Resonance Tube: Speed of Sound
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flagWhat you'll discover
- arrow_forwardExplain resonance of a closed air column at odd quarter-wavelengths
- arrow_forwardLocate the first and second resonance lengths by loudness
- arrow_forwardCompute v = 2f(l₂ − l₁) and compare with 331.4 + 0.6t m/s
- arrow_forwardExplain why the difference method cancels the end correction
Standing waves in a closed pipe
A tube closed at the bottom by water supports standing waves with a node at the water surface and an antinode just above the open top. That happens when the air column length is an odd number of quarter wavelengths: l = λ/4, 3λ/4, 5λ/4… So as you lower the water with a fork of frequency f singing above the tube, the sound swells dramatically at l₁ ≈ λ/4 and again at l₂ ≈ 3λ/4.
Subtracting, l₂ − l₁ = λ/2 exactly, so v = fλ = 2f(l₂ − l₁). The antinode actually forms slightly ABOVE the tube mouth — the end correction e ≈ 0.3 × diameter — but because it shifts l₁ and l₂ equally, the subtraction wipes it out. That cancellation is the whole genius of the two-resonance method.
Procedure: hunting the loud spots
Strike the fork on a rubber pad (never on the bench — it dents the prongs and changes f) and hold it horizontally just above the tube mouth. Lower the reservoir slowly; the hum swells to a maximum and fades. Bracket the loudest point from both directions and read the water level on the metre scale — that is l₁. Continue down to find l₂.
A fork rings for only a few seconds, so re-strike often. Take each length twice (water falling and rising) and average. With f = 512 Hz at 25 °C expect l₁ ≈ 16 cm and l₂ ≈ 49 cm, giving v ≈ 343 m/s. The accepted value at temperature t °C is v = 331.4 + 0.6t, so always note the room temperature.
Errors and precautions
Judging "loudest" by ear is the dominant random error — repeat and average. Temperature matters: sound travels about 0.6 m/s faster per degree, so a chilly morning lab and a warm afternoon lab disagree by several m/s. Humid air is slightly faster again.
Further precautions for the report: keep the fork’s prongs vibrating in a vertical plane just above the mouth without touching the tube, avoid noisy surroundings, read the scale at eye level, and use l₂ − l₁ rather than l₁ alone so the end correction cancels. Examiners often ask: "Why is the second resonance fainter?" — because the column loses more energy at the larger length.