The fundamental frequency of a vibrating string of length L, tension T…

Question

The fundamental frequency of a vibrating string of length L, tension T, linear density μ is

Accepted Answer

C. {'text': '(1/2L) × √(T/μ)', 'label': 'C'}

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: NCERT Class 11 Physics, Ch 14 "Waves", §14.6_

Answer

{'text': '(2L) × √(T/μ)', 'label': 'A'}

Answer

{'text': '(1/L) × √(T × μ)', 'label': 'B'}

Answer

{'text': '(1/L) × T / μ', 'label': 'D'}