Q.An air column is of length 17 cm long. Calculate the frequency of the 5th overtone if the air column is

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.

(2) Correspondence need not be 1-to-1: In systems like an open organ pipe or a stretched string, all harmonics ($f_0, 2f_0, 3f_0,\dots$) are present, so the $n$th overtone coincides with the $(n{+}1)$th harmonic. But in a pipe closed at one end, only the odd harmonics ($f_0, 3f_0, 5f_0,\dots$) are physically present — so the 1st overtone there is the 3rd harmonic, the 2nd overtone is the 5th harmonic, and so on; the even harmonics simply do not occur as overtones in that case.

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).

Overtones are the modes of vibration with frequency higher than the fundamental that a system actually produces, listed in the order they occur — the first overtone is the second-lowest frequency actually present, the second overtone the third-lowest, and so on — regardless of whether that frequency is an exact integral multiple of $f_1$. For a stretched string and an open pipe, all overtones coincide with integral harmonics ($2f_1, 3f_1,\dots$), but for a pipe closed at one end, only the odd harmonics ($3f_1, 5f_1,\dots$) are present, so the first overtone there is the third harmonic, not the second.

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.

2. Overtones are the frequencies higher than the fundamental that are actually produced by a specific vibrating system (e.g. a string vibrates in all harmonics, so its overtones coincide with the 2nd, 3rd, ... harmonics; a pipe closed at one end vibrates only in odd harmonics, so its 1st overtone is the 3rd harmonic, and so on).