Resonance in Organ Pipes — Open, closed pipes
Waves & Sound
7
JEE Qs
8%
Hard
75
min
Master the boundary conditions for displacement and pressure waves in both open and closed pipes, and diligently apply end correction to effective lengths.
🧮 Key Formulas
✅ Key Points for JEE
- 1Open organ pipes have displacement antinodes at both ends and resonate at all integer harmonics (f, 2f, 3f,...).
- 2Closed organ pipes have a displacement node at the closed end and an antinode at the open end, resonating only at odd integer harmonics (f, 3f, 5f,...).
- 3End correction (e ≈ 0.6r) must be added to the physical length (L) of the pipe to get the effective length (L_eff) for accurate frequency calculations; 2e for open pipes, e for closed pipes.
- 4The speed of sound (v) in air is temperature-dependent and is crucial for calculating resonance frequencies; typically given or calculated using v = sqrt(γRT/M).
- 5Harmonics are integer multiples of the fundamental frequency (f_1); overtones are frequencies higher than the fundamental (1st overtone = 2f, 2nd overtone = 3f for open pipes; 1st overtone = 3f, 2nd overtone = 5f for closed pipes).
⚠️ Common Mistakes
- ✕Confusing the formulas for open and closed pipes, especially regarding which harmonics are present.
- ✕Incorrectly applying end correction: forgetting to add it, using L+e for an open pipe, or L+2e for a closed pipe.
- ✕Misidentifying harmonics and overtones, leading to errors when calculating higher resonant frequencies.
- ✕Not understanding the boundary conditions (displacement node/antinode, pressure node/antinode) at the open and closed ends of the pipe.
📝 Practice Questions
See allQ27.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: A sound wave has higher speed in solids than gases. Reason R: Gases have higher value of Bulk modulus than solids. In the light of the above statements, choose the correct answer from the options given below ⎪ ⎪ 2025 (28 Jan Shift 1) JEE Main Previous Year Paper (1) Both A and R are true but R is NOT the correct (2) A is true but R is false explanation of A (3) A is false but R is true (4) Both A and R are true and R is the correct explanation of A
Q40.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number A, for nuclei with mass numbers between 30 and 170. Reason (R): Nuclear force is long range. In the light of the above statements, choose the correct answer from the options given below : (1) (A) is true but (R) is false (2) (A) is false but (R) is true (3) Both (A) and (R) are true and (R) is the correct (4) Both (A) and (R) are true but (R) is NOT the explanation of (A) correct explanation of (A)
Q36.A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities ρ1 and ρ2′ , respectively. The frequency of 9th harmonic of closed tube is identical with 4th harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is ρ1 : ρ2 = 1 : 16, then the length of the open tube is : (1) 15 7 cm (2) 207 cm (3) 15 9 cm (4) 209 cm
Q24.A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is ( a−1a ) then the value of a is ________ → 2^i+6^j+8^k 2^i+^j+^k . The
Q24.Two open organ pipes of lengths 60 cm and 90 cm resonate at 6th and 5th harmonics respectively. The difference of frequencies for the given modes is _______ Hz . (Velocity of sound in air = 333 m/s )
Q2. The equation of stationary wave is : y = 2a sin ( 2πntλ ) cos ( 2πxλ ). Which of the following is NOT correct : (1) The dimensions of n/λ is [T] (2) The dimensions of n is [LT−1] (3) The dimensions of x is [L] (4) The dimensions of nt is [L]
NCERT Chapters
- Class 11 Physics Ch 15: Waves