An air column in a pipe closed at one end produces:

Musical wind instruments, such as the flute, clarinet, organ pipes and shehnai, produce sound by setting up standing (stationary) waves in a column of air. The type of pipe decides which frequencies (harmonics) can be produced.

In a pipe closed at one end (a closed pipe):

• At the closed end, the air cannot move, so there is always a node (a point of no displacement).
• At the open end, the air can move freely, so there is always an antinode (a point of maximum displacement).
• The simplest (fundamental) mode has a quarter of a wavelength in the pipe: L = λ/4, so the fundamental frequency is f₁ = v/4L, where v is the speed of sound and L is the length of the pipe.

The next possible modes have three-quarters, five-quarters and so on of a wavelength in the pipe. Their frequencies are 3f₁, 5f₁, 7f₁ and so on.

So a closed pipe produces only the odd harmonics (1st, 3rd, 5th, 7th...). The even harmonics (2nd, 4th...) are absent. This gives closed pipes, such as the clarinet (which behaves approximately like a closed pipe), a characteristic "hollow" tone quality (timbre).

In a pipe open at both ends (an open pipe):

• There are antinodes at both ends.
• The fundamental mode has half a wavelength in the pipe: L = λ/2, so f₁ = v/2L.

The harmonics are 2f₁, 3f₁, 4f₁ and so on, so an open pipe produces all harmonics, both odd and even. The flute behaves roughly like an open pipe.

Comparing the two: for the same length, the fundamental frequency of an open pipe is twice that of a closed pipe.

A stretched string fixed at both ends, as in a sitar, guitar or violin, also produces all harmonics, with f₁ = v/2L.

Harmonics give musical instruments their distinctive quality or timbre, which allows us to distinguish a flute from a violin playing the same note. The resonance tube experiment in school laboratories uses a closed air column to find the speed of sound in air.

Why not the other options?

• ✗Only even harmonics are not produced by any simple pipe.
• ✗Both odd and even harmonics are produced by an open pipe.
• ✗No harmonics is incorrect; all musical pipes produce harmonics.