Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String
Two wires A and B , possessing identical geometrical construction, are stretched by a small but equal amount from their natural length. The Young's moduli of the wires are Y_A and Y_B while their densities are ho_A and ho_B . It is given that Y_A > Y_B and ho_A > ho_B . A transverse signal initiated at one end requires a time t₁ to reach the opposite end for wire A , and t₂ for wire B .
Options
- At₁ > t₂
- Bthe information is insufficient to find the relation between t₁ and t₂
- Ct₁ < t₂
- Dt₁ = t₂
Correct answer
B. the information is insufficient to find the relation between t₁ and t₂
Step-by-step solution
The speed of a transverse wave on a stretched wire is given by v = T The tension T in the wire is T = YA L L The linear mass density is = A Substituting T and , we get v = Y L L The time taken by the transverse signal to travel the length L is t = L v = L^3 Y L Since L and L are identical for both wires, t Y For wire A , t₁ _A Y_A and for wire B , t₂ _B Y_B Given that Y_A > Y_B and _A > _B , both the numerator and the denominator for wire A are greater than those for wire B . The ratio _A Y_A can be greater than, e