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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» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :`(i) y _(1) = A sin (omega t _(1) - kx _(1))` <br/> `therefore 5 = 10 sin (2 omega -2k)` <br/> `therefore sin (2 omega -2k) =1/2 = sin ""(pi)/(6)` <br/> `therefore 2 omega - 2k = (pi)/(6)` <br/> `therefore 12 omega - 12k =pi ""...(1)` <br/> `(ii) y _(2) = A sin (omega t _(2) - kx _(2))` <br/> `therefore 5 sqrt3 = 10 sin (8 omega -<a href="https://interviewquestions.tuteehub.com/tag/16k-277853" style="font-weight:bold;" target="_blank" title="Click to know more about 16K">16K</a>)` <br/> `therefore sin (8 omega - 16k ) = (sqrt3)/( 2) = sin ""(pi)/(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>)` <br/> `therefore 8 omega - 16 <a href="https://interviewquestions.tuteehub.com/tag/k-527196" style="font-weight:bold;" target="_blank" title="Click to know more about K">K</a> = (pi)/(3)` <br/> `therefore 24 omega - 48 k =pi ""...(2)` <br/> Multiplying equation (1) by `(-2)` we <a href="https://interviewquestions.tuteehub.com/tag/get-11812" style="font-weight:bold;" target="_blank" title="Click to know more about GET">GET</a>, <br/> `-24 omega + 24 k =- 2pi` <br/> Adding equation (2) and (3),<br/> `- 24 k =- pi` <br/> `therefore k = (pi)/(24) (rad)/(m) ""...(4),` <br/> From (1) and (4), <br/> `12 omega -12 ((pi)/(24)) = pi` <br/> `therefore 12 omega -(pi)/(2) =pi` <br/> `therefore 12 omega = (3pi)/(2)` <br/> `therefore omega = (pi)/(8) (rad)/(s) ""...(5)`</body></html>


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