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 wireis 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

Options

A. `3:5`
B. `1:4`
C. `4:9`
D. `1:2`

Answer

D

Explanation

Frequency will be same in both
`(pc_(1))/(2l)=(qc_(2))/(2l) rArr pc_(1) =qc_(2)`
Tension will be same in both but mass per unit length will be 4 times in 2 (as radius is twice) `therefore mu_(2) = 4mu_(1)` `therefore Psqrt((T)/(mu_(1))) = q sqrt((T) /(mu_(2)))` `therefore (p)/(q)= sqrt(mu_(1))/(mu_(2)) = (1)/(2)`