Vibrations of Air Columns — MH-CET Physics MCQs with Solutions
Free MH-CET Physics Vibrations of Air Columns MCQs with step-by-step solutions (21 questions). Part of Superposition of Waves. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Vibrations of Air Columns · easy · theory
In an organ pipe open at both ends, the ends are:
A. Points of zero displacement
B. Nodes
C. Antinodes ✓ Correct
D. One node and one antinode
Solution: Air at an open end is free to move, so a displacement antinode forms there.
Q2 — Vibrations of Air Columns · medium · theory
A pipe closed at one end can produce:
A. Only odd harmonics ✓ Correct
B. Only even harmonics
C. All integral harmonics
D. Only the fundamental
Solution: The closed end must be a node and the open end an antinode, which permits only $\lambda = \dfrac{4L}{2p-1}$, giving frequencies $n, 3n, 5n, \ldots$
Q3 — Vibrations of Air Columns · easy · theory
The fundamental frequency of an open organ pipe of length $L$ is:
A. $\dfrac{v}{L}$
B. $\dfrac{v}{2L}$ ✓ Correct
C. $\dfrac{v}{4L}$
D. $\dfrac{2v}{L}$
Solution: The fundamental has an antinode at each end and a node in the middle, so $\lambda = 2L$ and $n = \dfrac{v}{2L}$.
Q4 — Vibrations of Air Columns · easy · theory
The fundamental frequency of a closed organ pipe of length $L$ is:
A. $\dfrac{v}{L}$
B. $\dfrac{v}{4L}$ ✓ Correct
C. $\dfrac{v}{2L}$
D. $\dfrac{3v}{4L}$
Solution: A node at the closed end and an antinode at the open end make the pipe a quarter of a wavelength long, so $\lambda = 4L$.
Q5 — Vibrations of Air Columns · medium · theory
The first overtone of a closed organ pipe is its:
A. Second harmonic
B. Third harmonic ✓ Correct
C. Fifth harmonic
D. Fourth harmonic
Solution: Only odd harmonics exist in a closed pipe, so the first tone above the fundamental is $3n$.
Q6 — Vibrations of Air Columns · medium · theory
In the fundamental mode of an open organ pipe, the stationary wave contains:
A. Two antinodes and one node ✓ Correct
B. Two nodes and two antinodes
C. One node and one antinode
D. Two nodes and one antinode
Solution: Both open ends are antinodes, with a single node at the centre of the pipe.
Q7 — Vibrations of Air Columns · hard · theory
The end correction for an organ pipe of internal diameter $d$ is approximately:
A. $0.3d$ ✓ Correct
B. $3d$
C. $d$
D. $0.3L$
Solution: The antinode forms slightly beyond the physical opening; the correction is about $0.3$ times the diameter at each open end.
Q8 — Vibrations of Air Columns · medium · theory
A closed organ pipe and an open organ pipe of the same length are sounded. The closed pipe gives a fundamental frequency that is:
A. Three times that of the open pipe
B. Half that of the open pipe ✓ Correct
C. Twice that of the open pipe
D. Equal to that of the open pipe
Solution: Comparing $\dfrac{v}{4L}$ with $\dfrac{v}{2L}$ shows the closed pipe sounds an octave lower.
Q9 — Vibrations of Air Columns · easy · theory
The resonance tube experiment is used primarily to determine:
A. The speed of sound in air ✓ Correct
B. The surface tension of water
C. The viscosity of air
D. The frequency of a sonometer wire
Solution: Measuring two successive resonance lengths gives $v = 2n(l_2 - l_1)$, which eliminates the end correction.
Q10 — Vibrations of Air Columns · hard · numerical
An open pipe of length $L_1$ and a closed pipe of length $L_2$ have the same fundamental frequency. The ratio $L_1 : L_2$ is:
A. $4 : 1$
B. $2 : 1$ ✓ Correct
C. $1 : 2$
D. $1 : 4$
Solution: Equating $\dfrac{v}{2L_1} = \dfrac{v}{4L_2}$ gives $2L_1 = 4L_2$, so $\dfrac{L_1}{L_2} = 2$.
Q11 — Vibrations of Air Columns · medium · numerical
A closed organ pipe has a fundamental frequency of $300\text{ Hz}$. Its first overtone is:
A. $900\text{ Hz}$ ✓ Correct
B. $1500\text{ Hz}$
C. $1200\text{ Hz}$
D. $600\text{ Hz}$
Solution: A closed pipe sounds only odd harmonics, so the first overtone is $3 \times 300 = 900\text{ Hz}$.
