Q. The equation of a simple harmonic wave is given by $\ y = 5\sin{\frac{\pi}{2}(100t - x)}$, 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) $5$
Explanation
(a) The given equation is
$y = 5\sin\frac{\pi}{2}(100t - x)$ …(i)
Comparing Eq. (i) with standard wave equation, given by
$y = A\sin{(\omega t - kx)}$ …(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
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.