Two wires of same material of length l and 2l vibrate with frequencies 100 Hz and 150 Hz respectively. The ratio of their tensions is

Options

A. `2:3`
B. `3:2`
C. `1:9`
D. `1:3`

Answer

C

Explanation

As `n=(1)/(2l)sqrt((T)/(m))`
`therefore100=(1)/(2l)sqrt((T_(1))/(m))` . . . (i)
and `150=(1)/(4l)sqrt((T_(2))/(m))` . . . (ii)
On dividing Eq. (i) by (ii), we get
`(4l)/(2l)sqrt((T_(1))/(T_(2)))=(100)/(150)` or `sqrt((T_(1))/(T_(2)))=(100)/(300)`
or `sqrt((T_(1))/(T_(2)))=(1)/(3)` or `(T_(1))/(T_(2))=(1)/(9)`.