A string vibrates with a frequency of 200 ~Hz . When its length is doubled and tension is altered, it begins to vibrate with a frequency of 300 ~Hz . The ratio of the new tension to the original tension is

Step-by-step solution

Given, L₂=2 L₁, f₁=200 ~Hz , f₂=300 ~Hz We know that, frequency of vibrating string is given as f= 1 2 L T where, = mass per unit length of string and L= length of the string. array ll & f T L & f₂ f₁ = T₂ T₁ , L₁ L₂ T₂ T₁ = f₂ L₂ f₁ L₁ = 300 200 2 L₁ L₁ & T₂ T₁ =3 & T₂ T₁ =9 & T₂: T₁=9: 1 array