Two second sources produce progressive waves given by `y_(1) = 12 cos 100pit` and `y_(2) = 4 cos 102pit` neart the ear of an observer. When sounded together, the observer will hear

Options

A. `2` beats per two sound source with an intesity ratio of maximum nearly `sqrt(2) : 1`
B. `1` beat per second with an intentsity ratio of maximum to minimum to manimum nearly `sqrt(2) : 1`
C. `2` beat per second with an intensity ratio maximum to minimum nealy `9 : 1`
D. `1` beat per second with an intensity ratio of maximum to minimum nearly `4 : 1`

Answer

D

Explanation

frequency of two source `n_(1) = 50, n_(2) = 51`
so beat frequency `= 1//sec`
Now intensity ratio of maximum & minimum value `= (l_(max))/(l_(min)) = ((a_(1) + a_(2))^(2))/((a_(1) - a_(2))) = ((16)/(8))^(2) = (4)/(1)`