In melde's experiment, when tension in the string is 100gm wt and the tuning fork vibrates transversely , then the number of loops are 4. then the string in turned through `90^@`, so that is vibrates longitudinally. What is the extra tension required to form one loop in the string ?

Explanation

In first case the string vibrates in four loops and if `n_(0)` be the oscillation frequency of turning fork we have
`N = (4)/(2l) sqrt((T_(1))/(mu))`
In second case if string vibrate in one segment, we have
`(N)/(2) = (1)/(2l)sqrt((T_(2))/(mu))`
`sqrt(T_(2)) = 2sqrt(T_(1))`
`T_(2) = 4T_(1)`
`T_(1) = 100 gm`, we get
`T_(2) = 400 gm`
This additional weight required is 300 gm.