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A light string is tied at one end to fix...

A light string is tied at one end to fixed support and to a heavy string of equal length L at the other end as shown in figure. Mass per unit length of the strings are `mu` and `9mu` and the tension is T. Find the possible values of frequencies such that point A is a node/ antinode.
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For `A_(1)` be a node
Suppose `n_(1)` and `n_(2)` are the complete loops formed on left and right side of point `A`.
`n_(1)(lambda_(1))/(2)=L rArr f=(v_(1)n_(1))/(2L)`
`(n_(2)lambda_(2))/(2)=L rArr f=(v_(2)n_(2))/(2L)`
`rArr v_(1)n_(1)=v_(2)n_(2) rArr n_(1) : n_(2) = 1 : 3` (`n_(1)` being any positive integer)
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