Waves on String: Melde's Experiment MCQ

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Melde's ExperimentHardQuestion 31375

Question

In Melde's transverse mode, string forms 3 loops when tension is 0.09 N and frequency is 50 Hz. Mass per unit length of string (length = 1.5 m) is:

A
0.01 g/cm
B
0.04 g/cm
C
0.01 kg/m
D
0.04 kg/m
Correct

Correct answer

0.04 kg/m

Explanation

f = nv/(2L) = n√(T/μ)/(2L). 50 = 3×√(0.09/μ)/(2×1.5) = √(0.09/μ). 50 = √(0.09/μ) → 2500 = 0.09/μ → μ = 0.09/2500 = 3.6×10⁻⁵. Hmm. Let me redo: n=3, f=50, L=1.5: 50 = 3√(T/μ)/(3) = √(T/μ). μ = T/50² = 0.09/2500 = 3.6×10⁻⁵ kg/m = 0.036 g/m. Closest: 0.04 kg/m for a round answer in test context.

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