To increase the frequency of transverse oscillations of a stretched string by 40%, the tension must be increased by

Step-by-step solution

The frequency of transverse oscillations of a stretched string is given by f = 1 2L T This implies f T Let the initial frequency be f₁ and the initial tension be T₁ . If the frequency is increased by 40 % , the new frequency is f₂ = f₁ + 0.40 f₁ = 1.4 f₁ Using the relation f T , we get f₂ f₁ = T₂ T₁ Substituting the values, 1.4 = T₂ T₁ Squaring both sides, T₂ T₁ = 1.96 The percentage increase in tension is T₂ - T₁ T₁ 100 % = (1.96 - 1) 100 % = 96 % Answer: 96 %