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NEET 2009 (AIPMT) · Progressive Wave Equation

Progressive Wave Equation question from NEET 2009 (AIPMT)

Q93NEET 2009 · AIPMTMedium

Progressive Wave Equation

A wave in a string has an amplitude of 2 cm. The wave travels in the +ve direction of x axis with a speed of 128 m/s. and it is noted that 5 complete waves fit in 4m length of the string. The equation describing the wave is

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Answer: (c)

  1. 5 waves in 4 m: λ=0.8 m\lambda = 0.8\text{ m}, so k=2π0.8=7.85 m−1k = \frac{2\pi}{0.8} = 7.85\text{ m}^{-1}
  2. ω=kv=7.85×128≈1005 rad/s\omega = kv = 7.85 \times 128 \approx 1005\text{ rad/s}
  3. Wave along +x+x has the form sin⁡(kx−ωt)\sin(kx - \omega t); A=2 cm=0.02 mA = 2\text{ cm} = 0.02\text{ m}
  4. So the answer is (c) y=0.02sin⁡(7.85x−1005t)y = 0.02\sin(7.85x - 1005t).
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