Properties of Wave Pulses and Waves
Distinguish disturbance from energy transport and connect wave speed with the medium.
AP Physics 2 Topic 14.1 · College Board CED printed p. 110, 111 / PDF p. 117, 118 · See this topic in the course outline
A wave moves a disturbance and its energy. Follow the material separately, and the motion makes much more sense.
Before you start
- Energy transfer
- Force and mass
- Equilibrium displacement
A pulse passes; the material stays local
Flick a rope once and a single pulse travels to the other end. Shake it repeatedly and an ideal periodic wave follows. Each short rope segment moves away from equilibrium and returns; it does not ride the crest along the entire rope. Neighboring segments exert forces and transfer energy. A sound pulse similarly transfers energy through local compressions without carrying the same air molecules from the loudspeaker to your ear.
A continuous wave is modeled with a repeatable wavelength and frequency. Real sources may start, stop, or make several frequencies; use the pulse or periodic model that fits the observation. In the ideal wave description there is no net bulk transport of matter. Water can also have currents and breaking waves, so do not confuse those motions with the small-wave model.
What fixes the propagation speed?
Rope and sound disturbances are mechanical: particles and their interactions supply the medium. Electromagnetic radiation can cross a vacuum. All electromagnetic waves in vacuum have speed , regardless of color or frequency.
For a taut, flexible, uniform string in the small-disturbance model, . More tension makes the restoring interaction stronger, so the disturbance travels faster. More mass per length makes segments harder to accelerate, so it travels slower. Four times the tension doubles v; four times μ halves v. This speed is along the string, not the vertical speed of a segment.
Sound speed depends on the medium and its properties. In a given gas, increasing temperature increases sound speed because the particles' thermal motion and response change. Do not assume sound speed is the same in air, water, and steel, or that making a louder source automatically changes it. Frequency dependence of speed is called dispersion; the ideal string and ordinary-air models here neglect it. If a real medium is dispersive, each frequency needs its own v in the wave relation.
Compare disturbance and travel directions
In a transverse wave, the disturbance is perpendicular to propagation: a right-moving rope pulse can displace rope segments up and down. In a longitudinal wave, the disturbance is parallel to propagation. Sound in a fluid is modeled as longitudinal: particles move back and forth along the travel direction, creating high-pressure compressions and low-pressure rarefactions.
Describe a right-moving sound wave with two drawings: horizontal arrows show particle oscillation; alternating shaded bands show pressure. The bands travel right even though each particle oscillates about its own equilibrium location. A sinusoidal pressure-versus-position curve is a graph of pressure, not a literal sideways snake of air.
Amplitude measures the largest departure
Displacement amplitude A is the largest distance from equilibrium, not peak-to-trough distance (which is 2A). For pressure amplitude, use the largest magnitude of pressure change from the equilibrium pressure: . If air pressure ranges from p₀ − 0.80 Pa to p₀ + 0.80 Pa, the pressure amplitude is 0.80 Pa.
With frequency and medium fixed, increasing amplitude increases the energy carried and the average intensity. In linear waves the relevant energy or intensity is proportional to the square of the corresponding amplitude. A larger sound pressure amplitude generally sounds louder, though human loudness perception is not a simple linear meter. Loudness and pitch describe different properties.
A taut string, with a marked segment
A 2.0 m uniform string has mass 0.020 kg and tension 9.0 N. Find the travel time of a small pulse and explain what a marked segment does.
Model the string as taut and uniform; .
Why this step? The wave responds to mass per unit length, not total string mass alone.
; .
Why this step? Propagation covers the string length at the medium-dependent speed.
The mark oscillates transversely as the pulse passes and returns near its starting location.
Why this step? The energy travels along the rope without bulk material transport.
Answer and check
30 m/s and about 0.067 s; the marked material does not travel 2.0 m.
Decide when wavelength and frequency are well defined
A single flick produces one pulse: there may be a width and travel time, but no repeating crest-to-crest spacing or cycle rate for the disturbance as a whole. A steady sinusoidal source instead produces a continuous periodic wave in the ideal model. It repeats in space with a well-defined wavelength λ and at a fixed place with a well-defined frequency f. Continuous here refers to the sustained repeating disturbance; the ideal model omits its startup and stopping edges.
