During the propagation of one progressive harmonic wave having amplitude 10 m, displacements and particles at 2 m and 16 m at respectively 2s and 8 s are5 mand 5sqrt3 m respectively. Find angular frequency and wave vector for this wave.

During the propagation of one progressive harmonic wave having amplitu

1.	During the propagation of one progressive harmonic wave having amplitude 10 m, displacements and particles at 2 m and 16 m at respectively 2s and 8 s are5 mand 5sqrt3 m respectively. Find angular frequency and wave vector for this wave.
Answer» SOLUTION :`(i) y _(1) = A sin (omega t _(1) - kx _(1))` `therefore 5 = 10 sin (2 omega -2k)` `therefore sin (2 omega -2k) =1/2 = sin ""(pi)/(6)` `therefore 2 omega - 2k = (pi)/(6)` `therefore 12 omega - 12k =pi ""...(1)` `(ii) y _(2) = A sin (omega t _(2) - kx _(2))` `therefore 5 sqrt3 = 10 sin (8 omega -16K)` `therefore sin (8 omega - 16k ) = (sqrt3)/( 2) = sin ""(pi)/(3)` `therefore 8 omega - 16 K = (pi)/(3)` `therefore 24 omega - 48 k =pi ""...(2)` Multiplying equation (1) by `(-2)` we GET, `-24 omega + 24 k =- 2pi` Adding equation (2) and (3), `- 24 k =- pi` `therefore k = (pi)/(24) (rad)/(m) ""...(4),` From (1) and (4), `12 omega -12 ((pi)/(24)) = pi` `therefore 12 omega -(pi)/(2) =pi` `therefore 12 omega = (3pi)/(2)` `therefore omega = (pi)/(8) (rad)/(s) ""...(5)`