A sonometer wire ' A ' of diameter ' d ' under tension ' T ' having density ' ₁ ' vibrates with fundamental frequency ' n '. If we use another wire 'B' which vibrates with same frequency under tension ' 2 ~T ' and diameter ' 2 D ' then density ' ₂ ' of wire ' B ' will be

Step-by-step solution

The formula for frequency of a sonometer is f = 1 2 l T D ^2 Here l is length, T is tension, D is diameter and is density. The frequency of both the wires is same. The frequency of the wire A is f _ A = 1 2 l T ₁ D ^2 The frequency of the wire B is f_ B = 1 2 l 2 ~T ₂(2 D )^2 Equating both the frequencies aligned & 1 2 l T D ^2 = 1 2 l 2 ~T ₂(2 D )^2 & 1 ₁ = 1 2 ₂ & 1 ₁ = 1 2 ₂ & ₂= ₁ 2 aligned