JEE Main 2023 · 31 January · evening · Single correct · +4 / −1

For a solid rod, the Young's modulus of elasticity is 3.2 × 10¹¹ Nm⁻² and density is 8 × 10³ kg m⁻³. The velocity of longitudinal wave in the rod will be.

  1. (a) 3.65 × 10³ ms⁻¹
  2. (b) 6.32 × 10³ ms⁻¹
  3. (c) 18.96 × 10³ ms⁻¹
  4. (d) 145.75 × 10³ ms⁻¹
Answer and solution

Answer (b) 6.32 × 10³ ms⁻¹

Solution

Physics sir · 3 steps

A longitudinal wave in a solid rod is driven by Young's modulus, so take the root of Y over density.

  1. Right formula. A thin rod stretches and compresses along its length, so the restoring property is Young's modulus Y. The inertia comes from the density ρ.

    v = √(Y/ρ)

  2. Put in numbers. Y/ρ = (3.2 × 10¹¹)/(8 × 10³) = 4 × 10⁷ m² s⁻². Write this as 40 × 10⁶ so the square root is easy: v = √40 × 10³ m s⁻¹.
  3. So. √40 ≈ 6.32, so v ≈ 6.32 × 10³ m s⁻¹, which is option (b).

The idea to keep. Wave speed is always the square root of an elastic modulus over density. Use Y for a rod, bulk modulus for fluids. Make the power of ten even before taking a square root.

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 2023.