Question

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

Answer 1

Correct Answer - d
Fundamental frequency,
`v= 1/(2l) sqrt(T/m)=1/(2l)sqrt(T/(pir^(2)p))or v prop 1/(lr)`
`therefore v_(1)/v_(2)= (l_(2)r_(2))/(l_(1)r_(1)) = (2Lxxr)/(Lxx2r)=1`