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A uniform rope of length 12 m and mass6 kg hangs vertically from a rigid support . A block of mass2 kg is attached to the free end of the rope . A transverse pulse of wavelengths 0.06 m is produced at the lower end of the rope . What is the wavelength of the pulse when it reaches the top of the rope?

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> :Tension at the <a href="https://interviewquestions.tuteehub.com/tag/lower-1080637" style="font-weight:bold;" target="_blank" title="Click to know more about LOWER">LOWER</a> end of the rope , <br/> `T_(1) = 2 <a href="https://interviewquestions.tuteehub.com/tag/g-1003017" style="font-weight:bold;" target="_blank" title="Click to know more about G">G</a> = 2 xx 9.8 = 19.6 N` <br/> Tension at the upper end of rope , <br/> Let `v_(1) and v_(2)` be the <a href="https://interviewquestions.tuteehub.com/tag/speeds-650188" style="font-weight:bold;" target="_blank" title="Click to know more about SPEEDS">SPEEDS</a> of pulse at the lower and upper end , respectively . So <br/> `v = <a href="https://interviewquestions.tuteehub.com/tag/sqrt-1223129" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT">SQRT</a> (((T_(1))/(m))), v_(2) = sqrt(((T_(2))/(m)))` <br/> On dividing , we get <br/> `(v_(2))/( v_(1)) = sqrt(((T_(2))/( T_(1)))) = sqrt(((78.4)/(19.6))) = sqrt(4) = 2` <br/> As frequency is independent of medium , therefore if `lambda_(1) and lambda_(2)` are wavelengths at lower and upper ends respectively . Then <br/> `v_(1) = n lambda_(1) and v_(2) = n lambda_(2)` <br/> So, `(lambda_(2))/(lambda_(1)) = (v_(2))/( v_(1)) = 2` <br/> Therefore , the wavelength of pulse at upper end ` = 2 lambda`. <br/> `= 2 xx 0.06 = 0.12 m`</body></html>


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