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Frequency (F): Units: (1/s), hertz (Hz)Fundamental frequency, first harmonic (F)1: The lowest frequency (longest wavelength) allowed for the system.Length of string (L): (or pipe, etc.) Units: meters (m).Wavelength (?): Units: meters (m). |
The first overtone is the first allowed harmonic above the fundamental frequency (F1).
In the case of a system with two different ends (as in the case of a tube open at one end), the closed end is a node and the open end is an antinode. The first resonant frequency has only a quarter of a wave in the tube. This means that the first harmonic is characterized by a wavelength four times the length of the tube.
| F1 = v/4L |
The wavelength of the first harmonic is equal to four times thelength of the string.
| ?1 = 4L |
The "nth" wavelength is equal to the fundamental wavelength divided by n.
| ?n = ?1/n |
Note that "n" must be odd in this case as only odd harmonics will resonate in this situation.
Harmonics for a system with two different ends*
| Harmonic number | Overtone number | F = | ? = | |
| F1 | First harmonic | --- | F1 = v/4L | ?1 = 4L |
| F2 | Third harmonic | First overtone | F2 = 3F1 | ?2 =2?1/3 |
| F3 | Fifth harmonic | Second overtone | F3 = 5F1 | ?3 = 2?1/5 |
| Fn | Nth harmonic? | (Nth - 1)/2 overtone | F(n-1)/2 = nF1 | ?n = 2?1/n |
* such as a pipe with one end open and one end closed?In this case only the odd harmonics resonate, so n is an odd integer.
Vs: velocity of sound
