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Concept module

Sound Waves and Longitudinal Motion

See sound as a longitudinal wave by keeping parcel motion, compression and rarefaction, probe timing, and energy transfer tied to one compact medium-first bench.

Interactive lab

Keep the stage, graph, and immediate control feedback in one working view.

Time

0.00 s / 3.00 sLivePause to inspect a specific moment, then step or scrub through it.

0.00 s3.00 s

Sound Waves and Longitudinal Motion

A compact sound-wave bench keeps particle motion, compression and rarefaction, probe timing, and energy-transfer direction on one honest longitudinal-wave stage.

Live setup

Sound state

A: 0.12 m
v_wave: 2.4 m/s
lambda: 1.8 m
f: 1.33 Hz
T: 0.75 s
I cue: 0.01
probe x: 2.25 m
probe shift: 0.12 m

Delay to the probe = 0.94 s.
Pitch follows frequency, while the bounded loudness/intensity cue follows amplitude and the A^2 response graph.
Local state = transition; pressure cue = -3.06e-16.
Particles oscillate along the tube while the disturbance and energy travel to the right.

Graphs

Switch graph views without breaking the live stage and time link.

Source and probe particle motion

Tracks the source parcel and the selected probe parcel on the same time axis so travel delay stays attached to the live sound bench.

time (s): 0 to 3particle displacement (m): -0.5 to 0.5

Source parcelProbe parcel

Hover or scrub to link the graph back to the stage.time (s) / particle displacement (m)

Controls

Adjust the physical parameters and watch the motion respond.

Particle amplitude

A

0.12 m

Controls how far each parcel swings left and right from its resting position.

Wave speed

v_{w a v e}

2.4 m/s

Controls how quickly the disturbance and its energy move through the medium.

Wavelength

λ

1.8 m

Controls the spacing between neighboring compressions.

Probe position

x_{p}

2.25 m

Moves the tracked parcel farther downstream or back toward the source.

More tools

Secondary controls, alternate presets, and less-used toggles stay nearby without crowding the main bench.

Show

More presets

Presets

Predict -> manipulate -> observe

Keep the active prompt next to the controls so each change has an immediate visible consequence.

ObservationPrompt 1 of 1

Notice that the parcel arrow points left-right while the disturbance arrow points right. Sound propagation and particle motion are linked, but they are not the same motion.

Try this

Keep the motion-direction overlay on and watch the probe parcel for one full cycle before touching any controls.

Equation map

See each variable before you move it.

Select a symbol to highlight the matching control and the graph or overlay it most directly changes.

A

Particle amplitude

0.12 m

Changes how far each parcel swings from equilibrium and therefore how strong the compression and rarefaction cue becomes.

Graph: Source and probe particle motionGraph: Probe shift and compression cueOverlay: Motion directionsOverlay: Compression / rarefaction

Equations in play

Choose an equation to sync the active symbol, control highlight, and related graph mapping.

More tools

Detailed noticing prompts, guided overlays, and challenge tasks stay available without taking over the main bench.

Hide

What to notice

Use one cue at a time. Each prompt should point at a real longitudinal-wave effect that the current stage and graph already show.

ObservationPrompt 1 of 1

Graph: Source and probe particle motion

Notice that the parcel arrow points left-right while the disturbance arrow points right. Sound propagation and particle motion are linked, but they are not the same motion.

Try this

Keep the motion-direction overlay on and watch the probe parcel for one full cycle before touching any controls.

Why it matters

This is the core distinction between a longitudinal wave and a parcel drifting with the wave.

Control: Probe positionGraph: Source and probe particle motionOverlay: Motion directions

Guided overlays

Focus one overlay at a time to see what it represents and what to notice in the live motion.

2 visible

Overlay focus

Motion directions

Shows parcel motion along the tube and the right-moving disturbance direction at the same time.

What to notice

The parcels sway back and forth along the tube even while the disturbance itself keeps moving to the right.

Why it matters

It separates local particle motion from wave propagation, which is the core longitudinal-wave idea.

Control: Probe positionControl: Wave speedGraph: Source and probe particle motionEquation

v_{w a v e}

Equation

x_{p}

Challenge mode

Use the linked particle bench and probe graphs to turn longitudinal-wave ideas into compact positioning tasks.

