Q22 of 36 Page 109

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?

We know that the frequency if wire in tension is given by the equation



where n is the number of node, l is the length of the wire, T is the tension of the wire and μ is the mass per unit length of the wire. Let r be the radius of the wire and ρ be its density, then mass per unit length is given by,



then the frequency becomes



when r = 3r,




Therefore, when the radius is tripled the frequency is reduced by a factor of .


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