JEE Main 2020 · 2 September · morning · Single correct · +4 / −1

Two identical strings X and Z made of same material have tension T X and T Z in them. If their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio T X /T Z is

  1. (a) 2.25
  2. (b) 0.44
  3. (c) 1.25
  4. (d) 1.5
Answer and solution

Answer (a) 2.25

Solution

Physics sir · 3 steps

Same length, same material: only tension changes, and frequency goes as the square root of tension.

  1. Fundamental frequency. For a string fixed at both ends, the fundamental is f = 1/2L√(T/μ), where μ is the mass per unit length. The strings are identical and made of the same material, so L and μ are the same for both.
  2. Take the ratio. With L and μ cancelling, f ∝ √T. So the tension ratio is the square of the frequency ratio.

    T_X/T_Z = (f_X/f_Z)² = (450/300)² = (1.5)²

  3. So. T_X/T_Z = 2.25, which is option (a).

The idea to keep. Wave speed on a string is √(T/μ), so frequency follows the square root of tension. To get a tension ratio, square the frequency ratio.

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.