Speed of Sound — Theoretical Results

Closed-End Air Column Resonance

The first-harmonic condition L = λ/4 combined with v = fλ predicts L = (v/4)(1/f) − 0.4d. The tubes below show the standing-wave pattern for each of the seven tuning forks used in this lab; the graph plots their resonant lengths against 1/f. Adjust temperature and tube diameter to see how the theoretical predictions shift.

Air Temperature
20 °C
Speed of Sound
343.0 m/s
Slope (v / 4)
85.8 m/s
y-intercept (−0.4 d)
−0.010 m
Standing waves inside each resonance tube
Resonant length vs. 1 / frequency
Air temperature, T 20 °C
Tube inside diameter, d 2.5 cm
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What the visualizations show

Seven tuning-fork frequencies (288, 320, 341.3, 384, 426.7, 480, and 512 Hz — a C-major scale at scientific pitch) are used. For each fork, the air column resonates at the first harmonic when its length is L = v/(4f) − 0.4d.

  • In the tubes panel: the wave has a displacement node at the water surface and an antinode at the open end. Lower frequencies need longer air columns — a direct visual of λ = v/f.
  • In the graph: every theoretical point sits exactly on the line. Slope = v / 4, so v = 4 × slope. The y-intercept = −0.4 d shows the open-end correction.
  • Warming the air increases v, which steepens the slope and lengthens every air column.
  • Widening the tube lowers the intercept (more negative) but leaves the slope alone.