Question

Two wires $W_1$ and $W_2$ have the same radius $r$ and respective densities $\rho_1$ and $\rho_2$ such that $\rho_2 =4 \rho_1$. They are joined together at the point $O$, as shown in the figure. The combination is used as a sonometer wire and kept under tension $T$. The point $O$ is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in $W_1$ to $W_2$ is :

• A. 1 : 1
• B. 1 : 2
• C. 1 : 3
• D. 4 : 1

Answer 1

Answer: (B)

$n_{1} = n_{2}$
T $\to$ same
r $\to$ same
l $\to$ same
$n = \frac{p}{2l} \sqrt{\frac{T}{\pi r^{2}d}}$
$n_{1} = n_{2}$
$\frac{p_{1}}{\sqrt{d_{1}}} = \frac{p_{1}}{\sqrt{d_{2}}}$
$\frac{p_{1}}{p_{2}} = \frac{1}{2}$