Two sonometer wires of the same material and cross - section are of lengths `50 cm and 60 cm` and are stretched by tensions of `4.5 kg and 5.12 kg`, respectively . If the number of beats heard ( when the two wires are vibrating ) be ` 2 per second ` , find the mass per unit length of the wires . Take `g = 10 m//s^(2)`.

Explanation

`n_(1) = (1)/( 2 xx 0.5) sqrt ((4.5 xx 10)/(m))`
`n_(2) = (1)/( 2 xx 0.6) sqrt ((5.12 xx 10)/(m))`
Dividing `(n_(1))/(n_(2)) = (9)/(8) (Obviously n_(1) gt n_(2))`
`:. N_(1) - n_(2) = 2 rArr (9)/(8) n_(2) - n_(2) = 2`
`rArr n_(2) = 16 , n_(1) = 18`
`:. 16 = (1)/( 2 xx 0.6) sqrt ((5.12 xx 10)/(m)) rArr m = 0.14 kg//m`