A composite wire of length 2L is made by joining two different wires A and B having the same length, made of the same material but of different radii r and 2r respectively. The composite wire is vibrating at such a frequency, that the junction of the two wires form a node. If the number of antinodes in the wire A is p and that in the wire B is q , then the ratio p:q is

Question

A composite wire of length 2L is made by joining two different wires A and B having the same length, made of the same material but of different radii r and 2r respectively. The composite wire is vibrating at such a frequency, that the junction of the two wires form a node. If the number of antinodes in the wire A is p and that in the wire B is q , then the ratio p:q is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-qfeq5t3hcbyh.png" /> (A)  text1:2 (B)  text3:5 (C)  text1:4 (D)  text4:9

Tardigrade Admin · Accepted Answer

f1=(n/2 ℓ )√(T/ÏA); f2=(m/2 ℓ )√(T/ρ 4 A) Given f1=f2 (f1/f2)=(n/m)× 2 (n/m)=(1/2)

$1:2$

$3:5$

$1:4$

$4:9$

$f_{1} = \frac{n}{2 ℓ} \frac{T}{ρ A}; f_{2} = \frac{m}{2 ℓ} \frac{T}{ρ 4 A}$
Given $f_{1} = f_{2}$
$\frac{f _{1}}{f _{2}} = \frac{n}{m} \times 2$
$\frac{n}{m} = \frac{1}{2}$

1:2

3:5

1:4

4:9

f1​=2ℓn​ρAT​​;f2​=2ℓm​ρ4AT​​ Given f1​=f2​ f2​f1​​=mn​×2 mn​=21​

$1:2$

$3:5$

$1:4$

$4:9$

$f_{1} = \frac{n}{2 ℓ} \frac{T}{ρ A}; f_{2} = \frac{m}{2 ℓ} \frac{T}{ρ 4 A}$
Given $f_{1} = f_{2}$
$\frac{f _{1}}{f _{2}} = \frac{n}{m} \times 2$
$\frac{n}{m} = \frac{1}{2}$