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Exam level5 past questions

Standing Waves and Harmonics

Understand the formation of standing waves, harmonics in strings and organ pipes (open and closed), and the relationship between displacement and pressure in stationary waves.

Why this shows up in the exam

NEET often asks about harmonics, resonance, and standing wave patterns in strings and pipes.

How NEET tests this

Numerical · 2 QsDirect recall · 2 QsStatement analysis

Learn the idea

A standing wave is formed when two identical waves travel in opposite directions and interfere, producing fixed nodes and antinodes; the pattern of nodes dictated by the end conditions decides which harmonics are allowed.

🧠 Memory hook: Open ends ‘shout’ displacement (big swing) but ‘whisper’ pressure (quiet), while a closed end ‘silences’ displacement but ‘booms’ pressure.

Get this one clearly and it pays off every single time it shows up in the paper. 🎯

Formulas & facts to keep ready

  • For a string fixed at both ends, λ_n = 2L/n and f_n = n·v/2L (n = 1,2,3…)
  • For a pipe open at both ends, displacement antinode ↔ pressure node at each end; λ_n = 2L/n and all harmonics appear
  • For a pipe closed at one end, displacement node ↔ pressure antinode at the closed end; only odd n are allowed, λ_n = 4L/(2n‑1)
  • Displacement antinode ⇔ pressure node and vice‑versa
  • Wave speed v = f·λ for any medium
  • Fundamental frequency f₁ = v/2L for strings and open pipes, f₁ = v/4L for a closed pipe

How to approach it

  1. 11. Write down the boundary condition (node or antinode) for displacement at each end of the system.
  2. 22. Translate the condition to the allowed wavelength pattern (λ = 2L/n for both ends free, λ = 4L/(2n‑1) for one end closed).
  3. 33. Use v = f·λ to obtain the frequency formula and identify which harmonics (all n or only odd n) are possible.
  4. 44. Apply the formula to the given numbers (lengths, speed, changes in tension/radius) to get the answer.

Worked example — watch it click

If we study the vibration of a pipe open at both ends, then the following statement is not true:

  • ✅Pressure change will be maximum at both ends.
  • B)Open ends will be antinode.
  • C)Odd harmonics of the fundamental frequency will be generated.
  • D)All harmonics of the fundamental frequency will be generated.

The concept behind this problem

The question asks which statement about an open‑open pipe is NOT true; it tests the student’s grasp of the node‑antinode relationship for pressure versus displacement in standing waves.

Step by step

  1. 1Open pipe at both ends: (a) Pressure change maximum at both ends - TRUE (open ends are pressure nodes, but the statement about maximum change needs context).
  2. 2(b) Open ends are antinodes - TRUE (displacement antinodes).
  3. 3(c) Only odd harmonics - FALSE (all harmonics present).
  4. 4(d) All harmonics generated - TRUE.
  5. 5The false statement is (c).

Watch out

Students often pick the odd‑harmonic option, forgetting that an open‑open pipe supports every harmonic, not just the odd ones.

Common slip-ups that cost marks

  • •Confusing pressure nodes with displacement nodes – they are opposite!
  • •Assuming a closed pipe can produce even harmonics – it cannot.
  • •Ignoring the effect of changing string radius on linear mass density when frequency is asked.

🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.

Practise it

These are real questions from past NEET papers that test this exact idea.

Question 1 of 5NEET 2016

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L m long. The length of the open pipe will be:

Push further

More challenging

3 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.

Question 1 of 3

A piano wire of length 0.5 m and diameter 1 mm is under a tension of 100 N. If the density of the wire material is 8000 kg/m³, what is its fundamental frequency of vibration?

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