Question

Two wires $W_1$ and $W_2$ have the same radius r and respective densities ${\rho }_2=4{\rho }_1$ . They are joined together at the point O, 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 anti nodes formed in $W_1$ to $W_2$ is :

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

Answer 1

The correct option is D 1 : 2

$n_1=n_2$

$T\to$ same

$r\to$ same

$i\to$ same

$n=\frac{p}{2i}\sqrt{\frac{T}{\pi r^{2}d}}$

$n_1=n_2$

$\frac{p_1}{\sqrt{d_1}}=\frac{p_2}{\sqrt{d_2}}$

$\frac{p_1}{p_2}=\frac{1}{2}$