A sitar wire is replaced by another wire of same length and material but of three times the earlier radius. If the tension in the wire remains the same, by what factor will the frequency change?

A sitar wire is replaced by another wire of same length and material b

1.	A sitar wire is replaced by another wire of same length and material but of three times the earlier radius. If the tension in the wire remains the same, by what factor will the frequency change?
Answer» <html><body><p></p>Solution :We have, `mu =(M)/(L) = (V rho )/( L ) = (AL rho )/( L ) = A rho` <br/> `therefore mu = (<a href="https://interviewquestions.tuteehub.com/tag/pir-591537" style="font-weight:bold;" target="_blank" title="Click to know more about PIR">PIR</a> ^(2) ) rho ` <br/> Now, we have, `f = (<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)/(2L) sqrt ((T)/( mu))` <br/> `therefore f = (1)/(2L) sqrt ((T)/( pi r ^(2) rho ))implies f prop (1)/( r )` <b r=""> `( because ` other <a href="https://interviewquestions.tuteehub.com/tag/factors-458933" style="font-weight:bold;" target="_blank" title="Click to know more about FACTORS">FACTORS</a> are constants) <br/> `therefore (f_(1))/( f _(2)) = (r _(2))/( r _(1)) = (<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>)/(1) (because r _(2) = <a href="https://interviewquestions.tuteehub.com/tag/3r-311113" style="font-weight:bold;" target="_blank" title="Click to know more about 3R">3R</a> _(1))` <br/> `therefore f_(2) = ((1)/(3)) f _(1)`</b></body></html>