Two vibrating strings of the same material but lengths `L` and `2L` have radii `2r` and `r` respectively. They are stretched under the same tension. Both the string vibrate in their fundamental nodes, the one of length `L` with freuqency `v_(1)` and the other with frequency `v_(2)`. the ratio `v_(1)//v_(2)` is given by

Options

A. `2`
B. `4`
C. `3`
D. `1`

Answer

D

Explanation

`v=(1)/(2l)sqrt((T)/(m))=(1)/(2l)sqrt((T)/(pir^(2)p)` or `v prop (1)/(lr)`
`:.(v_(1))/(v_(2))=(l_(2)r_(2))/(l_(1)r_(1))=(2Lxxr)/(Lxx2r)=1`