Question

Three plane sources of sound of frequency n₁ = 400Hz, n₂ = 401Hz and n₃ = 402Hz of equal amplitude a each, are sounded together. A detector receives, waves from all the three sources simultaneously. It can detect signals of amplitude ≥ a . 

Calculate 

(i) period of one complete cycle of intensity received by the detector and 

(ii) time for which the detector remains ideal in each cycle of intercity

Answer 1

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.