﻿ 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 : Kaysons Education

# 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

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## Question

### 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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