Physics · Class 11

Compare open and closed air columns

An open end allows air displacement while a closed end constrains it. Two open ends support every integer harmonic; one closed end supports only odd harmonics. The mode index counts allowed modes, not necessarily harmonic number.

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Compare open and closed air columns

திறந்த முனையில் இடப்பெயர்ச்சி எதிர்கணு; மூடிய முனையில் கணு. ஒரு முனை மூடிய குழாயில் ஒற்றைப் படை இசைசுரங்கள் மட்டும் வரும்.

Key notes, relationships and model limits

Key relationship

Open-open: fn=nv/(2L). Closed-open: fn=(2n−1)v/(4L).

Remember

Common trap

Pressure nodes and displacement nodes are at opposite positions in an air column.

Model limits

Ideal narrow pipe without end corrections. Graph shows longitudinal displacement amplitude against axial position: closed end is a displacement node, open end an antinode. Animation can alias at acoustic frequencies.

What you will learn

Use air-displacement boundary conditions to distinguish pipe spectra.

Try the experiment

Try both scenarios, change one control, and predict the result before checking the graph and readouts.

Think of it this way

Change one input while keeping the others fixed, as you would in a controlled experiment.

Worked example

At L=1 m and v=340 m/s, the closed-open fundamental is 85 Hz. The open-open fundamental is 170 Hz; the next closed-open mode is 255 Hz.

Why this matters

The model connects compare open and closed air columns with an observable reading. Check the equation and assumptions before applying it.

Before you start

SI units · algebra · graph reading

Check your understanding

What is the second allowed mode of a closed-open pipe?

The second harmonic
The third harmonic
The fourth harmonic

Read the explanation

Allowed harmonic numbers are 1,3,5,… so the second mode is harmonic 3.

Course connection: Class XI Chapter 14. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.