The displacement of a periodically vibrating particle isy = 4 cos ^(2)((1)/(2)t)sin (1000t) .Calculate the number of harmonic waves that are superposed .

The displacement of a periodically vibrating particle isy = 4 cos ^(2)

1.	The displacement of a periodically vibrating particle isy = 4 cos ^(2)((1)/(2)t)sin (1000t) .Calculate the number of harmonic waves that are superposed .
Answer» <html><body><p></p>Solution :`y = 4 <a href="https://interviewquestions.tuteehub.com/tag/cos-935872" style="font-weight:bold;" target="_blank" title="Click to know more about COS">COS</a>^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>) ((1)/(2)t) ` sin (1000t)<br/>`2 * 2 cos^(2) ((1)/(2)t)* ` sin (1000 t)<br/>= 2 (1 + cos t ) sin (1000 t )<br/>= 2 sin (1000 t) + 2 sin (1000 t ) cos t<br/>= 2 sin (1000 t ) + sin (1000 t + t ) + sin ( 1000 t - t)<br/>= 2 sin (1000 t) + 1 sin (101 t ) + 1 sin (999 t )<br/>` = y_(1) + y_(2) + y_(<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/>Here each of `y_(1),y_(2) and y_(3)`in the form of `a sin omegat` .Thus,each of them represents a harmonic wave .<br/>Hence, the number of <a href="https://interviewquestions.tuteehub.com/tag/superposed-7715918" style="font-weight:bold;" target="_blank" title="Click to know more about SUPERPOSED">SUPERPOSED</a> harmonic <a href="https://interviewquestions.tuteehub.com/tag/waves-13979" style="font-weight:bold;" target="_blank" title="Click to know more about WAVES">WAVES</a> = 3 .</body></html>