Question

Two wires of the same material and radii r and 2r are welded together end to end. The combination is used as a sonometer wire and kept under tension T. The welded point is mid-way between the two bridges. When stationary waves are set up in the composite wire, the joint is a node. Then the ratio of the number of loops formed in the thinner to thicker wire is

Solution

Correct option is

1:2

 

The frequency of a string of length L, mass m per unit length, stretched with a tension T and vibrating in p segments, is given by

                        

If the radius of the wire is r and ρ its density, then

                     

Since VTL and ρ are the same for both wires,  constant or p ∝ r. Hence the number of loops formed in the thicker wire will be two times that in the thinner wire.      

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