Physics · Waves · NEET
No. The 1st harmonic is always the fundamental (lowest frequency). The 1st overtone is the FIRST mode above the fundamental. For a string or open pipe, the 1st overtone equals the 2nd harmonic (2f). So overtone counting always starts one step above the fundamental, while harmonic counting starts AT the fundamental. This mismatch is the single most common trap in NEET wave questions.
A pipe closed at one end must have a node at the closed end and an antinode at the open end. The shortest fit is L = lambda/4, giving f1 = v/4L. The next allowed pattern that keeps node-at-closed and antinode-at-open is L = 3 lambda/4, giving 3f1, then 5f1, and so on. Even multiples would need an antinode at the closed end, which is not allowed. So only odd harmonics (1, 3, 5...) exist. Its 1st overtone is therefore the 3rd harmonic, not the 2nd.
For a string or open pipe (all harmonics): harmonic number = overtone number + 1. So 2nd overtone = 3rd harmonic. For a closed pipe (odd only): harmonic number = 2 x (overtone number) + 1. So 2nd overtone = 5th harmonic, and 4th overtone = 9th harmonic. Write this conversion FIRST before touching frequency formulas.
A normal mode is one specific standing-wave pattern in which every particle of the system oscillates with the SAME frequency. A bounded system (a fixed string, an air column) can only vibrate in certain discrete patterns that fit the boundary conditions. Each such allowed pattern is a normal mode, and its frequency is a natural (resonant) frequency of the system.
The fundamental is the 1st harmonic (n = 1) but it is NOT any overtone. Overtones only count modes ABOVE the fundamental. So the fundamental has no overtone label, the next mode is the 1st overtone, and so on. Remember: every overtone is a harmonic, but the fundamental harmonic is never called an overtone.
Two nearest (successive) harmonics of a tube closed at one end and open at the other are 220 Hz and 260 Hz. The fundamental frequency of the system is:
The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe of length L. The length of the open pipe is:
For sound waves, if the number of nodes for the 5th harmonic of an open-ended pipe is n and that for the 9th harmonic of the same pipe with one end closed is m, the ratio n/m is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Harmonics number all natural frequencies starting from the fundamental (1st harmonic = f); overtones number only the frequencies above the fundamental (1st overtone = first mode after f).
No. A string fixed at both ends and an open pipe have ALL harmonics (1, 2, 3...). A pipe closed at one end has only ODD harmonics (1, 3, 5...). This is decided purely by the boundary conditions.
In principle infinitely many, each a whole-number related standing-wave pattern. In practice the lower modes (fundamental and first few overtones) dominate because they carry most of the energy and are what NEET problems ask about.
It is the lowest natural frequency and usually the loudest. Every other harmonic is a whole-number multiple of it (nf for strings/open pipes; odd multiples for closed pipes), so once you know the fundamental you know the whole spectrum.
f_n = n v / (2L) with n = 1, 2, 3..., where v = sqrt(T/mu). n = 1 is the fundamental (1st harmonic), n = 2 the 2nd harmonic (also 1st overtone), and so on.
