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

  • Option 1)

    1:2

  • Option 2)

    4:9

  • Option 3)

    1:4

     

  • Option 4)

    3:5

 

Answers (1)

\begin{matrix} &A &B \\ Length&L & L\\ radii&r & 2r\\ density& \rho & \rho \\ no. of antinodes &p &q \end{matrix}

So f_{A}=\frac{p}{2l_{A}}\sqrt{\frac{T}{\rho \: A_{A}}}=\frac{p }{2l_{A}}\sqrt{\frac{T}{\rho (\pi r^{2})}}

f_{B}=\frac{q}{2l_{B}}\sqrt{\frac{T}{\rho \: A_{B}}}=\frac{ q }{2l_{B}}\sqrt{\frac{T}{\rho (\pi r^{2})\times 4}}

\frac{f_{A}}{f_{B}}=\frac{p}{q}\times 2=1

So\; \frac{p}{q}=\frac{1}{2}

p:q\; ::\; 1 : 2


Option 1)

1:2

Option 2)

4:9

Option 3)

1:4

 

Option 4)

3:5

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