HomeConcept libraryOscillations and Waves

OscillationsIntroStarter tracks

Concept module

Pitch, Frequency, and Loudness / Intensity

Keep one compact sound bench while separating pitch from frequency, loudness from amplitude and an amplitude-squared intensity cue, and probe delay from the source sound itself.

Interactive lab

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

Time

0.00 s / 3.64 sLivePause to inspect a specific moment, then step or scrub through it.

0.00 s3.64 s

Pitch, Frequency, and Loudness / Intensity

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: 0.1 m
v_wave: 2.4 m/s
lambda: 2.18 m
f: 1.1 Hz
T: 0.91 s
I cue: 0.01
probe x: 2.2 m
probe shift: 5.23e-3 m

Delay to the probe = 0.92 s.
Pitch follows frequency, while the bounded loudness/intensity cue follows amplitude and the A^2 response graph.
Local state = rarefaction; pressure cue = -1.
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 motion

Tracks how quickly the sound repeats, so pitch stays tied to frequency and period.

time (s): 0 to 3.64particle 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.

Amplitude

A

0.1 m

Controls how strong the loudness / intensity cue is.

Frequency

f

1.1 Hz

Controls pitch while the medium speed stays fixed.

Probe position

x_{p}

2.2 m

Moves the tracked parcel without changing the source sound.

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 raising frequency makes the traces cycle faster and packs the compression pattern closer together. That is the pitch change.

Try this

Start from Conversation tone, then move to Higher pitch without touching amplitude.

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

0.1 m

Changes how strong the parcel motion and loudness cue are.

Graph: Source and probe motionGraph: Amplitude and intensity cueOverlay: Energy-transfer cue

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 points to a pitch-versus-loudness distinction already visible on the bench.

ObservationPrompt 1 of 1

Graph: Source and probe motion

Notice that raising frequency makes the traces cycle faster and packs the compression pattern closer together. That is the pitch change.

Try this

Start from Conversation tone, then move to Higher pitch without touching amplitude.

Why it matters

It keeps pitch tied to timing and spacing, not to wave height.

Control: FrequencyGraph: Source and probe motionOverlay: Compression spacingEquation

f

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 and the right-moving disturbance at the same time.

What to notice

Pitch and loudness are both being read from the same sound wave.

Why it matters

It keeps the sound model honest while you focus on pitch and loudness.

Control: FrequencyControl: Probe positionGraph: Source and probe motionEquation

f

Equation

x_{p}

Challenge mode

Use compare mode to separate faster cycling from stronger driving without switching models.

0/1 solved

MatchStretch

0 of 8 checks

Louder, same pitch

Enter compare mode and make Setup B louder than Setup A while keeping the pitch the same.

Compare modeGraph-linkedGuided start2 hints

Suggested start

Clone Conversation tone into A and B, then edit only Setup B.

Pending

Switch into compare mode and edit Setup B.

Explore

Pending

Keep the amplitude-to-intensity graph open.

Source and probe motion

Pending

Keep Setup A near the conversation frequency.

Pending

Keep Setup B on the same frequency.

Pending

Keep Setup A on the baseline amplitude.

Pending

Raise Setup B to a clearly louder amplitude.

Pending

Keep Setup A on the baseline intensity cue.

Pending

Raise Setup B to the louder intensity cue.

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 2.18 m, so the source frequency is 1.1 Hz and the period is 0.91 s. The tracked parcel at x = 2.2 m is 1.01 cycles behind the source after a travel delay of 0.92 s. That parcel is displaced 5.23e-3 m, the local medium state is rarefaction, and the bounded intensity cue is 0.01 in amplitude-squared units.

Equation detailsDeeper interpretation, notes, and worked variable context.

Longitudinal sound displacement

Amplitude sets the size of the parcel motion, while frequency sets how quickly the sound repeats.

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

A

Amplitude 0.1 m

f

Frequency 1.1 Hz

x_{p}

Probe position 2.2 m

Frequency and period

Higher frequency means a shorter period and a higher pitch.

f = \frac{1}{T}

f

Frequency 1.1 Hz

Spacing at fixed medium speed

If the medium speed is fixed, a higher frequency packs the compression pattern more tightly.

λ = \frac{v _{w a v e}}{f}

f

Frequency 1.1 Hz

Bounded loudness / intensity cue

This intro bench uses amplitude squared as an honest intensity cue, so larger amplitude means a stronger loudness cue without changing pitch by itself.

