Resonance in Air Columns: The Resonance Tube Experiment

The resonance tube experiment is the classic school-lab way to measure the speed of sound in air with nothing fancier than a tuning fork and a tube of water. Hold a vibrating tuning fork over a tall tube, raise or lower the water level, and at certain air-column lengths the sound suddenly booms — the column is resonating, vibrating in sympathy with the fork.

It turns an abstract idea (standing waves in air columns) into a measurement you can do with your own ears, accurate to a few percent. The two-resonance trick cancels the end correction — good experimental design beating fancier equipment.

Key Concepts

• Setup: a tall glass tube partly filled with water (the water surface is the closed end), a tuning fork of known frequency f held horizontally just above the open top.
• First resonance: as the water level falls, the first loud boom occurs when the air column is about λ/4 long (length L_1).
• Second resonance: lowering the water further, a second boom occurs at about 3λ/4 (length L_2).
• End correction e: the antinode sits slightly above the tube's rim, so each measured length is e short of the ideal quarter wavelengths: L_1 + e = λ/4 and L_2 + e = 3λ/4.
• The trick: subtracting eliminates e — λ = 2(L_2 - L_1) — then v = fλ. No ruler-to-the-rim guesswork needed.

Formulas

• λ = 2(L_2 - L_1) (in metres)
• v = fλ (v in m/s, f in Hz)
• End correction: e = (L_2 - 3L_1)/2 (≈ 0.6 x tube radius, a check on your technique)
• Assumptions and limits: uniform cylindrical tube, fork frequency exact, water surface flat and still, room temperature steady (v changes ~0.6 m/s per °C — note the thermometer!). Works best with forks of 256–1024 Hz.

Worked Example

A 512 Hz tuning fork is used; room temperature 25°C.

1. First resonance found at water level giving air column L_1 = 16.2 cm; second resonance at L_2 = 48.9 cm.
2. Wavelength: λ = 2(L_2 - L_1) = 2(48.9 - 16.2) = 2 x 32.7 = 65.4 cm = 0.654 m.
3. Speed of sound: v = fλ = 512 x 0.654 = 334.8 m/s ≈ 335 m/s.
4. Reality check: the accepted value at 25°C is about 346 m/s — within ~3%, excellent for a school lab (small errors come from temperature gradients and fork handling).
5. End correction: e = (L_2 - 3L_1)/2 = (48.9 - 48.6)/2 = 0.15 cm — tiny and positive, as theory expects (≈ 0.6r for a narrow tube).

Common Misconceptions

• "The first resonance is at exactly λ/4." Almost — the end correction shifts it slightly, which is exactly why the experiment uses two resonances: λ = 2(L_2 - L_1) cancels e automatically.
• "Any loud point is a resonance." True resonance is the sharp maximum — move water slowly and listen for the distinct boom.
• "The water changes the sound's pitch." No — the water merely sets the boundary (closed end). The pitch is fixed by the fork; the water level only decides which air-column length can resonate with it.

Real-World Applications

• School and college labs worldwide still use this to measure v and verify closed-pipe theory hands-on.
• Wind-instrument making: the same resonance principle sizes organ pipes and woodwind bores.
• Muffler and silencer design tunes cavity lengths to resonate at (and cancel) engine frequencies.

In short: find the booms at L_1 (≈ λ/4) and L_2 (≈ 3λ/4), then λ = 2(L_2 - L_1) and v = fλ — the end correction cancels out. Our 512 Hz example gave 335 m/s from a tube, water, and careful listening.