Two wires W1 and W2 have the same radius r and respective densities ρ1 and ρ2 such that ρ2 =4 ρ1. 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 :

Question

Two wires W1 and W2 have the same radius r and respective densities ρ1 and ρ2 such that ρ2 =4 ρ1. 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 : (A) 1: 1 (B) 1: 2 (C) 1: 3 (D) 4: 1

Tardigrade Admin · Accepted Answer

n1 = n2 T → same r → same l → same n = (p/2l) √(T/π r2d) n1 = n2 (p1/√d1) = (p1/√d2) (p1/p2) = (1/2)

1 : 1

1 : 2

1 : 3

4 : 1

$n_{1} = n_{2}$
T $\to$ same
r $\to$ same
l $\to$ same
$n = \frac{p}{2 l} \frac{T}{π r ^{2} d}$
$n_{1} = n_{2}$
$\frac{p _{1}}{d _{1}} = \frac{p _{1}}{d _{2}}$
$\frac{p _{1}}{p _{2}} = \frac{1}{2}$

1 : 1

1 : 2

1 : 3

4 : 1

n1​=n2​ T → same r → same l → same n=2lp​πr2dT​​ n1​=n2​ d1​​p1​​=d2​​p1​​ p2​p1​​=21​

$n_{1} = n_{2}$
T $\to$ same
r $\to$ same
l $\to$ same
$n = \frac{p}{2 l} \frac{T}{π r ^{2} d}$
$n_{1} = n_{2}$
$\frac{p _{1}}{d _{1}} = \frac{p _{1}}{d _{2}}$
$\frac{p _{1}}{p _{2}} = \frac{1}{2}$