Q.4 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 4 Solution

Topic: Waves · Official NTA Booklet Code G5

Question

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is:

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Verified Against NTA Final Answer Key

Option (3) : 2 : 1

📚 Waves Easy

📋 Given Parameters & Problem Setup

Pipe Length Same length L for both pipes

Acoustic Medium Same sound speed v

⚡

The 30-Second Exam Hall Shortcut: ⚡ Open-to-Closed Acoustic Doubling Law

⏱️ Save ~40 seconds

An open pipe has antinodes at both ends (λ = 2L), while closed has a node at one end (λ = 4L); thus f_open = 2 × f_closed → 2 : 1!

1 Recall that an open organ pipe supports fundamental wavelength λ_open = 2L, so f_open = v / (2L).

2 A closed organ pipe supports fundamental wavelength λ_closed = 4L, so f_closed = v / (4L).

3 Take the ratio: f_open / f_closed = [v / (2L)] / [v / (4L)] = 4 / 2 = 2 : 1.

4 Lock Option (3) instantly in under 10 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Fundamental Wave Mechanics · Standing Acoustic Waves (Boundary conditions: open pipe has λ = 2L; closed pipe has λ = 4L).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Fundamental Mode of Open Organ Pipe

An open pipe of length L has antinodes at both open ends and a displacement node at the center. The pipe length accommodates half a wavelength:

L = \frac{\lambda_{\text{open}}}{2} \implies \lambda_{\text{open}} = 2L \implies f_{\text{open}} = \frac{v}{\lambda_{\text{open}}} = \frac{v}{2L}

Step 2

Fundamental Mode of Closed Organ Pipe

A closed pipe of length L has a displacement node at the closed end and an antinode at the open end. The pipe length accommodates one-quarter of a wavelength:

L = \frac{\lambda_{\text{closed}}}{4} \implies \lambda_{\text{closed}} = 4L \implies f_{\text{closed}} = \frac{v}{\lambda_{\text{closed}}} = \frac{v}{4L}

Step 3

Ratio Evaluation

Divide the two fundamental frequencies for pipes of identical length:

\frac{f_{\text{open}}}{f_{\text{closed}}} = \frac{\frac{v}{2L}}{\frac{v}{4L}} = \frac{4L}{2L} = \frac{2}{1} = 2 : 1

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 (1)

✗ Incorrect

Verdict & Scientific Reason:

Incorrect ratio corresponding to overtone comparison, not fundamental harmonics.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate confused the first overtone of a closed pipe (3f) with the fundamental harmonic.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Inverted ratio (closed pipe to open pipe).

⚠️

Student Fallacy (Why candidates pick this trap): Candidate inverted the order of ratio (calculated closed : open instead of open : closed).

3 (3)

✓ 100% Correct

Verdict & Scientific Reason:

Exact ratio of fundamental frequencies for open to closed organ pipes of equal length.

💡

Why this is airtight: None. Candidate correctly recalled boundary node-antinode patterns.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Inverted third harmonic ratio.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate confused harmonic numbering with fundamental ratio.

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NTA Trap Alert: Order of Ratio Inversion (Open : Closed vs Closed : Open)

The question asks for "open pipe TO closed pipe". Selecting 1 : 2 is the most frequent blunder when students derive f_closed = f_open / 2 and write the ratio backwards.

🛡️ How to avoid the -1 mark: Always write Numerator : Denominator explicitly as "Open / Closed = 2 / 1".

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Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Waves Standard Benchmark

Core Scientific Principle Tested:

"An open pipe of length L produces a fundamental frequency twice that of a closed pipe of the same length."

Syllabus Focus: Standing Waves in Organ Pipes and Harmonics

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 4 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Open-to-Closed Acoustic Doubling Law

Step-by-Step Rigorous Workflow & Mathematical Proof

Fundamental Mode of Open Organ Pipe

Fundamental Mode of Closed Organ Pipe

Ratio Evaluation

360° Option Elimination Engine Key Feature

NTA Trap Alert: Order of Ratio Inversion (Open : Closed vs Closed : Open)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Waves

Harmonic Modes & Node Counts in Open vs Closed Organ Pipes

Fundamental Frequency of Open Pipe Dipped Halfway into Water

Beat Frequency and String Tension: f_beat = |f_A - f_B|

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