A sonometer wire resonates with 4 antinodes between the two bridges for a given tuning fork when 1 kg mass is suspended from the wire. Using same fork, when mass M is suspended, the wire resonates producing 2 antinodes between the two bridges. (Distance between the bridges as before) The value of M is

Step-by-step solution

The frequency of a sonometer wire is given by f = p 2L T , where p is the number of antinodes, L is the length, T is the tension, and is the linear mass density. Since the frequency f , length L , and linear mass density are constant, we have p T = constant . Therefore, p₁ T₁ = p₂ T₂ . Given p₁ = 4 , T₁ = 1 g , p₂ = 2 , and T₂ = M g . Substituting the values, we get 4 1 g = 2 M g . Dividing by 2 g , we get 2 = M . Squaring both sides, M = 4 kg. Answer: 4 kg