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Question: Answered & Verified by Expert
Two wires W1 and W2 have the same radius r and respective, densities ρ1 and ρ2, such that ρ2=4ρ1 . 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 W1 to W2 is 

PhysicsWaves and SoundJEE MainJEE Main 2017 (08 Apr Online)
Options:
  • A 4:1
  • B 1:2
  • C 1:1
  • D 1:3
Solution:
1894 Upvotes Verified Answer
The correct answer is: 1:2

Let p1 and p2 be the number of antinodes of both wires.

Fundamental frequency remains the same for both wires. 

n1=n2

Tsame

rsame

lsame

n=p2l Tπr2ρ

From the above equation, we have 
p1ρ1  =p2ρ2  

p1p2= ρ1ρ2

The ratio of antinodes is p1p2=12

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