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Q.

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 is positioned to detect the sound.So,in a given time interval of 12 seconds, find the total duration (in seconds) in which detector is active.

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answer is 8.

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Detailed Solution

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$y_{1} = A \sin ω_{1} t y_{2} = A \sin ω_{2} t y_{r} = 2 A \cos {\frac{(ω_{2} - ω_{1})}{2} t} {\sin \frac{(ω_{2} + ω_{1})}{2}}$

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Resultant amplitude $A_{r} = 2 A_{0} | \cos (Δ ω) t / 2 |$
$(Δ ω) \frac{t}{2} = \frac{π}{2} \Rightarrow t = \frac{1}{4} s (Δ ω) \frac{t}{2} = \frac{π}{3} \Rightarrow t = \frac{1}{6} s$
In one cycle of intensity of 1/2s, the detector remains idle for

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