Question:
The equation of a simple harmonic wave is given by $y = 5= \,\sin \frac {\pi} {2} (100 \,t-x)$ where $x$ and $y$ are in metre and time is in second. The period of the wave in second will be
The equation of a simple harmonic wave is given by $y = 5= \,\sin \frac {\pi} {2} (100 \,t-x)$ where $x$ and $y$ are in metre and time is in second. The period of the wave in second will be
Updated On: Feb 23, 2024
- 0.04
- 0.01
- 1
- 5
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The Correct Option is A
Solution and Explanation
The given equation is
$y = 5\, sin \frac{\pi}{2}\left(100t - x\right) \,\,\,\, \, \dots(i) $
Comparing E (i) with standard wave equation, given by
$y = A sin \left(\omega t - kx\right) \,\,\,\,\,\dots(ii)$
we have
$ \omega = \frac{100 \pi}{2} = 50 \pi$
$ \Rightarrow \frac{2\pi}{T} = 50\pi $
$ \Rightarrow T = \frac{2\pi}{50\pi} = 0.04\, s$
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