Q12 — Vibrations of Air Columns · medium · numerical
The third harmonic of an open organ pipe is $900\text{ Hz}$. Its fundamental frequency is:
A. $450\text{ Hz}$
B. $150\text{ Hz}$
C. $300\text{ Hz}$ ✓ Correct
D. $225\text{ Hz}$
Solution: An open pipe supports all harmonics, so $900 = 3n$ and $n = 300\text{ Hz}$.
Q13 — Vibrations of Air Columns · medium · numerical
An open organ pipe of length $0.5\text{ m}$ is sounded where the speed of sound is $340\text{ m/s}$. Its fundamental frequency is:
A. $680\text{ Hz}$
B. $85\text{ Hz}$
C. $170\text{ Hz}$
D. $340\text{ Hz}$ ✓ Correct
Solution: $n = \dfrac{v}{2L} = \dfrac{340}{1} = 340\text{ Hz}$.
Q14 — Vibrations of Air Columns · medium · numerical
A closed organ pipe of length $0.25\text{ m}$ is sounded where the speed of sound is $340\text{ m/s}$. Its fundamental frequency is:
A. $1360\text{ Hz}$
B. $170\text{ Hz}$
C. $680\text{ Hz}$
D. $340\text{ Hz}$ ✓ Correct
Solution: $n = \dfrac{v}{4L} = \dfrac{340}{1} = 340\text{ Hz}$.
Q15 — Vibrations of Air Columns · hard · numerical
In a resonance tube experiment the first two resonance lengths are $16\text{ cm}$ and $50\text{ cm}$. The end correction is:
A. $1.5\text{ cm}$
B. $2.0\text{ cm}$
C. $0.5\text{ cm}$
D. $1.0\text{ cm}$ ✓ Correct
Solution: $e = \dfrac{l_2 - 3l_1}{2} = \dfrac{50 - 48}{2} = 1.0\text{ cm}$.
Q16 — Vibrations of Air Columns · hard · numerical
In a resonance tube sounded by a $512\text{ Hz}$ fork, the first two resonance lengths are $16\text{ cm}$ and $50\text{ cm}$. The speed of sound is approximately:
A. $348\text{ m/s}$ ✓ Correct
B. $164\text{ m/s}$
C. $512\text{ m/s}$
D. $328\text{ m/s}$
Solution: Using $v = 2n(l_2 - l_1) = 2 \times 512 \times 0.34 \approx 348\text{ m/s}$, which needs no end correction.
Q17 — Vibrations of Air Columns · medium · numerical
A closed organ pipe of length $0.85\text{ m}$ is sounded where the speed of sound is $340\text{ m/s}$. Its fundamental frequency is:
A. $400\text{ Hz}$
B. $50\text{ Hz}$
C. $100\text{ Hz}$ ✓ Correct
D. $200\text{ Hz}$
Solution: $n = \dfrac{v}{4L} = \dfrac{340}{3.4} = 100\text{ Hz}$.
Q18 — Vibrations of Air Columns · medium · numerical
An open organ pipe has a fundamental frequency of $200\text{ Hz}$. Its second overtone is:
A. $400\text{ Hz}$
B. $600\text{ Hz}$ ✓ Correct
C. $1000\text{ Hz}$
D. $800\text{ Hz}$
Solution: For an open pipe the second overtone is the third harmonic: $3 \times 200 = 600\text{ Hz}$.
Q19 — Vibrations of Air Columns · hard · numerical
A closed organ pipe has a fundamental frequency of $150\text{ Hz}$. Its second overtone is:
A. $450\text{ Hz}$
B. $600\text{ Hz}$
C. $300\text{ Hz}$
D. $750\text{ Hz}$ ✓ Correct
Solution: A closed pipe sounds $n, 3n, 5n, \ldots$, so the second overtone is the fifth harmonic: $5 \times 150 = 750\text{ Hz}$.
Q20 — Vibrations of Air Columns · easy · numerical
An open organ pipe of length $1\text{ m}$ is sounded where the speed of sound is $330\text{ m/s}$. Its fundamental frequency is:
A. $165\text{ Hz}$ ✓ Correct
B. $330\text{ Hz}$
C. $660\text{ Hz}$
D. $82.5\text{ Hz}$
Solution: $n = \dfrac{v}{2L} = \dfrac{330}{2} = 165\text{ Hz}$.
Q21 — Vibrations of Air Columns · medium · numerical
An open pipe of length $L$ has fundamental frequency $n$. If one end is closed, the new fundamental frequency is:
A. $2n$
B. $\dfrac{n}{4}$
C. $\dfrac{n}{2}$ ✓ Correct
D. $n$
Solution: Closing one end changes $\dfrac{v}{2L}$ to $\dfrac{v}{4L}$, halving the fundamental frequency.