Since, during propagation of sound waves medium particles execute SHM, therefore, displacement of a particle due to a wave of frequency n is given by
Hence, period of one complete cycle of intensity is one second.
Since, single is detected only when A ≥ a, therefore from equation (5), cos2πt ≥ 0 or 2πt should lie in either first quadrant or fourth quadrant.
It means 2πt should lie between either 0 and π/2 or 3π/2 and 2π.
It means signal is detected when 0 ≤ t ≤ 1/4 and 3/4 ≤ t ≤ 1 during first cycle of intensity.
In other words detector remains idle from t = 1/4sec. To t = 3/4sec during first cycle of intensity or in each cycle of intensity the defector remains idle for 0.5sec.