alleryThe fundamental frequency of a vibrating string of length L, tension T, linear density μ is
A(2L) × √(T/μ)
B(1/L) × √(T × μ)
C(1/2L) × √(T/μ)
D(1/L) × T / μ
Answer & Solution
Correct answer: C. (1/2L) × √(T/μ)
1. Wavelength of fundamental on both-ends-fixed string is 2L (single antinode).
2. Wave speed v = √(T / μ).
3. Frequency f = v / λ = (1 / 2L) × √(T / μ).
4. Higher harmonics are integer multiples: f_n = n × f₁.
_Source: syllabus Physics, Ch 14 "Waves", §14.6_
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