Show that when a string fixed at its two ends vibrates in 1 loops, 2 loops , 3 loops and 4 loops , the frequencies are in the ratio `1:2:3:4.`

Explanation

The frequency of the string fixed at two ends having length L and speed `upsilon` having n-loops, is given by
`v_(n) = n (upsilon)/(2L)`
If we have 1-loop, `v_(1) = (1 upsilon)/(2L)`
Similarly `v_(2) = (2 upsilon)/(2L), v_(3) = (3 upsilon)/(2L), v_(4) = (4 upsilon)/(2L)`
So `v_(1) : v_(2) : v_(3) : v_(4) : : 1 : 2 : 3 : 4`