Question

Fundamental frequency of a sonometer wire is n. If its length, diameter and tension all are doubled, the new fundamental frequency will be-

• A. n
• B. $\sqrt{2}$n
• C. n/$\sqrt{2}$
• D. $\frac{n}{2\sqrt{2}}$

Answer 1

Answer: (A)

n

Answer 2

n = $\frac{1}{2\mathcal{l}}\sqrt{\frac{T}{\pi r^{2}\rho}}$= 450

n' = $\frac{1}{2\left( \frac{\mathcal{l}}{2} \right)}\sqrt{\frac{T/4}{\pi 4r^{2}\rho}}$ = $\frac{n}{2}$ = $\frac{450}{2}$ = 225 Hz