In case of beats, produced by the superposition of two waves of equal amplitudes, if maximum intensity is x times the intensity of superposing wave then x = ……..

Explanation

Amplitude of resultant wave in beats is,
`A. =2A cos {((omega _(1) - omega _(2))/(2)) t }`
`implies (A.) _(max) = 2A`
`(because cos {( (omega _(1) - omega _(2))/(2) )t }` has maximum value equal to 1)
Now, `I _(max) prop (2A) ^(2)`
Also we knwo that `I prop A ^(2)`
`therefore (I _(max))/(I) = (4A ^(2))/(A ^(2)) =4 " "...(1)`
But, as per the statement `I _(max)=xI,`
`therefore (I _(max))/(I) =x" "...(2)`
From equations (1) and (2),` x =4`