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  4. 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 />

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Q. 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

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NTA AbhyasNTA Abhyas 2020Waves

Solution:

$f_{1}=\frac{n}{2 \ell }\sqrt{\frac{T}{ρA}}; \, \, f_{2}=\frac{m}{2 \ell }\sqrt{\frac{T}{\rho 4 A}}$
Given $f_{1}=f_{2}$
$\frac{f_{1}}{f_{2}}=\frac{n}{m}\times 2$
$\frac{n}{m}=\frac{1}{2}$