0/2 solved

ConditionCore

1 of 4 checks

Find a strong compression

Starting from Baseline, move the probe until it sits inside a strong compression while the probe-pressure graph and compression overlay stay visible.

Graph-linkedGuided start2 hints

Suggested start

Use the pressure labels and the probe graph together while you move the probe.

Pending

Open the probe shift and compression graph.

Source and probe particle motion

Matched

Keep the compression overlay visible.

Pending

Make the normalized compression cue strongly positive.

-3.06e-16

Pending

Bring the probe parcel close to its center position.

0.12 m

The checklist updates from the live simulation state, active graph, overlays, inspect time, and compare setup.

At t = 0 s, the longitudinal wave moves right at 2.4 m/s with wavelength 1.8 m, so the source frequency is 1.33 Hz and the period is 0.75 s. The tracked parcel at x = 2.25 m is 1.25 cycles behind the source after a travel delay of 0.94 s. That parcel is displaced 0.12 m, the local medium state is transition, and the bounded intensity cue is 0.01 in amplitude-squared units.

Equation detailsDeeper interpretation, notes, and worked variable context.

Longitudinal parcel displacement

Each parcel moves back and forth along the same line the disturbance travels, rather than riding across the whole medium.

s (x, t) = A sin (2 π (\frac{x}{λ} - f t))

A

Particle amplitude 0.12 m

λ

Wavelength 1.8 m

Wave timing relation

Wave speed links the source timing to the spacing between compressions.

v_{w a v e} = f λ

v_{w a v e}

Wave speed 2.4 m/s

λ

Wavelength 1.8 m

Travel delay

A parcel farther from the source responds later because the disturbance still has to travel through the medium.

Δ t = \frac{x}{v _{w a v e}}

v_{w a v e}

Wave speed 2.4 m/s

x_{p}

Probe position 2.25 m

Compression and rarefaction cue

Positive cue means neighboring parcels are crowded together, while negative cue means they are spread farther apart.

compression cue \propto - \frac{\partial s}{\partial x}

A

Particle amplitude 0.12 m

Progress

Not startedMastery: NewLocal-first

Start exploring and Open Model Lab will keep this concept's progress on this browser first. Challenge mode has 2 compact tasks ready. No finished quick test, solved challenge, or completion mark is saved yet.

Let the live model runChange one real controlOpen What to notice

Try this setup

Copy the live bench state and reopen this concept with the same controls, graph, overlays, and compare context.

Stable links

Starter track

Step 3 of 90 / 9 complete

Waves

Earlier steps still set up Sound Waves and Longitudinal Motion.

1. Simple Harmonic Motion2. Wave Speed and Wavelength3. Sound Waves and Longitudinal Motion4. Pitch, Frequency, and Loudness / Intensity+5 more steps

Previous step: Wave Speed and Wavelength.

Start from track beginning

Starter track

Step 1 of 50 / 5 complete

Sound and Acoustics

Next after this: Pitch, Frequency, and Loudness / Intensity.

1. Sound Waves and Longitudinal Motion2. Pitch, Frequency, and Loudness / Intensity3. Beats4. Doppler Effect+1 more steps

This concept is the track start.

See next concept

Short explanation

What the system is doing

Sound in a gas or liquid is a longitudinal wave. The disturbance moves through the medium, but the parcels in the medium do not ride across the whole tube with it. They oscillate back and forth around local resting positions while compressions and rarefactions move onward.

This bench keeps one source piston, one particle train, one pressure ribbon, and one movable probe on the same stage. The source and probe timing, the local compression cue, and the right-moving disturbance all come from the same displacement field, so sound stays visually honest without turning into a full acoustics engine.

Key ideas

01In a longitudinal wave, parcel motion is parallel to the direction the disturbance travels, not perpendicular to it.

02A compression is a region where neighboring parcels are crowded more tightly than usual, while a rarefaction is a region where they are spread farther apart.

03Sound transfers energy through the medium because each parcel pushes on its neighbor, so the disturbance and its energy move onward even though each parcel only oscillates locally.

