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The displacement of an elastic wave is given by the function y = 3 sin omega t + 4 cos omega t.where y is in cm and t is in second. Calculate the resultant amplitude.

Answer» <html><body><p></p>Solution :Here `y =3 sin (<a href="https://interviewquestions.tuteehub.com/tag/omega-585625" style="font-weight:bold;" target="_blank" title="Click to know more about OMEGA">OMEGA</a> t ) + <a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a> cos (omega t) ""…(1)` <br/> But for a harmonic wave, `y = sin (omega t + phi)` <br/> `therefore y = a [sin (omega t) cos phi+ cos (omega t ) sin phi]` <br/> `therefore y = (a cos phi ) sin (omega t ) + (a sin phi) cos (omega t ) ...(2)` <br/> Comparing equations (1) and (2), we get, <br/> `a cos phi =3""...(3)` <br/> `a sin phi =4""...(4)` <br/> Squaringand adding `a ^(2) cos ^(2) phi + a ^(2) sin ^(2) phi = <a href="https://interviewquestions.tuteehub.com/tag/9-340408" style="font-weight:bold;" target="_blank" title="Click to know more about 9">9</a> + 16 ` <br/> `therefore a ^(2) (sin ^(2) phi + cos ^(2) phi ) = 25` <br/> `thereofre a ^(2) (1) = 25` <br/> `therefore a ^(2) = 25` <br/> `therefore a = 5 cm (because a gt <a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a>)` <br/> Taking ratio of <a href="https://interviewquestions.tuteehub.com/tag/equation-974081" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATION">EQUATION</a> (4) to equation (3), <br/> `(a sin phi)/( a cos phi) = 4/3` <br/> `therefore tan phi = (4)/(3) implies phi = tan^(-1) ((4)/(3))`</body></html>


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