Two wires W_1 and W_2 have the same radius rand respective, densities ρ _1 and ρ _2, such that ρ _2=4ρ _1 . They are joined together at the point O,…
JEE Main 2017 — Physics Waves & Oscillations
2017mcqhard
Two wires W1 and W2 have the same radius rand 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
Official previous-year question
Held on 8 Apr 2017 · Verified 6 Jul 2026.
Options
A
4:1
B
1:2
C
1:1
D
1:3
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Solution
Let p1 and p2 be the number of antinodes of both wires.
Fundamental frequency remains the same for both wires.
n1=n2
T→same
r→same
l→same
n=2lpπr2ρT
From the above equation, we have
ρ1p1=ρ2p2
→p2p1=ρ2ρ1
The ratio of antinodes is p2p1=21.
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