Closed Pipes: Measuring the Speed of Sound

Strike a tuning fork over a pipe in water. Slide the pipe up and down to find the lengths where the sound is loudest, then use them to measure the speed of sound.

Tuning fork frequency (f)512 Hz

LoudnessSilent

Wavelength from your readings—

Speed of sound from your readings—

Drag the pipe or the ruler, or use the sliders. Read the length of the pipe from the ruler, with its zero at the water surface.

The tuning fork

Play the sound Frequency (f) 512 Hz Air temperature 20 °C

Height of the pipe move it and listen

Realistic pipe (with an end correction) Ruler: left and right Ruler: up and down

Your results

1st length L₁ (cm)2nd length L₂ (cm)

Show the answers and the working

Why these lengths? The air in a closed pipe has a displacement node at the closed end (the water) and an antinode near the open end. The air column resonates when its length plus the end correction is an odd number of quarter wavelengths:

L₁ + e = λ/4, L₂ + e = 3λ/4, L₃ + e = 5λ/4

The end correction e is there because the antinode sits just outside the open end. For a pipe of radius r, e ≈ 0.6r. Here r = 1.5 cm, so e = 0.9 cm.

The speed of sound. Subtract the first two equations: L₂ − L₁ = λ/2. The end correction cancels, so:

λ = 2(L₂ − L₁) and v = fλ = 2f(L₂ − L₁)

If you used only L₁ and forgot the end correction, v = 4fL₁ would come out too low. The speed of sound in air depends on the temperature: v ≈ 331.3 + 0.606T m/s, with T in °C.

The motion of the air in the picture is slowed down enormously, so that you can see it.

Learn more in the Resonance lesson and the Standing waves lesson.