Waves on String: Quantum Analogy MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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Quantum AnalogyHardQuestion 31390

Question

Standing waves on a string are analogous to quantum mechanical particle-in-a-box because:

A
Both involve photons
B
Boundary conditions impose quantised energy levels via discrete allowed wavelengths
Correct
C
Both are relativistic
D
String tension equals Planck's constant

Correct answer

Boundary conditions impose quantised energy levels via discrete allowed wavelengths

Explanation

In a quantum particle-in-a-box: ψ = 0 at walls → standing waves with λ_n = 2L/n → quantised k_n → quantised E_n = ℏ²k_n²/(2m). The mathematics is identical to string standing waves.

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