Live sound checks

Solve the exact state on screen.

These checks read the same source, probe, and compression state that the stage and graphs already show, so the algebra never disconnects from the longitudinal wave.

Live valuesFollowing current parameters

For the current sound wave with $v_{w a v e} = 2.4 m/s$ and $λ = 1.8 m$ , what source frequency does that require, and how long does the disturbance take to reach the probe at $x_{p} = 2.25 m$ ?

v_{w a v e}

Wave speed

2.4 m/s

λ

Wavelength

1.8 m

x_{p}

Probe position

2.25 m

f

Frequency

1.33 Hz

Δ t

Travel delay

0.94 s

1. Start from the wave timing relations

Use

v_{w a v e} = f λ

, so

f = \frac{v _{w a v e}}{λ}

, and use

Δ t = \frac{x _{p}}{v _{w a v e}}

for the probe delay.

2. Substitute the live speed, spacing, and probe position

f = \frac{2}{.} 41.8 = 1.33 Hz

and

Δ t = \frac{2}{.} 252.4 = 0.94 s

3. Interpret what the source and probe must do

That means the source launches 1.33 cycles each second, each cycle lasts 0.75 s, and the probe parcel repeats that motion after a delay of 0.94 s.

Current sound timing

f = 1.33 Hz, Δ t = 0.94 s

The probe is close enough to the source that the travel delay is short, but the same right-moving disturbance still has to propagate through the medium before the parcel responds.

Compression checkpoint

The medium stays the same, so the wave speed is fixed. What single change makes compressions pack closer together while the particle motion stays longitudinal?

Prediction prompt

Decide whether you should increase amplitude, shorten wavelength, or move the probe farther right.

Check your reasoning

Shorten the wavelength.

Compression spacing follows the wavelength. Shortening

λ

packs more compressions and rarefactions into the same distance without changing the fact that each parcel still oscillates back and forth along the tube.

Common misconception

If the sound wave moves to the right, each air parcel must also drift steadily to the right with it.

The disturbance travels to the right, but each parcel mainly oscillates back and forth around its own equilibrium position.

What moves onward are the compression and rarefaction pattern and the energy transfer through the medium, not one chunk of matter riding all the way across the stage.

Quick test

Misconception check

Question 1 of 4

Use the linked particle and pressure views, not memory alone. These checks focus on what longitudinal sound waves mean physically.

Which statement best describes the difference between parcel motion and wave propagation in this sound model?

Choose one answer to reveal feedback, then test the idea in the live system if a guided example is available.

Accessible description

The simulation shows a horizontal tube with a source piston on the left, a row of parcel markers inside the tube, and a movable probe parcel. A colored ribbon inside the tube marks local compression and rarefaction, while optional overlays label parcel-motion direction, compression regions, and the rightward energy-transfer cue.

Changing particle amplitude, wave speed, wavelength, or probe position updates the same stage, probe graphs, and readout card so parcel motion, compression state, and travel delay stay synchronized.

Graph summary

The first graph compares source and probe parcel displacement over time so the downstream delay stays tied to the live sound bench.

The second graph compares the probe parcel's normalized shift with the local compression cue, which helps the learner separate one parcel's position from the local crowding of the medium.

Carry sound into later wave ideas

Keep moving through the concept map.

These suggestions come from the concept registry, so the reason label reflects either curated guidance or the fallback progression logic.

Pitch vs loudnessOscillations

Sound Waves and Longitudinal Motion

See each variable before you move it.

Motion directions

Find a strong compression

Waves

Sound and Acoustics

What the system is doing

Solve the exact state on screen.

For the current sound wave with vwave​=2.4m/s and λ=1.8m, what source frequency does that require, and how long does the disturbance take to reach the probe at xp​=2.25m?

Which statement best describes the difference between parcel motion and wave propagation in this sound model?

Keep moving through the concept map.

Pitch, Frequency, and Loudness / Intensity

Beats

Doppler Effect

For the current sound wave with $v_{w a v e} = 2.4 m/s$ and $λ = 1.8 m$ , what source frequency does that require, and how long does the disturbance take to reach the probe at $x_{p} = 2.25 m$ ?