The equation of the wave is Y = 10sin ((2π t)/(30) + α) If the displacement is 5 cm at t = 0 then the total phase at t = 7.5 s will be (sin 30° = 0.5) (a) π/3 rad (b) π/2 rad (c) 2π/5 rad (d) 2π/3 rad

Answer: (d). At t = 0: 10sin α = 5 ⇒ α = π/6 Phase at t = 7.5 s: (2π(7.5))/(30) + π/6 = π/2 + π/6 = 2π/3 rad So the answer is (d) 2π/3 rad.

The equation of the wave is Y = 10sin ((2π t)/(30) + α) If the… | MHT CET 2023 (14 May, Shift 1)

Q61MHT CET 2023 · 14 MAY · SHIFT 1Medium

Progressive Wave Equation

The equation of the wave is $Y = 10\sin\left(\frac{2\pi t}{30} + \alpha\right)$ If the displacement is $5\text{ cm}$ at $t = 0$ then the total phase at $t = 7.5\text{ s}$ will be $(\sin 30^\circ = 0.5)$

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Answer: (d)

At $t = 0$ : $10\sin\alpha = 5 \Rightarrow \alpha = \frac{\pi}{6}$
Phase at $t = 7.5\text{ s}$ : $\frac{2\pi(7.5)}{30} + \frac{\pi}{6} = \frac{\pi}{2} + \frac{\pi}{6}$
$= \frac{2\pi}{3}\text{ rad}$
So the answer is (d) $\frac{2\pi}{3}\text{ rad}$ .

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Progressive Wave Equation question from MHT CET 2023 (14 May, Shift 1)

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