Two vibrating strings of same material stretched under same tension and vibrating with same frequency in the same overtone have radii 2r and r. Then the ratio of their lengths is:

Options

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

Answer

A

Explanation

We use
`n_(1) = (1)/(2l_(1)) sqrt(((T)/(4pir^(2)l)))` and `n_(2) =(1)/(2l_(2)) sqrt(((T)/(4pir^(2)s)))`
`n_(1) = n_(2)`
implies ` (1)/(2l_(1))sqrt((T)/(4pir^(2)l)) = (1)/(2l_(2)) sqrt((T)/(pir^(2)l))`
`(1)/(2l_(1)) xx (1)/(2) = (1)/(2l_(2))`
`l_(1) : l_(2) = 1:2`