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

Answer 1

Answer: (C)

Fundamental frequency $(n)=\frac{v}{2l}$
or $n=\sqrt{\frac{T}{\mu }}\times \frac{1}{2l}$ (i)
Tension becomes $2T\dots$ (ii)
$V=$ Ap per metre
or $v=\pi r^2\rho$
Now, ${\mu }^{\prime }=\pi (2r{)}^2\frac{\rho }{2}$
or ${\mu }^{\prime }=2\pi r^2\rho$
or ${\mu }^{\prime }=2\mu$...(iii)
Putting (ii) and (iii) in equation (i),
$n^{\prime }=n$