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OscillationsIntroStarter track

Concept module

Wave Speed and Wavelength

Follow one traveling wave across the same medium and connect crest spacing, travel delay, source timing, and the relation v = f lambda on one honest live stage.

Interactive lab

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

Time

0.00 s / 2.67 sLivePause to inspect a specific moment, then step or scrub through it.

0.00 s2.67 s

Wave Speed and Wavelength

One traveling wave, one movable probe, and linked space-time guides keep wave speed, wavelength, frequency, and period on the same live stage.

Live setup

Wave state

v: 2.4 m/s
lambda: 1.6 m
f: 1.5 Hz
T: 0.67 s
probe x: 2.4 m
probe y: 3.67e-16 m

Delay to the probe = 1 s.
Phase lag = 1.5 cycles (opposite-phase).
One period of travel covers 1.6 m.

Graphs

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

Source and probe motion

Tracks the source point and one downstream probe on the same time axis, so travel delay and phase lag stay tied to the live stage.

time (s): 0 to 2.67displacement (m): -2 to 2

Source pointProbe point

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

Controls

Adjust the physical parameters and watch the motion respond.

Amplitude

A

1 m

Changes the wave height without changing v, lambda, f, or T.

Wave speed

v

2.4 m/s

Controls how quickly the crest train moves through the medium.

Wavelength

λ

1.6 m

Controls the crest spacing along the medium.

Probe position

x_{p}

2.4 m

Moves the live measurement point farther from or closer to 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 source and probe traces stay on the same frequency story as the moving crest train. Faster travel or tighter spacing changes both the time graph and the live stage together.

Try this

Keep the probe fixed, then change wave speed or wavelength one at a time and compare the card readouts with the stage motion.

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

Amplitude

1 m

Changes the height of the wave without changing how quickly crests travel or how far apart they are.

Graph: Source and probe motion

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. The best prompt should point at a real spatial or timing change that the current wave, graph, and overlays are already showing.

ObservationPrompt 1 of 1

Graph: Source and probe motion

Notice that the source and probe traces stay on the same frequency story as the moving crest train. Faster travel or tighter spacing changes both the time graph and the live stage together.

Try this

Keep the probe fixed, then change wave speed or wavelength one at a time and compare the card readouts with the stage motion.

Why it matters

The graph is not a separate math panel. It is the same traveling wave seen at two locations.

Control: Wave speedControl: WavelengthGraph: Source and probe motionOverlay: Delay guide

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

Wavelength guide

Marks one crest-to-crest spacing directly on the live wave.

What to notice

Changing lambda re-spaces the crests on the stage and changes the slope of the phase map by the same underlying amount.

Why it matters

It keeps wavelength spatial and visible instead of treating it as a formula-only quantity.

Control: WavelengthGraph: Position to cycle lagEquation

λ

At t = 0 s, the traveling wave moves at 2.4 m/s with wavelength 1.6 m, so the source frequency is 1.5 Hz and the period is 0.67 s. The probe at x = 2.4 m is 1.5 cycles behind the source after a travel delay of 1 s, and its displacement is 3.67e-16 m.

Equation detailsDeeper interpretation, notes, and worked variable context.

Traveling-wave model

Amplitude sets the vertical size, while wavelength and frequency set how the repeating pattern varies in space and time.

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

A

Amplitude 1 m

λ

Wavelength 1.6 m

Wave relation

Wave speed links the spatial spacing of crests to the time rate at which new cycles are launched.

v = f λ

v

Wave speed 2.4 m/s

λ

Wavelength 1.6 m

Frequency and period

Frequency counts cycles each second, while period is the time for one full cycle.

f = \frac{1}{T}

Travel delay

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

Δ t = \frac{x}{v}

v

Wave speed 2.4 m/s

x_{p}

Probe position 2.4 m

Phase lag by position

Every extra wavelength of distance adds one full cycle of lag between the source and a downstream point.

Δ ϕ = 2 π \frac{x}{λ}

λ

Wavelength 1.6 m

x_{p}

Probe position 2.4 m

Progress

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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 2 of 90 / 9 complete

Waves

Earlier steps still set up Wave Speed and Wavelength.