For a steady sound tone with period 0.0200 s and compression-to-next-compression distance 6.80 m, f = 1/T = 50.0 Hz and λ = 6.80 m. Thus the compressions propagate at fλ = 340 m/s. Air particles oscillate locally along the travel direction; the same air particles do not travel 6.80 m every cycle. A one-time clap is better described as a pulse and need not have one well-defined repeating wavelength and frequency.
A tone has two repeat measurements
A loudspeaker supplies a sustained single-frequency tone in still air. At a fixed sensor, adjacent equal-phase pressure maxima are 0.0200 s apart. At one instant, successive compressions are 6.80 m apart.
- A stable train of repetitions supports the ideal continuous periodic wave model, unlike a single clap.
- T = 0.0200 s gives f = 50.0 Hz. Equal-phase compression spacing gives λ = 6.80 m.
- v = fλ = 340 m/s describes the propagation of the pressure disturbance, not bulk transport of air.
Answer and check
The periodic model has well-defined 50.0 Hz frequency and 6.80 m wavelength. Its propagation speed is 340 m/s.
Try it from memory
Write your answer and reason before opening the worked answer. Your self-assessment is a study decision; it is not an automatically graded score.
Question 1
A pressure trace oscillates between 101 324 Pa and 101 326 Pa about 101 325 Pa. What is its amplitude, and which point is a compression?
Worked answer and reason
Amplitude is 1 Pa. The 101 326 Pa region is a compression; 101 324 Pa is a rarefaction.
Subtract equilibrium rather than using total pressure or peak-to-trough range.
Question 2
A bell and a flash are inside an evacuated transparent chamber. Which disturbance can cross the vacuum, and why?
Worked answer and reason
The electromagnetic flash can; sound cannot propagate through the vacuum because its longitudinal pressure disturbance needs matter.
Identify the carrier of the disturbance before applying a speed.
JavaScript enables saved drafts and self-assessment. You can always work on paper.
Catch the tempting mistake
- The crest is a piece of matter traveling down the rope.
- A crest is a moving pattern. Follow a mark on the rope to see local oscillation while the disturbance and energy travel.
Put it to work
Give the physical reason as well as the calculation. The worked solutions are on a separate page.
- Problem 1 · mixed
- Problem 2 · experimental
- Problem 19 · experimental
Explain and apply the model
Try these problems before opening the solutions. Show the physical model, your calculation or sketch, and the reason your conclusion follows.
Identify the repeating model from observations
A speaker emits a sustained pure tone in still air. A fixed pressure sensor records equal-phase maxima every 0.0100 s. A simultaneous spatial pressure map shows successive compressions 3.40 m apart. The speaker is then switched off and makes one short isolated click.
(a) State the appropriate continuous-wave model for the sustained tone, explicitly identify its well-defined wavelength and frequency from the two observations, and calculate propagation speed. Explain why the fixed-location measurement and snapshot cannot exchange their horizontal units.
(b) Compare the isolated click with the sustained tone: state which is a pulse and why assigning the click one repeating crest spacing and cycle rate is not justified by these observations. Describe local air-particle motion relative to propagation and explain why sound does not carry those same particles from the speaker to the sensor.
Written working workspace
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. Keep your work on paper or in your own notes; the source problem above remains available.
Worked solution and rubric →Revisit the explanation →Revisit the explanation →
Scientific calculator workspace
Keep intermediate precision and report units. This calculator supports arithmetic and elementary functions.
Scientific calculator
This calculator requires JavaScript. Use the physics formula sheets and show your working manually.
+ − * / ^ ! · pi · e · sqrt · sin, cos, tan · asin, acos, atan · atan2(y,x) · ln, log · abs · exp · hypot(x,y). Use * between factors. Keep units in your written working.
For the teacher
- Mark one rope segment and ask whether it reaches the far end. Ask students to identify compression from a pressure graph rather than from a drawing of particles.
Source objectives and scope
- 14.1.A — Describe the physical properties of waves and wave pulses.
Suggested skills are teaching guidance. The course applies all science practices across its objectives.
