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

• A. 0.04
• B. 0.01
• C. 1
• D. 5

Answer 1

Answer: (A)

0.04

Answer 2

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 $\omega = \frac{100 \pi}{2} = 50 \pi$ $\Rightarrow \frac{2\pi}{T} = 50\pi$ $\Rightarrow T = \frac{2\pi}{50\pi} = 0.04\, s$