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

Previous step: Simple Harmonic Motion.

Start from track beginning

Short explanation

What the system is doing

A traveling wave ties together two kinds of spacing at once. Along the medium, lambda tells you how far it is from one crest to the next. At one point in the medium, the period tells you how long it takes for that pattern to repeat in time.

This lab keeps one source, one moving wave train, and one probe on the same compact stage so the relation v = f lambda stays honest. If a crest train moves faster through the medium, or if the crests are packed differently, the source timing and probe delay must change with it.

Key ideas

01Wave speed tells you how quickly one phase point such as a crest moves through the medium, while wavelength tells you how far apart repeating spatial features are.

02Frequency and period describe the time behavior at one location. For the same traveling wave, f = v / lambda and T = 1 / f = lambda / v.

03Moving the probe does not change the wave itself. It only changes how much travel delay and phase lag separate that point from the source.

Live worked example

Solve the exact state on screen.

These examples read the current wave speed, wavelength, and probe position from the same live stage, so the algebra stays tied to the crest train you are actually watching.

Live valuesFollowing current parameters

For the current traveling wave with v = 2.4\,\mathrm{m/s} and lambda = 1.6\,\mathrm{m}, what frequency and period must the source have?

v

Wave speed

2.4 m/s

λ

Wavelength

1.6 m

f

Frequency

1.5 Hz

T

Period

0.67 s

1. Start from the wave relation

Use

v = f λ

, so

f = \frac{v}{λ}

, and then

T = \frac{1}{f}

2. Substitute the live values

f = \frac{2}{.} 41.6 = 1.5 Hz

3. Convert to a time period

That gives

T = \frac{1}{f} = 0.67 s

, so one full source cycle launches one more wavelength every 0.67 seconds.

Current timing

f = 1.5 Hz, T = 0.67 s

The wave cycles more slowly here, so each point waits longer for the next full oscillation and the period stays noticeably longer.

Common misconception

A faster wave must always have a higher frequency because it is moving more quickly.

Wave speed and frequency are not the same idea. Speed is how fast the pattern travels through the medium, while frequency is how often one point oscillates.

If the speed changes while the crest spacing stays fixed, the frequency changes. If the speed changes while the source frequency is fixed instead, the wavelength changes. The relation keeps all four quantities consistent.

Mini challenge

You are not allowed to move the probe, and the wave speed stays fixed. What one change makes the source oscillate more slowly while the crest train still reaches the same point?

Prediction prompt

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

Check your reasoning

Increase the wavelength.

With v fixed, the frequency is f = v / lambda. A larger wavelength means fewer cycles fit into each meter, so the source frequency drops and the period gets longer.

Quick test

Variable effect

Question 1 of 4

Use the live wave relation, not memory alone. These checks are about how spacing, timing, and downstream delay fit together.

The wave speed stays fixed, but lambda doubles. What happens to f and T?

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 one source on the left launching a transverse traveling wave across a horizontal medium. A movable probe marks one downstream position on the wave, and optional overlays can label one wavelength, the source-to-probe delay, and the distance a crest covers in one period.

A readout card summarizes the current wave speed, wavelength, frequency, period, probe position, and probe displacement so the key relation stays visible without leaving the stage.

Graph summary

The displacement graph compares source motion with probe motion on the same time axis, so the user can read delay and phase differences honestly. The phase-map graph shows how many cycles of lag accumulate with downstream distance, and hovering that graph moves the live probe to the matching position.

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.

Longitudinal soundOscillations

Wave Speed and Wavelength

See each variable before you move it.

Wavelength guide

Waves

What the system is doing

Solve the exact state on screen.

For the current traveling wave with v = 2.4\,\mathrm{m/s} and lambda = 1.6\,\mathrm{m}, what frequency and period must the source have?

The wave speed stays fixed, but lambda doubles. What happens to f and T?

Keep moving through the concept map.

Sound Waves and Longitudinal Motion

Wave Interference

Standing Waves