Physics · Sound

Sound Waves and Longitudinal Motion

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Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Pitch / Frequency / Loudness / IntensitySeparate timing from strength in sound

Key takeaway

Air parcels in this sound model oscillate parallel to the wave direction rather than drifting with the wave.
Compressions and rarefactions describe local crowding and spreading of neighboring parcels.
Wave speed, wavelength, frequency, and probe position connect spacing to timing through v_wave = f lambda and Delta t = x / v_wave.

Common misconception

If sound travels to the right, the air itself must steadily flow to the right with it.

The wave pattern and its energy move to the right, but each parcel mainly oscillates back and forth around equilibrium.

Carry sound into later wave ideas

Keep this idea moving

Open the next concept, route, or track only when you want the current model to widen into a larger branch.

Pitch vs loudnessSound

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.

Nearby tonesSound

Beats

Superpose two nearby sound frequencies, watch the fast carrier sit inside a slower envelope, and connect beat rate to the frequency difference on one compact bench.

Motion-shifted pitchWaves

Doppler Effect

Watch a moving sound source compress wavefronts ahead and stretch them behind, then see how source motion and observer motion combine to change the heard pitch on one bounded classical bench.

Stay with this concept

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Reference and support

Use these calmer sections when you want a fuller explanation, examples, or accessibility support after the guided flow.

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Equation snapshotMotion, spacing, and timing snapshot · Wave timing relationShow 3 equations

Use these equations to keep three ideas separate: parcel displacement is local back-and-forth motion, wavelength sets compression spacing, and wave speed controls travel delay.

Motion, spacing, and timing snapshot
$s (x, t) = A sin (2 π (\frac{x}{λ} - f t))$
Describes parcel motion along the tube. Each parcel oscillates around equilibrium instead of traveling across the whole medium.
Wave timing relation
$v_{w a v e} = f λ$
Links the spacing between compressions to how quickly the source must oscillate.
Travel delay
$Δ t = \frac{x}{v _{w a v e}}$
A parcel farther from the source responds later because the disturbance needs time to travel there.

Why it behaves this way

Explanation

Watch one parcel in the tube. It moves left and right parallel to the wave direction, then returns near its starting position. The sound disturbance still moves to the right because what travels onward is a pattern of compressions and rarefactions, not a clump of matter being carried down the tube.

This bench keeps the piston, parcel row, pressure ribbon, and movable probe tied to the same wave. The displacement graph shows when the source parcel and probe parcel repeat their motion. The probe-pressure graph shows whether the local region is compressed or rarefied. Read both together, because parcel position alone does not tell you the full local sound state.

Key ideas

01In a longitudinal wave, parcels oscillate parallel to the direction the disturbance travels.

02A compression is a crowded region of the medium, while a rarefaction is a more spread-out region.

03The disturbance and its energy move onward through the medium even though each parcel mainly oscillates around its own equilibrium position.

Worked examples

Live sound checks

Open examples when you want to see the same idea walked through step by step.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

These checks use the live source, probe, and compression state already shown on the stage and graphs, so the calculation stays tied to the same sound wave you are inspecting.

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Example 1 of 2

Frozen valuesUsing frozen parameters

For the current sound wave with v_wave = 2.4 m/s, λ = 1.8 m, and the probe at x_p = 2.25 m, what source frequency is required and how long does the disturbance take to reach the probe?

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. Use the wave-speed and delay relations

Use f = v_wave / λ and Δt = x_p / v_wave. The first relation sets the source frequency; the second relation gives the travel delay to the probe.

2. Substitute the live values

f = 2.4 / 1.8 = 1.33 Hz. Δt = 2.25 / 2.4 = 0.94 s.

3. Interpret the timing at the source and probe

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, Δt = 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.

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Starter track

Step 1 of 5

Sound and Acoustics

Pitch, Frequency, and Loudness / Intensity is what this track opens next.

This concept is the track start.

Also appears in Waves.

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