Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String
Two wires are held tight between the same pair of supports. The tensions in the wires are in the ratio 2 : 1 , their radii are in the ratio 3 : 1 , and their densities are in the ratio 1 : 2 . Determine the ratio of their fundamental frequencies.
Options
- A1 : 3
- B3 : 2
- C4 : 9
- D2 : 3
Correct answer
D. 2 : 3
Step-by-step solution
The fundamental frequency of a stretched wire is given by: f = 1 2L T The linear mass density can be written in terms of the volume density and radius r as = r^2 . Substituting this in the frequency formula: f = 1 2Lr T Since both wires are held between the same pair of supports, their lengths L are equal. The ratio of their fundamental frequencies is: f₁ f₂ = r₂ r₁ T₁ T₂ ₂ ₁ Given T₁ T₂ = 2 1 , r₁ r₂ = 3 1 , and ₁ ₂ = 1 2 , we substitute these values: f₁ f₂ = 1 3 2 1 2 1 f₁ f₂ = 1 3 4 = 2 3