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The ratio of loudness of sound produced ...

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

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Loudness `alpha " Amplitude"^(2)`
Given `(L_(1))/(L_(2)) (2)/(3): (A_(1))/(A_(2)) = ?`
`(L_(1))/(L_(2)) = ((A_(1))/(A_(2)))^(2) rArr (2)/(3) = (A_(1)^(2))/(A_(2))`
`rArr (A_(1))/(A_(2)) = (sqrt2)/(sqrt3) = sqrt2 : sqrt3`
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