Two sound waves of frequencies 100 Hz and 102 Hz and having same amplitude ' A ' are interfering. A stationary detector, which can detect waves of amplitude greater than or equal to A , So, in a given time interval of 12 seconds, find the total duration in which detector is active.

Step-by-step solution

aligned & y₁=A ₁ t & y₂=A ₂ t & y_r=2 A ( ₂- ₁ ) 2 t ( ₂+ ₁ ) 2 t aligned Resultant amplitude A _ r =2 ~A ₀| ( ) t / 2| aligned & ( ) t 2 = 2 t= 1 4 s & ( ) t 2 = 3 t= 1 6 s aligned In one cycle of intensity of 1 / 2 ~s , the detector remain idle for 2 ( 1 4 - 1 6 ) s= 1 6 In 1 / 2 sec cycle, active time is ( 1 2 - 1 6 )=1 / 3 sec In 12 sec interval, active time is 12 (1 / 3) (1 / 2) =8 sec