Question

If the vibrations of a string are to be increased to a factor of 2,then what should the tension in the string be made?

Answer 1

`4` times the initial

Explanation:

Increased to a factor of `2` means, the vibration frequency is made twice the initial.

we know, vibration frequency(`n`) and string tension(`T`) varies as `n prop sqrt(T)` (The full formula is `n=1/(2L) sqrt(T/mu)` where, `L` is the length of the string,`T` is the tension and `mu` is linear density)

So,we can make a comparison,

`(n_f)/(n_i)=sqrt((T_f)/(T_i))` (`n` means final values and `i` means initial values)

So,`T_f = T_i ((n_f)/(n_i))^2 = T_i(2)^2 =4T_i`