Science references for this teaching
- AP Physics 2 Course and Exam Description, official Unit 14 — Official topic/LO/EK scope and boundaries; local pinned source pages 117–134, equations visually checked on 118,120,130,132,134.
- OpenStax University Physics 1, Energy and Power of a Wave — Verification of fixed-amplitude mechanical-wave frequency scaling and distinction from electromagnetic intensity.
- OpenStax University Physics 1, Interference of Waves — Linear superposition and pointwise addition model.
- OpenStax University Physics 3, Single-Slit Diffraction — Verification of aperture minima and small-angle conditions.
- OpenStax University Physics 3, Interference in Thin Films — Verification of reflection phase and normal-incidence thin-film paths.
Glossary and deeper reading · 14 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
-
Force
A force describes an interaction that can change an object’s momentum. It is a vector measured in newtons, so both size and direction matter when forces are added. For example, a rope can pull a cart while the floor exerts friction in another direction.
-
Mechanical equilibrium
Mechanical equilibrium means there is no translational or angular acceleration for the system being considered. For a rigid body, both the net external force and the net external torque must vanish. For example, a stationary ladder supported against a wall requires both force balance and torque balance.
-
Wavelength
Wavelength is the spatial distance between neighboring points at the same phase of a periodic wave. It connects propagation speed and frequency through speed equal to frequency times wavelength. For example, neighboring crests of a sinusoidal water wave are separated by one wavelength.
-
Frequency
Frequency is the number of complete repeating cycles per unit time. It is measured in hertz, meaning cycles per second, and is the reciprocal of the period. For example, a vibrating string with a higher frequency produces more cycles each second.
-
Electromagnetic wave
An electromagnetic wave contains oscillating electric and magnetic fields that transport energy. In the plane-wave vacuum model, both fields are perpendicular to each other and to the propagation direction. For example, visible light and radio waves can both travel through empty space.
-
Tension
Tension is a pulling force transmitted through a stretched rope, string, or similar connector. It acts along the connector away from the object it pulls, and an ideal massless rope has the same tension throughout an uninterrupted segment. For example, a rope supporting an accelerating load can have a tension different from the load’s weight.
-
Temperature
Temperature is a state quantity that determines the direction of net energy transfer through thermal contact. For a classical ideal gas it is proportional to the average translational kinetic energy per particle, rather than to the total energy of the sample. For example, a small hot metal sample can have a higher temperature but less total internal energy than a large cooler sample.
-
Transverse wave
In a transverse wave, the disturbance is perpendicular to the direction of propagation. The disturbance direction and the energy-transfer direction must therefore be distinguished. For example, a rope pulse can travel horizontally while rope segments move up and down.
-
Longitudinal wave
In a longitudinal wave, the disturbance is parallel to the direction of propagation. Compression and rarefaction can travel while particles oscillate locally along that direction. For example, sound in air is a longitudinal pressure disturbance rather than a stream of air traveling all the way from source to listener.
-
Pressure
Pressure is the normal force per unit area exerted on a surface. It is a scalar measured in pascals, with one pascal equal to one newton per square meter. For example, a gas exerts pressure throughout its volume through many microscopic collisions, even when its bulk motion is zero.
-
Displacement
Displacement is the vector change in position from the start of an interval to its end. It depends on those endpoints rather than the length or shape of the path traveled. For example, walking around a closed track and returning to the start gives zero displacement but a nonzero distance traveled.
-
Amplitude
Amplitude is the maximum magnitude of a repeating disturbance measured from its equilibrium value. It describes the size of the oscillation rather than its frequency or propagation speed. For example, pulling a spring-mounted mass farther from equilibrium increases its oscillation amplitude when it is released from rest.
-
Wave intensity
Wave intensity is the time-averaged energy-transfer rate per area perpendicular to propagation. It is measured in watts per square meter and differs from total power because area matters. For example, spreading the same sound power over a larger area reduces the intensity there.
-
Oscillation period
An oscillation period is the time required for one complete repeating cycle. It is the reciprocal of frequency and is measured in seconds. For example, measuring the time for several pendulum swings and dividing by the number of cycles estimates the period.