Stationary Waves & Vibrating Strings question from MHT CET 2026 (15 May, Shift 1)

Answer: (a)

1. $f = \dfrac{1}{2L}\sqrt{\dfrac{T}{\mu}}$ with $\mu = \rho \cdot \dfrac{\pi D^2}{4}$.
2. $f = \dfrac{1}{2L}\sqrt{\dfrac{4T}{\pi \rho D^2}} = \dfrac{1}{LD}\sqrt{\dfrac{T}{\pi\rho}}$.
3. For fixed $T$ and $\rho$: $f \propto \dfrac{1}{LD}$.
4. So the answer is (a) $f \propto \frac{1}{LD}$.