If a sonometer wire of length 110 cm fixed horizontally under a constant tension, then the bridge be placed below the wire so that the two segments can emits note whose frequency are in the ratio 3:2, is

Options

A. 44cm and 66 cm
B. 66 cm and 44cm
C. 25cm and 75cm
D. 41.5 cm and 58.5 cm

Answer

A

Explanation

`l_1 + l_2 = 1.1 ….(i) " As " n_1l_1=n_2l_2`
`therefore n_1/n_2 = l_2/l_1 = 3/2 therefore l_2 = 3/2 l_1`
Substitute `l_2` in eqn(i) we have ,
`l_1+3/2l_1 = 1.1 therefore 5/2l_1 = 1.1`
`therefore l_1=(2.2)/(5) = 0.44m`
Substitute in (i) we have ,
`0.44+l_2=1.1 therefore l_2 = 0.66m`