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Two strings A and B having linear densities $[ \mu_A = 2\times10^{-4}\ \text{kg/m},\quad \mu_B = 4\times10^{-4}\ \text{kg/m} ]$ and lengths $[ L_A = 2.5\ \text{m},\quad L_B = 1.5\ \text{m} ]$ are tied between rigid supports under tension 500 N. Identical pulses are sent from both ends. Find the ratio $(t_1/t_2)$

Options:
  1. 1.08
  2. 1.90
  3. 1.67
  4. 1.18

Solution:

Wave speed: $[ v = \sqrt{\frac{T}{\mu}} ]$ $[ v_A = \sqrt{\frac{500}{2\times10^{-4}}} ,\quad v_B = \sqrt{\frac{500}{4\times10^{-4}}} ]$ Time: $[ t = \frac{L}{v} \Rightarrow \frac{t_1}{t_2} = 1.18 ]$ ✅ Correct Answer: (4)
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