JEE Main 2020 · 8 January · evening · Single correct · +4 / −1

A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 10⁴ N. When the tension is changed to T, the velocity changed to v/2. The value of T is close to :

  1. (a) 30.5 × 10⁴ N
  2. (b) 2.50 × 10⁴ N
  3. (c) 10.2 × 10² N
  4. (d) 5.15 × 10³ N
Answer and solution

Answer (d) 5.15 × 10³ N

Solution

Physics sir · 4 steps

Speed goes as the square root of tension, so halving the speed needs one quarter of the tension.

  1. Wave speed on string. For a transverse wave on a stretched wire, the speed depends on the tension T and the mass per unit length μ. The wire is the same, so μ does not change.

    v = √(T/μ) ⇒ v₂/v₁ = √(T₂/T₁)

  2. Set up ratio. Here v₂/v₁ = 1/2, so √(T/T₁) = 1/2. Squaring both sides gives T = T₁/4.
  3. Put in numbers. T = (2.06 × 10⁴ N)/4 = 0.515 × 10⁴ N = 5.15 × 10³ N.
  4. So. The new tension is 5.15 × 10³ N, which is option (d).

The idea to keep. On the same string, v ∝ √T. Any change in speed by a factor k needs the tension changed by k², never by k itself.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Mechanical Waves

Asked about 60 times in JEE Main since 2020. This question is from 2020.