Q.A closed pipe and an open pipe have the same length. Show that no mode of the closed pipe has the same wavelength as any mode of the open pipe.

Harmonics are a theoretical list of whole-number multiples of the fundamental; overtones are whichever of those actually occur, renumbered in the order they appear.

(1) Definition basis: A harmonic of order $n$ is, by definition, a tone whose frequency is exactly $n$ times the fundamental frequency $f_0$ (i.e. $f_0, 2f_0, 3f_0,\dots$), regardless of whether that particular multiple is actually produced by the vibrating source. An overtone is a tone of frequency higher than the fundamental that is actually produced by the source; overtones are numbered serially in the order they are physically present — the 1st overtone is the next frequency actually heard after the fundamental, the 2nd overtone the one after that, and so on — not necessarily $2f_0$, $3f_0$, etc.

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Harmonics are integer multiples of the fundamental; overtones are simply the modes above the fundamental, which may or may not coincide with exact harmonics.

When a system (string, air column) vibrates, it can do so in several normal modes. The lowest frequency mode is the fundamental ($f_1$, or first harmonic). Frequencies that are exact integral multiples of the fundamental — $f_1, 2f_1, 3f_1, \dots$ — are called harmonics (first, second, third harmonic, and so on).

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Harmonics = all integer multiples of f₁; overtones = whichever of those are actually excited, renumbered from the first one up.

1. Harmonics are all the frequencies that are integral multiples of the fundamental frequency $f_1$: $f_1, 2f_1, 3f_1, \ldots$ — a mathematically complete set, whether or not each one is actually present in a given vibration. …