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Concept module

Resonance in Air Columns / Open and Closed Pipes

Compare open and closed pipe boundary conditions on one compact air column so standing-wave shapes, missing even harmonics, probe motion, and pressure cues stay tied to the same resonance state.

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Starter track

Step 5 of 50 / 5 complete

Sound and Acoustics

Earlier steps still set up Resonance in Air Columns / Open and Closed Pipes.

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

Previous step: Doppler Effect.

Also in Waves.

Start from track beginning

Why it behaves this way

Explanation

Air-column resonance is the sound-wave version of a standing-wave constraint. The tube length and the boundary conditions decide which standing-wave patterns can survive, so the allowed wavelengths and frequencies are not arbitrary.

This bench keeps one tube, one live probe parcel, and one authoritative resonance state in view. The tube picture, the displacement-shape graph, the harmonic ladder, and the probe trace all read from that same state, so open ends, closed ends, nodes, antinodes, and odd-only closed-pipe harmonics stay tied together.

Key ideas

01Open ends behave like displacement antinodes and pressure nodes, while a closed end behaves like a displacement node and a pressure antinode.

02Open-open tubes allow every integer harmonic, but closed-open tubes skip the even harmonics because one end must stay still while the other end breathes.

03Changing tube length or boundary type changes the allowed wavelength first, and the resonance frequency follows from the same sound speed.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

These examples read the current tube length, boundary condition, resonance order, and probe state directly from the live air column so the algebra stays attached to the same resonant pattern you are watching.

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Frozen valuesUsing frozen parameters

For the current tube length and boundary condition, what wavelength and resonance frequency are allowed?

L

Tube length

1.2 m

m

Resonance order

n_{e f f}

Harmonic multiple

v

Sound speed

34 m/s

1. Start from the boundary rule

For the current open-open tube, use

λ_{n} = \frac{2 L}{n}

and

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

2. Substitute the live tube

Here the selected mode is the 2nd resonance and the 2nd harmonic, so

λ = \frac{2 ( 1.2 )}{2}

with

L = 1.2 m

and

v = 34 m/s

3. Compute the allowed resonance

That gives

λ = 1.2 m

and

f = 28.33 Hz

, with all integer harmonics for this boundary.

Current resonance requirement

λ = 1.2 m, f = 28.33 Hz

Open-open tubes allow every integer harmonic, so each higher resonance adds one more half-wavelength segment across the same tube.

Boundary checkpoint

You want the same tube length but a lower fundamental resonance without changing the length. What is the most direct change?

Make a prediction before you reveal the next step.

Decide whether you should close one end, raise the resonance order, or move the probe.

Check your reasoning against the live bench.

Close one end of the tube.

Closing one end changes the boundary condition from a half-wave fundamental to a quarter-wave fundamental. That doubles the allowed wavelength from

2 L

4 L

and halves the fundamental frequency, while moving the probe only changes what you inspect and raising the resonance order moves to a higher mode instead.

Common misconception

An open end should be a node because the air can move out of the tube there.

For parcel displacement, an open end is where the air can move most freely, so it behaves like a displacement antinode.

What becomes small at an open end is the pressure variation, which is why pressure nodes and displacement antinodes trade places.

Quick test

Misconception check

Question 1 of 4

Use the tube, graph, and boundary ideas together. These checks ask what the resonance pattern means physically, not which formula you memorized.

A student says, "An open end must be a node because the air can just escape there." What is the best correction?

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

Accessibility

The simulation shows one horizontal air column with a movable probe parcel inside the tube, a colored pressure ribbon, and a ruler underneath. The left end can switch between open and closed, the right end stays open, and optional overlays mark boundary rules, parcel-motion nodes and antinodes, and the complementary pressure pattern.

Changing tube length, boundary type, resonance order, probe position, or amplitude immediately updates the same tube view, displacement-shape graph, harmonic ladder, and probe-motion graph so the resonance state stays synchronized.

Graph summary

The displacement-shape graph plots signed parcel-motion scale against position in the tube, so zero crossings correspond to displacement nodes and the end behavior changes when the boundary condition changes.

The probe-motion graph plots one selected parcel in time together with its local envelope, while the harmonic ladder graph plots the allowed resonance frequencies for the current tube and makes the missing even harmonics in a closed-open pipe visible.

Keep the acoustics path going

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Driven responseResonance