Two waves passing through a region are represented by y = ( 1.0 m) sin [( pi cm^(-1)) x - ( 50 pi s^(-1))t] and y = ( 1.5 cm) sin [( pi //2 cm^(-1)) x - ( 100 pi s^(-1)) t]. Find the displacement of the particle atx = 4.5 cm at timet = 5.0 ms.

Two waves passing through a region are represented by y = ( 1.0 m) si

1.	Two waves passing through a region are represented by y = ( 1.0 m) sin [( pi cm^(-1)) x - ( 50 pi s^(-1))t] and y = ( 1.5 cm) sin [( pi //2 cm^(-1)) x - ( 100 pi s^(-1)) t]. Find the displacement of the particle atx = 4.5 cm at timet = 5.0 ms.
Answer» SOLUTION :According to the PRINCIPLE of SUPERPOSITION , each wave produces its disturbance independent of the other and the resultant disturbnce is equal to the vector sum of the individual time ` t= 5.0 MS` due to the waves are, ` y_(1) = ( 1.0 cm) sin [( pi cm^(-1)) ( 4.5 cm) - ( 50 pi s^(-1)) ( 5.0 xx 10^(-3) s)]` ` = ( 1.0 cm) sin [ 4.5 pi - (pi)/( 4)]` `= ( 1.0 cm) sin [ 4 pi + (pi)/( 4)] = ( 1.0 cm)/( sqrt( 2))` and `y_(2)= ( 1.5 cm) sin[( pi//2 cm^(-1)) ( 4.5 cm) - ( 100 pi s^(-1) ( 5.0 xx 10^(-3) s)]` ` = ( 1.5 cm) sin [ 2.25 pi - (pi)/(2))]` `= ( 1.5 cm) sin [ 2 pi - (pi)/(4)] = - ( 1.5 cm) sin ( pi)/(4) = - ( 1.5 cm)/( sqrt (2))` The net displacement is `y = y_(1) + y_(2) = - 0.5 // sqrt(2) cm` ` = - 0.35 cm`