The equation of simple harmonic wave is given as $\mathrm{y}=5 \sin \frac{\pi}{2}(100…

The equation of simple harmonic wave is given as $\mathrm{y}=5 \sin \frac{\pi}{2}(100 \mathrm{t}-\mathrm{x})$, where ' $\mathrm{x}$ ' and ' $\mathrm{y}$ ' are in metre and time in second. The period of the wave is
  1. $0 \cdot 02 \mathrm{~s}$
  2. $0.06 \mathrm{~s}$
  3. $25 \mathrm{~s}$
  4. $0 \cdot 04 \mathrm{~s}$

Solution

The equation of simple harmonic wave is given as \(y=5 \sin \frac{\pi}{2}(100 t-x)\), where ' \(x\) ' and ' \(y\) ' are in metre and time in second. The period of the wave is \(0.0 4\). Explanation: \(\begin{aligned} & y=5 \sin \frac{\pi}{2}(100 t-x)=5 \sin \left(50 \pi t-\frac{x \pi}{2}\right) \\ & \therefore \omega=50 \pi \text { or } \frac{2 \pi}{T}=50 \pi \\ & \therefore T=\frac{1}{25}=0.04 \mathrm{~s} \end{aligned}\)

Asked in: MHT CET 2020 (19 Oct Shift 1)

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