Two radio stations broadcast their programs at the same amplitude A, and at slightly different frequencies `omega_(1) and omega_(2)` respectively, where `omega_(2)-omega_(1)=10^(3)Hz`. A detector receives the signals from the two stations simultaneously. It can detect signals only of intensity `ge2A^(2)`.
(i) Find the time intervals between successive maxima of the intensity of the signal received by the detector
(ii) Find the time for which the detector remains idle in each cycle of the intensity of the signal

Answer

(i) `6.28xx10^(-3)S`
(ii) `1.57xx10^(-3)S`

Explanation

`I=4I_(0)cos^(2)theta` where `theta =(omega_(1)-omega_(2))t=10^(3)t`
(i) For successive maxima
`Deltat=(2pi)/(10^(3))=6.28xx10^(-3)sec`
(ii) For detection of sound
`2A^(2)=4A^(2)cos^(2)theta`
`rArr cos theta = pm(1)/(sqrt(2))rArrtheta = (pi)/(4),(pi)/(4)`
`rArr 10^(3)t=2((pi)/(4))=(pi)/(2)`
`rArr t=(pi)/(2)xx10^(-3)=1.57xx10^(-3)s`.