Question

A Sonometer wire resonates with a given tuning fork forming standing waves with five anti-nodes between two bridges when a mass of $9kg$ is suspended from the wire. When this mass is replaced by mass $M$, the wire resonates with the same tuning fork forming three anti-nodes for the same positions of the bridges. The value of $M$ is

• A. $25kg$
• B. $5kg$
• C. $12.5kg$
• D. $\frac{1}{25}kg$

Answer 1

Answer: (A)

$25kg$

frequency $\propto \frac{1}{noofloops}$
$\frac{f_1}{f_2}=\frac{3}{5}$
but $f\propto \sqrt{T}\propto \sqrt{mg}$
$\therefore \frac{3}{5}=\sqrt{\frac{9}{M}}$
$\Rightarrow M=25kg$