Question

If the tension and diameter of a sonometer wire of fundamental frequency $n$ is doubled and density is halved then its fundamental frequency will become

• A. $\frac{n}{4}$
• B. $\sqrt{2}n$
• C. $n$
• D. $\frac{n}{\sqrt{2}}$

Answer 1

Answer: (C)

$ n=\frac{1}{2 l} \sqrt{\frac{T}{\pi r^{2} \rho}}$
$\rho_{1}^{\prime}=\frac{\rho}{2} ; T^{\prime}=2 T$
and $D^{\prime}=2 D$
or $r^{\prime}=2 r$
$n^{\prime}=\frac{1}{2 l} \sqrt{\frac{2 T}{\pi(2 r)^{2} \frac{\rho}{2}}}$
after solving, $n^{\prime}=\frac{1}{2 l} \sqrt{\frac{T}{\pi r^{2} l}}=n$.