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Physics OscillationsIntermediateStarter track

Concept module

Standing Waves

Track fixed nodes, moving antinodes, and harmonic mode shapes on one live string while the same probe trace shows the underlying oscillation in time.

Interactive lab

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Starter track

Step 8 of 90 / 9 complete

Waves

Earlier steps still set up Standing Waves.

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

Previous step: Wave Interference.

Start from track beginning

Why it behaves this way

Explanation

A standing wave is what you get when equal waves travel in opposite directions and keep interfering on the same bounded system. Some points cancel all the time, so they become nodes. Other points reinforce most strongly, so they become antinodes.

This lab keeps one string, one live probe, and one authoritative oscillation state in view. The mode-shape graph, the moving string, and the probe trace all come from the same harmonic, which is why mode number, nodes, antinodes, interference, and local oscillation stay tied together.

Key ideas

01Nodes are fixed points created by persistent destructive interference, not places where the wave has disappeared from the whole string.

02Antinodes are the points of largest oscillation, so the local time trace there reaches the full standing-wave amplitude.

03Higher harmonics fit more half-wavelength segments onto the same string, which adds nodes and raises the oscillation frequency.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

These examples read the current harmonic, string length, probe position, and inspected time directly from the live state so the algebra stays attached to the same string you are watching.

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Frozen valuesUsing frozen parameters

For the current mode number and string length, what wavelength and oscillation frequency does this standing wave require?

n

Mode number

L

String length

1.6 m

v

Wave speed

1.2 m/s

1. Start from the allowed-mode relations

For a string fixed at both ends, use

λ_{n} = \frac{2 L}{n}

and

f_{n} = \frac{n v}{2 L}

2. Substitute the live harmonic

λ_{n} = \frac{2 ( 1.6 )}{2}

and

f_{n} = \frac{( 2 ) ( 1.2 )}{2 ( 1.6 )}

3. Compute the allowed oscillation

That gives

λ_{n} = 1.6 m

and

f_{n} = 0.75 Hz

, with node spacing

0.8 m

Current harmonic requirements

λ_{n} = 1.6 m, f_{n} = 0.75 Hz

Raising the mode number adds another half-wavelength segment to the same string, which creates one more loop and one more interior node.

Node checkpoint

You want one more interior node, but you are not allowed to change the fixed-end boundary condition. What is the most direct change you can make?

Make a prediction before you reveal the next step.

Decide whether you should move the probe, raise the mode number, or just wait longer in time.

Check your reasoning against the live bench.

Raise the mode number to the next harmonic.

Moving the probe only changes where you inspect the string, and waiting changes only the time within the same oscillation. The number of interior nodes is set by the harmonic itself, so you must change the mode number.

Common misconception

A standing wave is frozen in place, so nothing is really oscillating once the pattern appears.

The spatial pattern is fixed, but almost every point between the nodes still oscillates up and down in time.

What stays fixed are the node positions and the overall mode shape, not the instantaneous displacement of the string.

Quick test

Misconception check

Question 1 of 4

Use the stage, graph, and interference idea together. These checks ask what must be happening on the string, not what one formula looks like by itself.

A student says, "A node is just a place where the whole wave vanished, so nothing interesting is happening there." What is the best correction?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows a fixed string stretched horizontally with one movable probe marker and a ruler underneath. The string oscillates in one selected harmonic while optional overlays can mark node positions, antinode positions, and the two traveling-wave components that interfere to make the standing pattern.

Changing amplitude, string length, mode number, or probe position immediately updates the same stage, mode-shape graph, and probe-motion graph so the standing-wave state stays synchronized.

Graph summary

The mode-shape graph plots signed standing-wave amplitude scale against position on the string, so zero crossings correspond to nodes and peaks correspond to antinodes.

The probe-motion graph plots the selected point's displacement in time together with its local envelope, which makes node points flatten while antinode points reach the full standing-wave amplitude.

Keep the wave story going

Keep this idea moving

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