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JEE Physics · Hard

Waves on String: Dispersion MCQ

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DispersionHardQuestion 31389

Question

For transverse waves on a string, in the long-wavelength limit (kL << 1 for a beaded string), the dispersion relation is:
  1. A
    ω = vk (non-dispersive)
    Correct
  2. B
    ω = Ak² (dispersive)
  3. C
    ω = constant
  4. D
    ω ∝ 1/k

Correct answer

ω = vk (non-dispersive)

Explanation

For a continuous string (or beaded string with λ >> bead spacing), the wave is non-dispersive: ω = vk = k√(T/μ). Dispersion (ω vs k non-linear) appears at short wavelengths comparable to the bead spacing.

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