The ratio of loudness of sound produced by two sources is `2 : 3`. What is the ratio of amplitude of their vibrations ?

Explanation

Loudness `alpha ` Amplitude`""^2`
Given ` (L_1)/(L_2) = 2/3 = (A_1)/( A_2) =?`
`(L_1 )/(L_2 ) = ((A_1)/(A_2))^2 implies 2/3 = (A_(1)^(2))/(A_2)`
` implies (A_1)/(A_2) = sqrt((2))/(sqrt(3))= sqrt(2) : sqrt(3)`