JEE Main 2017 · 8 Apr · Shift 1 · Physics Q13

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PhysicsSingle correct+4 / -1Question 13 of 90

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 sonometer wire fixed at the left, passing over two bridges and a pulley to a hanging weight; wire W₁ (density ρ₁) and wire W₂ (density ρ₂) meet at O midway between the bridges.

1 : 1

1 : 2

1 : 3

4 : 1

Answer and worked solution

Official answer: B

Both wires have the same tension and length, and $\mu_2=4\mu_1$ , so $v_2=\frac{v_1}2$ . With a node at O each wire vibrates in its own whole number of loops at the same frequency:
$\frac{p_1v_1}{2L}=\frac{p_2v_2}{2L}\implies p_2=2p_1.$
The ratio of antinodes is 1 : 2.

Topics:Standing waves in strings Speed of waves

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JEE Main 2017 · 8 Apr · Shift 1, Physics question 13