A wave is given by $Y=3 \sin 2 \pi\left(\frac{t}{0.04}-\frac{x}{0.01}\right)$ where $Y$ is in cm . Frequency…

A wave is given by $Y=3 \sin 2 \pi\left(\frac{t}{0.04}-\frac{x}{0.01}\right)$ where $Y$ is in cm . Frequency of the wave and maximum acceleration will be $\left(\pi^2=10\right)$
  1. $100 \mathrm{~Hz}, 4.7 \times 10^4 \mathrm{~cm} / \mathrm{s}^2$
  2. $50 \mathrm{~Hz}, 7.5 \times 10^3 \mathrm{~cm} / \mathrm{s}^2$
  3. $25 \mathrm{~Hz}, 4.7 \times 10^4 \mathrm{~cm} / \mathrm{s}^2$
  4. $25 \mathrm{~Hz}, 7.5 \times 10^4 \mathrm{~cm} / \mathrm{s}^2$

Solution

$y=3 \sin 2 \pi\left(\frac{t}{0.04}-\frac{x}{0.01}\right)$
Comparing with standard wave equation, $\begin{array}{ll} \mathrm{y} =\mathrm{A} \sin 2 \pi\left(\mathrm{ft} \pm \frac{\mathrm{x}}{\lambda}\right) \\ \frac{\mathrm{t}}{0.04} \\ \mathrm{f}=25 \mathrm{~Hz} \\ \omega =2 \pi \mathrm{f}=\frac{2 \pi}{0.04} \\ \mathrm{a}_{\max } =\omega^2 \mathrm{~A} \\ =\frac{4 \times \pi^2 \times 3}{(0.04)^2} \\ =7.4 \times 10^4 \mathrm{~cm} / \mathrm{s}^2 \approx 7.5 \times 10^4 \mathrm{~cm} / \mathrm{s}^2 \end{array}$

Asked in: MHT CET 2024 (15 May Shift 2)

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