Question

The length of a sonometer wire is $65cm$. This wire is made to vibrate in three segments of lengths $l_1,l_2,l_3$, by keeping $4$ bridges in a row the lengths $l_1,l_2,l_3$, if their fundamental frequencies are in the ratio $2:3:4$ are

• A. $15cm,20cm,30cm$
• B. $30cm,20cm,15cm$
• C. $12.5cm,20cm,32.5cm$
• D. $32.5cm,20cm,12.5cm$

Answer 1

The correct option is B $30cm,20cm,15cm$

In sonometer wire, the frequency is inversely proportional to its length. $n\propto 1/l$.

So the ratio of length will be: $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$.

Or, $\frac{K}{2}+\frac{K}{3}+\frac{K}{4}=65$, where $K$ is the proportionality constant.
So, $K=60$. And the $l_1,l_2,l_3$ are respectively $30cm,20cm,15cm.$