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JEE Main 2021 (17 Mar, Shift 2) · Progressive Wave Equation

Progressive Wave Equation question from JEE Main 2021 (17 Mar, Shift 2)

Q74JEE Main 2021 · 17 MAR · SHIFT 2Medium

Progressive Wave Equation

A sound wave of frequency 245 Hz travels with the speed of 300 ms−1{}^{-1} along the positive x-axis. Each point of the wave moves to and fro through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?

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Answer: (b)

  1. Total to-and-fro distance =2A=6 cm⇒A=0.03 m= 2A = 6\text{ cm} \Rightarrow A = 0.03\text{ m}
  2. ω=2πf=2π(245)≈1.5×103 rad/s\omega = 2\pi f = 2\pi(245) \approx 1.5 \times 10^3\text{ rad/s}
  3. k=ωv=1539300≈5.1 m−1k = \frac{\omega}{v} = \frac{1539}{300} \approx 5.1\text{ m}^{-1}
  4. So the answer is (b) Y=0.03sin⁡[5.1x−(1.5×103)t]Y = 0.03\sin[5.1x - (1.5\times10^3)t].
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