### JEE Main On 8 April 2017 Question 26

##### 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 waves 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 - [JEE Online 08-04-2017]

#### Options:

A) 4 : 1

B) 1 : 2

C) 1 : 1

D) 1 : 3

## Show Answer

#### Answer:

Correct Answer: B

#### Solution:

- $ 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 _2}{\sqrt{d _2}} $ $ \frac{p _1}{p _2}=\frac{1}{2} $