Question

When a string is divided into three segments of length `l_1,l_2` and `l_3` the fundamental frequencies of these three segments are `f_1,f_2` and `f_3` respectively. The original fundamental frequency `f` of the string is
A. `sqrt(v)=sqrt(v_(1))+sqrt(v_(2))+sqrt(v_(3))`
B. `v=v_(1)+v_(2)+v_(3)`
C. `(1)/(v)=(1)/(v_(1))+(1)/(v_(2))+(1)/(v_(3))`
D. `(1)/(sqrt(v))=(1)/(sqrt(v_(1)))+(1)/(sqrt(v_(2)))+(1)/(sqrt(v_(3)))`

Answer 1

Correct Answer - C
From `v=(1)/(2l)sqrt((T)/(m))`, we find that `v prop (1)/(l)`
As `l=l_(1)+l_(2)+l_(3)`
`:. (1)/(v)=(1)/(v_(1))+(1)/(v_(2))+(1)/(v_(3))`