I_{c u e} \propto A^{2}

This is a bounded beginner-friendly cue, not a full acoustic power model.

A

Amplitude 0.1 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 1 compact task 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 4 of 90 / 9 complete

Waves

Earlier steps still set up Pitch, Frequency, and Loudness / Intensity.

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

Previous step: Sound Waves and Longitudinal Motion.

Start from track beginning

Starter track

Step 2 of 50 / 5 complete

Sound and Acoustics

Earlier steps still set up Pitch, Frequency, and Loudness / Intensity.

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

Previous step: Sound Waves and Longitudinal Motion.

Start from track beginning

Short explanation

What the system is doing

Pitch and loudness should not be treated as the same sound property. In this bounded sound bench, pitch follows frequency: higher frequency means more cycles each second and a shorter period. Loudness follows amplitude and the strength of the energy-transfer cue, so a larger amplitude can sound louder without changing pitch.

The medium speed stays fixed so the page can separate the ideas cleanly. Raising frequency makes the compression pattern repeat faster and sit closer together, while raising amplitude makes the parcel motion larger and raises the amplitude-squared intensity cue.

Key ideas

01Pitch tracks frequency, not amplitude.

02Loudness or intensity tracks amplitude and a stronger energy-transfer cue.

03A sound can be higher pitch without being louder, or louder without being higher pitch.

Live worked example

Solve the exact state on screen.

These checks read the same sound bench the stage and graphs use, so the algebra stays tied to one live wave.

Live valuesFollowing current parameters

For the current sound wave with $v_{w a v e} = 2.4 m/s$ and $f = 1.1 Hz$ , what wavelength and period go with that pitch?

v_{w a v e}

Wave speed

2.4 m/s

f

Frequency

1.1 Hz

λ

Wavelength

2.18 m

T

Period

0.91 s

1. Use the sound timing relations

Use

λ = \frac{v _{w a v e}}{f}

and

T = \frac{1}{f}

2. Substitute the live values

λ = \frac{2}{.} 41.1 = 2.18 m

and

T = \frac{1}{1} .1 = 0.91 s

3. Interpret the pitch cue

A frequency of 1.1 Hz means the source repeats 1.1 cycles each second, so pitch is set by timing while the spacing becomes 2.18 m.

Current pitch timing

λ = 2.18 m, T = 0.91 s

The frequency sits in a middle range here, so the pitch cue is moderate and the cycle timing is neither especially slow nor especially fast.

Common misconception

A taller sound wave must have a higher pitch because the wave looks bigger.

Amplitude changes how strong the motion is, not how many cycles happen each second.

Frequency changes pitch. Amplitude changes the bounded loudness / intensity cue.

Mini challenge

You want the same pitch but a louder sound. What single change should you make?

Prediction prompt

Decide whether to raise amplitude, raise frequency, or move the probe farther downstream.

Check your reasoning

Raise amplitude.

Keeping pitch the same means keeping frequency fixed. Raising amplitude increases the loudness / intensity cue without changing pitch.

Quick test

Misconception check

Question 1 of 3

Use the live sound bench, not memory alone. These checks separate pitch, amplitude, and the bounded loudness cue.

Which change raises pitch without changing the loudness cue?

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 sound tube with a source piston, parcel markers, a movable probe, and a colored compression ribbon. Optional overlays mark motion direction, compression spacing, and a bounded energy-transfer cue.

Changing frequency changes how quickly the sound repeats and how closely the compression pattern is spaced. Changing amplitude changes the parcel swing size and the linked intensity cue.

Graph summary

The first graph compares source and probe displacement over time so pitch stays tied to frequency and period.

The second graph compares the probe shift with the local compression cue.

The third graph shows the bounded intensity cue as a function of amplitude.

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.

Hear superpositionOscillations

Pitch, Frequency, and Loudness / Intensity

See each variable before you move it.

Motion directions

Louder, same pitch

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 f=1.1Hz, what wavelength and period go with that pitch?

Which change raises pitch without changing the loudness cue?

Keep moving through the concept map.

Beats

Doppler Effect

Wave Interference

For the current sound wave with $v_{w a v e} = 2.4 m/s$ and $f = 1.1 Hz$ , what wavelength and period go with that pitch?