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MHT CET 2021 (20 Sep, Shift 1) · Progressive Wave Equation

Progressive Wave Equation question from MHT CET 2021 (20 Sep, Shift 1)

Q76MHT CET 2021 · 20 SEP · SHIFT 1Medium

Progressive Wave Equation

The equation of wave is given by y=10sin⁡(2πt30+α)y = 10\sin\left(\frac{2\pi t}{30} + \alpha\right). If the displacement is 5 cm5\text{ cm} at t=0t = 0, then the total phase at t=7.5 st = 7.5\text{ s} will be

[sin⁡30∘=cos⁡60∘=12,cos⁡30∘=sin⁡60∘=32]\left[\sin 30^\circ = \cos 60^\circ = \frac{1}{2}, \cos 30^\circ = \sin 60^\circ = \frac{\sqrt{3}}{2}\right]

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Answer: (d)

  1. At t=0t = 0: 10sin⁡α=5⇒sin⁡α=12, α=π610\sin\alpha = 5 \Rightarrow \sin\alpha = \frac{1}{2},\ \alpha = \frac{\pi}{6}
  2. Phase at t=7.5 st = 7.5\text{ s}: 2π(7.5)30+π6=π2+π6\frac{2\pi(7.5)}{30} + \frac{\pi}{6} = \frac{\pi}{2} + \frac{\pi}{6}
  3. =2π3 rad= \frac{2\pi}{3}\text{ rad}
  4. So the answer is (d) 2π3 rad\frac{2\pi}{3}\text{ rad}.
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