Harmonics vs Overtones: The Difference Students Get Wrong
Physics · Waves · NEET
A harmonic is any whole-number multiple of the fundamental frequency (1f, 2f, 3f...), counted including the fundamental. An overtone is any allowed frequency ABOVE the fundamental, counted after skipping it. So the 1st overtone is the 2nd allowed frequency of the system. Memory hook: "Overtone starts ONE step later" - the 1st overtone is the 2nd allowed mode.
For a string or open pipe every harmonic exists, so the nth overtone is the (n+1)th harmonic. A closed pipe skips even harmonics, so its pth overtone is the (2p+1)th harmonic - always convert the overtone to a harmonic number before using any frequency formula.
Your doubts, answered
Is the 1st overtone always the 2nd harmonic?
Only for a system that allows ALL harmonics, like a string fixed at both ends or an open pipe. There the allowed modes are 1f, 2f, 3f, 4f... so the 1st overtone (2nd allowed mode) is the 2nd harmonic. But in a closed pipe only ODD harmonics exist (1f, 3f, 5f...), so the 1st overtone is the 3rd harmonic, NOT the 2nd. Never assume 1st overtone = 2nd harmonic without checking the system.
Why does a closed organ pipe have only odd harmonics?
A pipe closed at one end must have a node (no motion) at the closed end and an antinode at the open end. Only wavelengths that fit a node-to-antinode pattern survive, which happens at odd multiples of v/4L. So allowed frequencies are f, 3f, 5f, 7f... The even harmonics (2f, 4f) would need an antinode at the closed end, which is not allowed. This is why closed-pipe overtones jump by 2 harmonic numbers each time.
How do I convert an overtone number to a harmonic number in NEET problems?
For an all-harmonics system (string, open pipe): harmonic number = overtone number + 1. So 3rd overtone = 4th harmonic. For a closed pipe (odd harmonics only): harmonic number = 2 x (overtone number) + 1. So 4th overtone = 2(4)+1 = 9th harmonic. Writing this conversion first is the single most reliable way to avoid mistakes in organ-pipe PYQs.
Do overtones include the fundamental frequency?
No. The fundamental (lowest frequency, first harmonic) is NOT an overtone. Overtones are only the frequencies above the fundamental. That is why counting is off by one: the fundamental is the 1st harmonic but has no overtone number. The first frequency above it is the 1st overtone.
For a string fixed at both ends, which overtone is the 3rd harmonic?
A string fixed at both ends allows all harmonics: f, 2f, 3f... The 3rd harmonic (3f) is the 2nd overtone, because you skip the fundamental when counting overtones. In general for a string: nth harmonic = (n-1)th overtone.
⚠️ The NEET trap ✗ Treating '2nd overtone' as '2nd harmonic', or applying harmonic = overtone + 1 to a closed pipe. ✓ For all-harmonic systems (string, open pipe): nth harmonic = (n-1)th overtone. For a closed pipe (odd only): pth overtone = (2p+1)th harmonic. 🧠 When NEET says 'overtone', immediately convert it to a harmonic number BEFORE using any frequency formula - and check whether the system is closed (odd only).
Real NEET questions
2016
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:
A · L
B · 2L ✓
C · L/2
D · 4L
Solution: Step 1 - Convert overtones to harmonics. Open pipe allows all harmonics, so 2nd overtone = 3rd harmonic, frequency = 3v/(2 L_open). Closed pipe allows only odd harmonics, so 1st overtone = 3rd harmonic, frequency = 3v/(4L). Step 2 - Equate: 3v/(2 L_open) = 3v/(4L). Step 3 - Cancel 3v: 1/(2 L_open) = 1/(4L), so 2 L_open = 4L, giving L_open = 2L. Answer: B.
2023
The 4th overtone of a closed organ pipe has the same frequency as the 3rd overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:
A · 9 : 8 ✓
B · 7 : 9
C · 8 : 9
D · 9 : 7
Solution: Step 1 - Convert overtones. Closed pipe (odd harmonics): 4th overtone = 2(4)+1 = 9th harmonic, f_c = 9v/(4 L_c). Open pipe (all harmonics): 3rd overtone = 4th harmonic, f_o = 4v/(2 L_o) = 2v/L_o. Step 2 - Set f_c = f_o: 9v/(4 L_c) = 2v/L_o. Step 3 - Cancel v and rearrange: 9 L_o = 8 L_c, so L_c/L_o = 9/8, i.e. 9 : 8. Answer: A.
2018
The fundamental frequency of an open organ pipe equals the third harmonic of a closed organ pipe. If the length of the closed pipe is 20 cm, the length of the open pipe is:
A · 12.5 cm
B · 8 cm
C · 13.2 cm ✓
D · 16 cm
Solution: Step 1 - Write frequencies. Open pipe fundamental (1st harmonic) = v/(2 L_o). Closed pipe 3rd harmonic = 3v/(4 L_c). Step 2 - Equate: v/(2 L_o) = 3v/(4 x 20). Step 3 - Solve for L_o: L_o = (4 x 20)/(2 x 3) = 80/6 = 13.33 cm, which rounds to about 13.2 cm. Answer: C. Note the 3rd harmonic of a closed pipe is its 1st overtone - the wording tests whether you can move between the two labels.
Solved Waves NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What is the simplest difference between a harmonic and an overtone?
A harmonic counts every allowed frequency starting from the fundamental (1st harmonic = fundamental). An overtone counts only the frequencies above the fundamental (1st overtone = first frequency after the fundamental). So overtones start one step later.
Are all harmonics also overtones?
No. The fundamental is a harmonic (the 1st harmonic) but it is not an overtone. Every overtone is a harmonic, but the fundamental harmonic is not an overtone.
Why is this a common NEET trap?
Because the safe rule 'harmonic = overtone + 1' works only for strings and open pipes. Closed pipes skip even harmonics, so the correct rule is 'pth overtone = (2p+1)th harmonic'. Students who apply the string rule to a closed pipe get the wrong answer.
How do harmonics relate to normal modes?
The normal modes of a vibrating string or air column are exactly its allowed standing-wave frequencies. NCERT calls the lowest normal mode the fundamental or first harmonic. The higher normal modes are the higher harmonics (and, above the fundamental, the overtones).
Does an open pipe have the same overtones as a closed pipe?
No. An open pipe (open at both ends) has all harmonics f, 2f, 3f... An identical-length closed pipe has only odd harmonics f, 3f, 5f... and its fundamental is half that of the open pipe, so their overtone patterns are completely different.
