Two plane harmonic sound waves are expressed by the equations. `y_(1)(x,t)-A cos (0.5 pi x-100 pit), y_(2)(x,t)=A cos(0.46 pix-92pi t)` (All parameters are in MKS) : How many times does an observer hear maximum intensity in one second :-A. `4`B. `6`C. `8`D. `10`

Two plane harmonic sound waves are expressed by the equations. `y_(1)(

1.	Two plane harmonic sound waves are expressed by the equations. `y_(1)(x,t)-A cos (0.5 pi x-100 pit), y_(2)(x,t)=A cos(0.46 pix-92pi t)` (All parameters are in MKS) : How many times does an observer hear maximum intensity in one second :-A. `4`B. `6`C. `8`D. `10`
Answer» Correct Answer - A `y_(1) = A cos (0.5 pi x - 100 pi t)` `y_(2) = A cos (0.46 pi x - 92 pi t)` For the first wave angular frequency is `omega_(1) = 100 pi , f_(1) = 50 Hz`. For the second wave angular frequency is `omega_(2) = 92 pi , f_(2) = 46 Hz`. Frequency at which the amplitude of resultant wave varies `f_(A) = (f_(1) - f_(2))/(2) = ( 50 - 46)/(2) = 2` Time interval between this is maximum. `Delta t = (1)/( 2 f_(A))` `Delta t = (1)/(4)` Therefore , the number of time intensity is maximum in time `1 s is 4`.

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Two plane harmonic sound waves are expressed by the equations. `y_(1)(x,t)-A cos (0.5 pi x-100 pit), y_(2)(x,t)=A cos(0.46 pix-92pi t)` (All parameters are in MKS) : How many times does an observer hear maximum intensity in one second :-A. `4`B. `6`C. `8`D. `10`

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