-properties-of-wave-pulses-and-waves/study-guide/Ql0FLnrI6dIHcNlL) and more unit resources (https://library.fiveable.me/ap-physics-2-revised/unit-14). For extra practice try the AP Physics 2 practice set (https://library.fiveable.me/practice/ap-physics-2-revised).

When a wave goes into a different medium, some key properties change and some don’t—this is exactly what Topic 14.1 and 14.2 cover on the CED. Mechanical vs electromagnetic: mechanical waves need a medium; EM waves don’t. Frequency stays the same at a boundary (so f is constant), but speed and wavelength usually change: v = f·λ, so if v changes in the new medium λ changes. For example, all EM waves travel at c = 3.00×10^8 m/s in vacuum, but slower in materials; a wave on a string has v_string = sqrt(F_T/(m/ℓ)), so changing tension or linear mass density changes v. Amplitude can drop (attenuation) when energy is absorbed; reflection and transmission at boundaries redistribute energy. Sound speed also depends on medium and temperature (higher T → faster sound). These ideas appear on the AP exam—review Topic 14.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-6/1-properties-of-wave-pulses-and-waves/study-guide/Ql0FLnrI6dIHcNlL), the unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-14), and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised) for extra practice.