Pipo

Meet Pipo, a pipe closed at one end who sings a note set by her length.

Sound reflects back and forth inside a pipe, and only certain wavelengths fit. At a closed end, the air cannot move, and at an open end it moves the most. The longest wave that fits has a quarter of its wavelength along the pipe, so λ = 4L.

The fundamental frequency is then f₁ = v / (4L). In air at 20 °C, sound travels at about 343 m/s, so a pipe 0.25 m long has f₁ = 343 / (4 × 0.25) = 343 Hz.

A closed pipe only produces odd harmonics: 3, 5, 7 times the fundamental, and so on. A pipe open at both ends of the same length has a fundamental twice as high and all harmonics. The air just past an open end also vibrates, so a pipe behaves as if it were slightly longer.

Blowing across the top of a bottle makes a closed-pipe note, and adding water shortens the air column, raising the pitch. The clarinet behaves roughly like a pipe closed at one end, which gives it its distinctive sound.